Artykuły w czasopismach: „Surrogate dynamics”

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Huang, C.-K., Q. Tang, Y. K. Batygin, O. Beznosov, J. Burby, A. Kim, S. Kurennoy, T. Kwan i H. N. Rakotoarivelo. "Symplectic neural surrogate models for beam dynamics". Journal of Physics: Conference Series 2687, nr 6 (1.01.2024): 062026. http://dx.doi.org/10.1088/1742-6596/2687/6/062026.

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Abstract Development of robust machine-learning (ML) based surrogates for particle accelerators can significantly benefit the modeling, design, optimization, monitoring and control of such accelerators. It is desirable that the surrogate models embed fundamental physical constraints to the interaction and dynamics of the beams, for which an accelerator must be designed to operate upon. We implement and train a class of phase space structure-preserving neural networks — Henon Neural Networks (HenonNets) [1], for nonlinear beam dynamics problems. It is demonstrated that the trained HenonNet model predicts the beam transfer matrix to a reasonably good accuracy while strongly maintaining the symplecticity. To explore such model’s applicability and flexibility for high brightness or intensity beams, we further test it with beam dynamics in the presence of electrostatic and radiative collective effects. Our results indicate that HenonNet may be used as a base ML model for the surrogate of complex beam dynamics, thus opening up a wide range of applications.

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NAKAMURA, TOMOMICHI, i MICHAEL SMALL. "APPLYING THE METHOD OF SMALL–SHUFFLE SURROGATE DATA: TESTING FOR DYNAMICS IN FLUCTUATING DATA WITH TRENDS". International Journal of Bifurcation and Chaos 16, nr 12 (grudzień 2006): 3581–603. http://dx.doi.org/10.1142/s0218127406016999.

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Recently, a new surrogate method, the Small–Shuffle (SS) surrogate method, has been proposed to investigate whether there is some kind of dynamics in irregular fluctuations, even if they are modulated by long term trends or periodicities. This situation is theoretically incompatible with the assumption underlying previously proposed surrogate methods. We apply the SS surrogate method to a variety of simulated data with known dynamics and actual time series with unknown dynamics.

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Koutsoupakis, Josef, i Dimitrios Giagopoulos. "Drivetrain Response Prediction Using AI-based Surrogate and Multibody Dynamics Model". Machines 11, nr 5 (28.04.2023): 514. http://dx.doi.org/10.3390/machines11050514.

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Numerical models, such as multibody dynamics ones, are broadly used in various engineering applications, either as an integral part of the preliminary design of a product or simply to analyze its behavior. Aiming to increase the accuracy and potential of these models, complex mechanisms are constantly being added to existing methods of simulation, leading to powerful modelling frameworks that are able to simulate most mechanical systems. This increase in accuracy and flexibility, however, comes at a great computational cost. To mitigate the issue of high computation times, surrogates, such as reduced order models, have traditionally been used as cheaper alternatives, allowing for much faster simulations at the cost of introducing some error to the overall process. More recently, advancements in Artificial Intelligence have also allowed for the introduction of Artificial Intelligence-based models in the field of surrogates. While still undergoing development, these Artificial Intelligence based methodologies seem to be a potentially good alternative to the high-fidelity/burden models. To this end, an Artificial Intelligence-based surrogate comprised of Artificial Neural Networks as a means of predicting the response of dynamic mechanical systems is presented in this work, with application to a non-linear experimental gear drivetrain. The model utilizes Recurrent Neural Networks to accurately capture the system’s response and is shown to yield accurate results, especially in the feature space. This methodology can provide an alternative to the traditional model surrogates and find application in multiple fields such as system optimization or data mining.

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Charles, Giovanni, Timothy M. Wolock, Peter Winskill, Azra Ghani, Samir Bhatt i Seth Flaxman. "Seq2Seq Surrogates of Epidemic Models to Facilitate Bayesian Inference". Proceedings of the AAAI Conference on Artificial Intelligence 37, nr 12 (26.06.2023): 14170–77. http://dx.doi.org/10.1609/aaai.v37i12.26658.

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Epidemic models are powerful tools in understanding infectious disease. However, as they increase in size and complexity, they can quickly become computationally intractable. Recent progress in modelling methodology has shown that surrogate models can be used to emulate complex epidemic models with a high-dimensional parameter space. We show that deep sequence-to-sequence (seq2seq) models can serve as accurate surrogates for complex epidemic models with sequence based model parameters, effectively replicating seasonal and long-term transmission dynamics. Once trained, our surrogate can predict scenarios a several thousand times faster than the original model, making them ideal for policy exploration. We demonstrate that replacing a traditional epidemic model with a learned simulator facilitates robust Bayesian inference.

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Chen, Menghui, Xiaoshu Gao, Cheng Chen, Tong Guo i Weijie Xu. "A Comparative Study of Meta-Modeling for Response Estimation of Stochastic Nonlinear MDOF Systems Using MIMO-NARX Models". Applied Sciences 12, nr 22 (14.11.2022): 11553. http://dx.doi.org/10.3390/app122211553.

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Complex dynamic behavior of nonlinear structures makes it challenging for uncertainty analysis through Monte Carlo simulations (MCS). Surrogate modeling presents an efficient and accurate computational alternative for a large number of MCS. The previous study has demonstrated that the multi-input multi-output nonlinear autoregressive with exogenous input (MIMO-NARX) model provides good discrete-time representations of deterministic nonlinear multi-degree-of-freedom (MDOF) structural dynamic systems. Model order reduction (MOR) is executed to eliminate insignificant modes to reduce the computational burden due to too many degrees of freedom. In this study, the MIMO-NARX strategy is integrated with different meta-modeling techniques for uncertainty analysis. Different meta-models including Kriging, polynomial chaos expansion (PCE), and arbitrary polynomial chaos (APC) are used to surrogate the NARX coefficients for system uncertainties. A nine-DOF structure is used as an MDOF dynamic system to evaluate different meta-models for the MIMO-NARX. Good fitness of statistical responses is observed between the MCS results of the original system and all surrogated MIMO-NARX predictions. It is demonstrated that the APC-NARX model with the advantage of being data-driven is the most efficient and accurate tool for uncertainty quantification of nonlinear structural dynamics.

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Liu, Shizhong, Ziyao Wang, Jingwen Chen, Rui Xu i Dong Ming. "The Estimation of Knee Medial Force with Substitution Parameters during Walking and Turning". Sensors 24, nr 17 (29.08.2024): 5595. http://dx.doi.org/10.3390/s24175595.

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Purpose: Knee adduction, flexion moment, and adduction angle are often used as surrogate parameters of knee medial force. To verify whether these parameters are suitable as surrogates under different walking states, we investigated the correlation between knee medial loading with the surrogates during walking and turning. Methods: Sixteen healthy subjects were recruited to complete straight walk (SW), step turn (ST), and crossover turn (CT). Knee joint moments were obtained using inverse dynamics, and knee medial force was computed using a previously validated musculoskeletal model, Freebody. Linear regression was used to predict the peak of knee medial force with the peaks of the surrogate parameters and walking speed. Results: There was no significant difference in walking speed among these three tasks. The peak knee adduction moment (pKAM) was a significant predictor of the peak knee medial force (pKMF) for SW, ST, and CT (p < 0.001), while the peak knee flexion moment (pKFM) was only a significant predictor of the pKMF for SW (p = 0.034). The statistical analysis showed that the pKMF increased, while the pKFM and the peak knee adduction angle (pKAA) decreased significantly during CT compared to those of SW and ST (p < 0.001). The correlation analysis indicated that the knee parameters during SW and ST were quite similar. Conclusions: This study investigated the relationship between knee medial force and some surrogate parameters during walking and turning. KAM was still the best surrogate parameter for SW, ST, and CT. It is necessary to consider the type of movement when comparing the surrogate predictors of knee medial force, as the prediction equations differ significantly among movement types.

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Gong, Xu, Zhengqi Gu i Zhenlei Li. "Surrogate model for aerodynamic shape optimization of a tractor-trailer in crosswinds". Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 226, nr 10 (9.05.2012): 1325–39. http://dx.doi.org/10.1177/0954407012442295.

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A surrogate model-based aerodynamic shape optimization method applied to the wind deflector of a tractor-trailer is presented in this paper. The aerodynamic drag coefficient of the tractor-trailer with and without the wind deflector subjected to crosswinds is analyzed. The numerical results show that the wind deflector can decrease drag coefficient. Four parameters are used to describe the wind deflector geometry: width, length, height, and angle. A 30-level design of experiments study using the optimal Latin hypercube method was conducted to analyze the sensitivity of the design variables and build a database to set up the surrogate model. The surrogate model was constructed based on the Kriging interpolation technique. The fitting precision of the surrogate model was examined using computational fluid dynamics and certified using a surrogate model simulation. Finally, a multi-island genetic algorithm was used to optimize the shape of the wind deflector based on the surrogate model. The tolerance between the results of the computational fluid dynamics simulation and the surrogate model was only 0.92% when using the optimal design variables, and the aerodynamic drag coefficient decreased by 4.65% compared to the drag coefficient of the tractor-trailer installed with the original wind deflector. The effect of the optimal shape of the wind deflector was validated by computational fluid dynamics and wind tunnel experiment.

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She, N., i D. Basketfield. "Streamflow dynamics at the Puget Sound, Washington: application of a surrogate data method". Nonlinear Processes in Geophysics 12, nr 4 (3.05.2005): 461–69. http://dx.doi.org/10.5194/npg-12-461-2005.

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Abstract. Recent progress in nonlinear dynamic theory has inspired hydrologists to apply innovative nonlinear time series techniques to the analysis of streamflow data. However, regardless of the method employed to analyze streamflow data, the first step should be the identification of underlying dynamics using one or more methods that could distinguish between linear and nonlinear, deterministic and stochastic processes from data itself. In recent years a statistically rigorous framework to test whether or not the examined time series is generated by a Gaussian (linear) process undergoing a possibly nonlinear static transform is provided by the method of surrogate data. The surrogate data, generated to represent the null hypothesis, are compared to the original data under a nonlinear discriminating statistic in order to reject or approve the null hypothesis. In recognition of this tendency, the method of "surrogate data" is applied herein to determine the underlying linear stochastic or nonlinear deterministic nature of daily streamflow data observed from the central basin of Puget Sound, and as applicable, distinguish between the static or dynamic nonlinearity of the data in question.

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Glaz, Bryan, Li Liu, Peretz P. Friedmann, Jeremy Bain i Lakshmi N. Sankar. "A Surrogate-Based Approach to Reduced-Order Dynamic Stall Modeling". Journal of the American Helicopter Society 57, nr 2 (1.04.2012): 1–9. http://dx.doi.org/10.4050/jahs.57.022002.

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The surrogate-based recurrence framework (SBRF) approach to reduced-order dynamic stall modeling associated with pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described. The SBRF is shown to effectively mimic full-order two-dimensional computational fluid dynamics solutions for unsteady lift, moment, and drag, but at a fraction of the computational cost. In addition to accounting for realistic helicopter rotor blade dynamics, it is shown that the SBRF can model advancing rotor shock induced separation as well as retreating blade stall associated with excessive angles of attack. Therefore, the SBRF is ideally suited for a variety of rotary-wing aeroelasticity and active/passive design optimization studies that require high-fidelity aerodynamic response solutions with minimal computational expense.

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MAKINO, Kohei, Makoto MIWA, Kohei SHINTANI, Atsuji ABE i Yutaka SASAKI. "Surrogate modeling of vehicle dynamics using deep learning". Proceedings of Design & Systems Conference 2019.29 (2019): 2209. http://dx.doi.org/10.1299/jsmedsd.2019.29.2209.

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Marin-Lopez, A., J. A. Martínez-Cadena, F. Martinez-Martinez i J. Alvarez-Ramirez. "Surrogate multivariate Hurst exponent analysis of gait dynamics". Chaos, Solitons & Fractals 172 (lipiec 2023): 113605. http://dx.doi.org/10.1016/j.chaos.2023.113605.

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Koutsoupakis, J., i D. Giagopoulos. "AI-Based Surrogate Models for Multibody Dynamics Systems". Journal of Physics: Conference Series 2647, nr 2 (1.06.2024): 022002. http://dx.doi.org/10.1088/1742-6596/2647/2/022002.

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Abstract Advancements in computer sciences and technology allow for implementation of detailed numerical models of a system such as the Finite Element (FE) or Multibody Dynamics (MBD) models. Complex mechanical systems can easily be modelled in detail, yielding accurate results. This opportunity provided by these high-fidelity numerical models has led to the broad application of such methods in development and prototyping of mechanical systems, their optimization and fault analysis and so on. The capability of detailed modelling however usually comes at a great computational cost, with the simulation time needed for a problem in many cases rising exponentially, rendering these models impractical. This problem becomes even more profound when one considers the recent integration of model-based data in data-driven methods where a large number of datasets is usually required, and multiple iterations of the same model must be simulated in order to produce the desired number of samples. To mitigate these short-comings, surrogate modelling has been extensively used in applications including large systems or repetitive runs in the form of Reduced Order Models (ROMs) to reduce the computations time and render these simulation-driven methods more viable. Use of these ROMs however is limited to cases where low loss of information is ensured, and the features lost due to the model simplification are insignificant. The developments in Artificial Intelligence (AI) and its applications have demonstrated its potential to accurately describe the relationships between a model’s inputs and outputs and as such using an AI algorithm as a surrogate model is a promising alternative. A properly trained AI algorithm can usually fit to FE and MBD models and yield accurate results at a fraction of the computational burden. To this end, an AI-based surrogate modelling framework is proposed in this work, with application on an experimental gear drivetrain system. A detailed MBD of the actual system is initially constructed and optimized via a black box optimization method in order to better simulate the physical system. A variety of supervised AI algorithms such as regression models and Convolutional Neural Networks (CNNs) is then examined as a surrogate to the various mechanisms of the system, aiming to replace them with the goal of reducing the simulation time while maintaining the high accuracy and fidelity of the original model. The various algorithms are then compared in terms of time reduction and accuracy both to each other and to the initial MBD model in order to conclude to the best suited for the application. The results are also compared to the measured response data of the physical system to ensure the validity of the models and prove the viability of the proposed method through its use on a relatively complex model. The proposed framework provides an alternative to the commonly used ROM methods and the presented application acts as a benchmark case for its implementation to more complex systems and different operating conditions.

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Serafino, Aldo, Benoit Obert i Paola Cinnella. "Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics". Algorithms 13, nr 10 (30.09.2020): 248. http://dx.doi.org/10.3390/a13100248.

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Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems.

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Blubaugh, Frank. "Surrogate modeling in structural vibration problems with dynamic mode decomposition". Journal of the Acoustical Society of America 152, nr 4 (październik 2022): A134. http://dx.doi.org/10.1121/10.0015794.

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Solving large-scale vibration problems presents a difficult challenge for complicated geometries that is only addressable through the use of large-scale compute resources. These problems not only require extensive compute time and cost, but are also expensive in engineering hours for modeling and analysis. While optimization techniques can help limit engineering time in the loop, the computational requirements of these models have made applying traditional optimization techniques to this class of problem untenable. Dynamic Mode Decomposition (DMD) is an approach that can help bridge this gap by building high-fidelity surrogate models allowing for the inline development of a surrogate model to dramatically reduce the computational time and complexity of a problem. This approach enables fast frequency sweeping while capturing the dominant dynamics of the model. DMD has historically been applied to other high-data volume models such as computational fluid dynamics, medical imaging and controls, as well as less structured problems including sociology and market behavior. This paper will cover the fundamentals of Dynamic Mode Decomposition, the extension of the theory to apply the technique to vibration problems, the demonstration of a potential workflow, and show how this technique performs on simple test cases illustrating performance speed ups for classic problems from existing literature.

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MAKINO, Kohei, Makoto MIWA, Kohei SHINTANI, Atsuji ABE i Yutaka SASAKI. "Surrogate modeling of vehicle dynamics using Recurrent Neural Networks". Transactions of the JSME (in Japanese) 86, nr 891 (2020): 20–00177. http://dx.doi.org/10.1299/transjsme.20-00177.

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Habecker, F., R. Röhse i T. Klüner. "Dissipative quantum dynamics using the stochastic surrogate Hamiltonian approach". Journal of Chemical Physics 151, nr 13 (7.10.2019): 134113. http://dx.doi.org/10.1063/1.5119195.

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Tokuda, Isao, Takaya Miyano i Kazuyuki Aihara. "Surrogate analysis for detecting nonlinear dynamics in normal vowels". Journal of the Acoustical Society of America 110, nr 6 (grudzień 2001): 3207–17. http://dx.doi.org/10.1121/1.1413749.

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Younis, Adel, i Zuomin Dong. "High-Fidelity Surrogate Based Multi-Objective Optimization Algorithm". Algorithms 15, nr 8 (7.08.2022): 279. http://dx.doi.org/10.3390/a15080279.

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The employment of conventional optimization procedures that must be repeatedly invoked during the optimization process in real-world engineering applications is hindered despite significant gains in computing power by computationally expensive models. As a result, surrogate models that require far less time and resources to analyze are used in place of these time-consuming analyses. In multi-objective optimization (MOO) problems involving pricey analysis and simulation techniques such as multi-physics modeling and simulation, finite element analysis (FEA), and computational fluid dynamics (CFD), surrogate models are found to be a promising endeavor, particularly for the optimization of complex engineering design problems involving black box functions. In order to reduce the expense of fitness function evaluations and locate the Pareto frontier for MOO problems, the automated multiobjective surrogate based Pareto finder MOO algorithm (AMSP) is proposed. Utilizing data samples taken from the feasible design region, the algorithm creates three surrogate models. The algorithm repeats the process of sampling and updating the Pareto set, by assigning weighting factors to those surrogates in accordance with the values of the root mean squared error, until a Pareto frontier is discovered. AMSP was successfully employed to identify the Pareto set and the Pareto border. Utilizing multi-objective benchmark test functions and engineering design examples such airfoil shape geometry of wind turbine, the unique approach was put to the test. The cost of computing the Pareto optima for test functions and real engineering design problem is reduced, and promising results were obtained.

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Qin, W. J., i J. Q. He. "Optimum Design of Local Cam Profile of a Valve Train". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, nr 11 (14.05.2010): 2487–92. http://dx.doi.org/10.1243/09544062jmes2116.

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In this paper, optimization of the local cam profile of a valve train modelled by a parameterized Bezier curve is described. Dynamic responses of the valve train are simulated through its multi-body system dynamics model built using ADAMS software. The kriging method is used to build the surrogate model, which presents the relationship between dynamic responses resulting from the multi-body system dynamics simulation and the parameters of the local Bezier profile. The local cam profile is optimized through a generic algorithm, such that the acceleration peak at the valve open phase is reduced significantly.

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Caron, Davide, Ángel Canal-Alonso i Gabriella Panuccio. "Mimicking CA3 Temporal Dynamics Controls Limbic Ictogenesis". Biology 11, nr 3 (26.02.2022): 371. http://dx.doi.org/10.3390/biology11030371.

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Mesial temporal lobe epilepsy (MTLE) is the most common partial complex epilepsy in adults and the most unresponsive to medications. Electrical deep brain stimulation (DBS) of the hippocampus has proved effective in controlling seizures in epileptic rodents and in drug-refractory MTLE patients. However, current DBS paradigms implement arbitrary fixed-frequency or patterned stimuli, disregarding the temporal profile of brain electrical activity. The latter, herein included hippocampal spontaneous firing, has been shown to follow lognormal temporal dynamics. Here, we present a novel paradigm to devise DBS protocols based on stimulation patterns fashioned as a surrogate brain signal. We focus on the interictal activity originating in the hippocampal subfield CA3, which has been shown to be anti-ictogenic. Using 4-aminopyridine-treated hippocampus-cortex slices coupled to microelectrode array, we pursue three specific aims: (1) address whether lognormal temporal dynamics can describe the CA3-driven interictal pattern, (2) explore the possibility of restoring the non-seizing state by mimicking the temporal dynamics of this anti-ictogenic pattern with electrical stimulation, and (3) compare the performance of the CA3-surrogate against periodic stimulation. We show that the CA3-driven interictal activity follows lognormal temporal dynamics. Further, electrical stimulation fashioned as a surrogate interictal pattern exhibits similar efficacy but uses less pulses than periodic stimulation. Our results support the possibility of mimicking the temporal dynamics of relevant brain signals as a straightforward DBS strategy to ameliorate drug-refractory epilepsy. Further, they herald a paradigm shift in neuromodulation, wherein a compromised brain signal can be recreated by the appropriate stimuli distribution to bypass trial-and-error studies and attain physiologically meaningful DBS operating modes.

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Mariani, Valerio, Leonardo Pulga, Gian Marco Bianchi, Stefania Falfari i Claudio Forte. "Machine Learning-Based Identification Strategy of Fuel Surrogates for the CFD Simulation of Stratified Operations in Low Temperature Combustion Modes". Energies 14, nr 15 (30.07.2021): 4623. http://dx.doi.org/10.3390/en14154623.

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Many researchers in industry and academia are showing an increasing interest in the definition of fuel surrogates for Computational Fluid Dynamics simulation applications. This need is mainly driven by the necessity of the engine research community to anticipate the effects of new gasoline formulations and combustion modes (e.g., Homogeneous Charge Compression Ignition, Spark Assisted Compression Ignition) to meet future emission regulations. Since those solutions strongly rely on the tailored mixture distribution, the simulation and accurate prediction of the mixture formation will be mandatory. Focusing purely on the definition of surrogates to emulate liquid phase and liquid-vapor equilibrium of gasolines, the following target properties are considered in this work: density, Reid vapor pressure, chemical macro-composition and volatility. A set of robust algorithms has been developed for the prediction of volatility and Reid vapor pressure. A Bayesian optimization algorithm based on a customized merit function has been developed to allow for the efficient definition of surrogate formulations from a palette of 15 pure compounds. The developed methodology has been applied on different real gasolines from literature in order to identify their optima surrogates. Furthermore, the ‘unicity’ of the surrogate composition is discussed by comparing the optimum solution with the most different one available in the pool of equivalent-valuable solutions. The proposed methodology has proven the potential to formulate surrogates characterized by an overall good agreement with the target properties of the experimental gasolines (max relative error below 10%, average relative error around 3%). In particular, the shape and the end-tails of the distillation curve are well captured. Furthermore, an accurate prediction of key chemical macro-components such as ethanol and aromatics and their influence on evaporative behavior is achieved. The study of the ‘unicity’ of the surrogate composition has revealed that (i) the unicity is strongly correlated with the accuracy and that (ii) both ‘unicity’ and accuracy of the prediction are very sensitive to the high presence of aromatics.

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Zeng, Wei, Xian Chao Wang i Ying Sheng Wang. "Surrogating for High Dimensional Computationally Expensive Multi-Modal Functions with Elliptical Basis Function Models". Applied Mechanics and Materials 733 (luty 2015): 880–84. http://dx.doi.org/10.4028/www.scientific.net/amm.733.880.

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In the engineering design process, approximation Technique could guarantee the fitting precision, speed up the design process and reduce design costs. To a certain extent, surrogate models could replace time-consuming and highly accurate computational fluid dynamics analysis gradually. In this paper, we take Optimal Latin Hypercube Sampling experimental design strategies to determine the sample space and error analysis test sample, adopt the principle of infilling criteria based on the maximum error to improve the accuracy of the surrogate model, test the unimodal and multimodal expensive functions of 10 dimension, 20 dimensions and 30 dimensions, study the performance and scope of EBF-NN surrogate model based on infilling criteria by comparing the RBF-NN surrogate model.

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Thiel, M., M. C. Romano, J. Kurths, M. Rolfs i R. Kliegl. "Generating surrogates from recurrences". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, nr 1865 (13.08.2007): 545–57. http://dx.doi.org/10.1098/rsta.2007.2109.

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In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.

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Ueki, Ryosuke, Shota Hayashi, Masaya Tsunoda, Momoko Akiyama, Hanrui Liu, Tasuku Ueno, Yasuteru Urano i Shinsuke Sando. "Nongenetic control of receptor signaling dynamics using a DNA-based optochemical tool". Chemical Communications 57, nr 48 (2021): 5969–72. http://dx.doi.org/10.1039/d1cc01968f.

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Preen, Richard J., i Larry Bull. "Design Mining Interacting Wind Turbines". Evolutionary Computation 24, nr 1 (marzec 2016): 89–111. http://dx.doi.org/10.1162/evco_a_00144.

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An initial study has recently been presented of surrogate-assisted evolutionary algorithms used to design vertical-axis wind turbines wherein candidate prototypes are evaluated under fan-generated wind conditions after being physically instantiated by a 3D printer. Unlike other approaches, such as computational fluid dynamics simulations, no mathematical formulations were used and no model assumptions were made. This paper extends that work by exploring alternative surrogate modelling and evolutionary techniques. The accuracy of various modelling algorithms used to estimate the fitness of evaluated individuals from the initial experiments is compared. The effect of temporally windowing surrogate model training samples is explored. A surrogate-assisted approach based on an enhanced local search is introduced; and alternative coevolution collaboration schemes are examined.

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Bender, Niels C., Torben Ole Andersen i Henrik C. Pedersen. "Feasibility of Deep Neural Network Surrogate Models in Fluid Dynamics". Modeling, Identification and Control: A Norwegian Research Bulletin 40, nr 2 (2019): 71–87. http://dx.doi.org/10.4173/mic.2019.2.1.

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Mooney, Barbara L., Brian H. Morrow, Keith Van Nostrand, Dianne Luning Prak, Paul C. Trulove, Robert E. Morris, J. David Schall, Judith A. Harrison i M. Todd Knippenberg. "Elucidating the Properties of Surrogate Fuel Mixtures Using Molecular Dynamics". Energy & Fuels 30, nr 2 (18.02.2016): 784–95. http://dx.doi.org/10.1021/acs.energyfuels.5b01468.

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Gan, Chunbiao, i Shimin He. "Surrogate test for noise-contaminated dynamics in the Duffing oscillator". Chaos, Solitons & Fractals 38, nr 5 (grudzień 2008): 1517–22. http://dx.doi.org/10.1016/j.chaos.2007.01.134.

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Wang, Xu, i Kai Liu. "A Crash Surrogate Metric considering Traffic Flow Dynamics in a Motorway Corridor". Journal of Advanced Transportation 2018 (27.06.2018): 1–7. http://dx.doi.org/10.1155/2018/9349418.

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We proposed a new crash surrogate metric, i.e., the maximum disturbance that a car following scenario can accommodate, to represent potential crash risks with a simple closed form. The metric is developed in consideration of traffic flow dynamics. Then, we compared its performance in predicting the rear-end crash risks for motorway on-ramps with other two surrogate measures (time to collision and aggregated crash index). To this end, a one-lane on-ramp of Pacific Motorway, Australia, was selected for this case study. Due to the lack of crash data on the study site, historical crash counts were merged according to levels of service (LOS) and then converted into crash rates. In this study, we used the societal risk index to represent the crash surrogate indicators and built relationships with crash rates. The final results show that (1) the proposed metric and aggregated crash index are superior to the time to collision in predicting the rear-end crash risks for on-ramps; (2) they have a relatively similar performance, but due to the simple calculation, the proposed metric is more applicable to some real-world cases compared with the aggregated crash index.

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30

Small, Michael, i Kevin Judd. "Detecting Nonlinearity in Experimental Data". International Journal of Bifurcation and Chaos 08, nr 06 (czerwiec 1998): 1231–44. http://dx.doi.org/10.1142/s0218127498000966.

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The technique of surrogate data has been used as a method to test for membership of particular classes of linear systems. We suggest an obvious extension of this to classes of nonlinear parametric models and demonstrate our methods with respiratory data from sleeping human infants. Although our data are clearly distinct from the different classes of linear systems we are unable to distinguish between our data and surrogates generated by nonlinear models. Hence we conclude that human respiration is likely to be a nonlinear system with more than two degrees of freedom with a limit cycle that is driven by high dimensional dynamics or noise.

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Forrester, Alexander I. J., Neil W. Bressloff i Andy J. Keane. "Optimization using surrogate models and partially converged computational fluid dynamics simulations". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, nr 2071 (6.03.2006): 2177–204. http://dx.doi.org/10.1098/rspa.2006.1679.

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Efficient methods for global aerodynamic optimization using computational fluid dynamics simulations should aim to reduce both the time taken to evaluate design concepts and the number of evaluations needed for optimization. This paper investigates methods for improving such efficiency through the use of partially converged computational fluid dynamics results. These allow surrogate models to be built in a fraction of the time required for models based on converged results. The proposed optimization methodologies increase the speed of convergence to a global optimum while the computer resources expended in areas of poor designs are reduced. A strategy which combines a global approximation built using partially converged simulations with expected improvement updates of converged simulations is shown to outperform a traditional surrogate-based optimization.

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Fouladinejad, Nariman, Nima Fouladinejad, Mohamad Kasim Abdul Jalil i Jamaludin Mohd Taib. "Development of a surrogate-based vehicle dynamic model to reduce computational delays in a driving simulator". SIMULATION 92, nr 12 (23.10.2016): 1087–102. http://dx.doi.org/10.1177/0037549716675956.

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The development of a real-time driving simulator involves highly complex integrated and interdependent subsystems that require a large amount of computational time. When advanced hardware is unavailable for economic reasons, achieving real-time simulation is challenging, and thus delays are inevitable. Moreover, computational delays in the response of driving simulator subsystems reduce the fidelity of the simulation. In this paper, we propose a technique to decrease computational delays in a driving simulator. We used approximation techniques, sensitivity analysis, decomposition, and sampling techniques to develop a surrogate-based vehicle dynamic model (SBVDM). This global surrogate model can be used in place of the conventional vehicle dynamic model to reduce the computational burden while maintaining an acceptable accuracy. Our results showed that the surrogate model can significantly reduce computing costs compared to the computationally expensive conventional model. In addition, the response time of the SBVDM is nearly five times faster than the original simulation codes. Also, as a method to reduce hardware cost, the SBVDM was used and the results showed that most of the responses were accurate and acceptable in relation to longitudinal and lateral dynamics. Based on the results, the authors suggested that the proposed framework could be useful for developing low-cost vehicle simulation systems that require fast computational output.

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Rubin, Sergio, i Michel Crucifix. "Earth’s Complexity Is Non-Computable: The Limits of Scaling Laws, Nonlinearity and Chaos". Entropy 23, nr 7 (19.07.2021): 915. http://dx.doi.org/10.3390/e23070915.

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Current physics commonly qualifies the Earth system as ‘complex’ because it includes numerous different processes operating over a large range of spatial scales, often modelled as exhibiting non-linear chaotic response dynamics and power scaling laws. This characterization is based on the fundamental assumption that the Earth’s complexity could, in principle, be modeled by (surrogated by) a numerical algorithm if enough computing power were granted. Yet, similar numerical algorithms also surrogate different systems having the same processes and dynamics, such as Mars or Jupiter, although being qualitatively different from the Earth system. Here, we argue that understanding the Earth as a complex system requires a consideration of the Gaia hypothesis: the Earth is a complex system because it instantiates life—and therefore an autopoietic, metabolic-repair (M,R) organization—at a planetary scale. This implies that the Earth’s complexity has formal equivalence to a self-referential system that inherently is non-algorithmic and, therefore, cannot be surrogated and simulated in a Turing machine. We discuss the consequences of this, with reference to in-silico climate models, tipping points, planetary boundaries, and planetary feedback loops as units of adaptive evolution and selection.

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Hulsman, Paul, Søren Juhl Andersen i Tuhfe Göçmen. "Optimizing wind farm control through wake steering using surrogate models based on high-fidelity simulations". Wind Energy Science 5, nr 1 (5.03.2020): 309–29. http://dx.doi.org/10.5194/wes-5-309-2020.

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Abstract. This paper aims to develop fast and reliable surrogate models for yaw-based wind farm control. The surrogates, based on polynomial chaos expansion (PCE), are built using high-fidelity flow simulations coupled with aeroelastic simulations of the turbine performance and loads. Developing a model for wind farm control is a challenging control problem due to the time-varying dynamics of the wake. The wind farm control strategy is optimized for both the power output and the loading of the turbines. The optimization performed using two Vestas V27 turbines in a row for a specific atmospheric condition suggests that a power gain of almost 3%±1% can be achieved at close spacing by yawing the upstream turbine more than 15∘. At larger spacing the optimization shows that yawing is not beneficial as the optimization reverts to normal operation. Furthermore, it was also identified that a reduction in the equivalent loads was obtained at the cost of power production. The total power gains are discussed in relation to the associated model errors and the uncertainty of the surrogate models used in the optimization, as well as the implications for wind farm control.

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Daniel Marjavaara, B., T. Staffan Lundström, Tushar Goel, Yolanda Mack i Wei Shyy. "Hydraulic Turbine Diffuser Shape Optimization by Multiple Surrogate Model Approximations of Pareto Fronts". Journal of Fluids Engineering 129, nr 9 (4.04.2007): 1228–40. http://dx.doi.org/10.1115/1.2754324.

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A multiple surrogate-based optimization strategy in conjunction with an evolutionary algorithm has been employed to optimize the shape of a simplified hydraulic turbine diffuser utilizing three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics solutions. Specifically, the diffuser performance is optimized by changing five geometric design variables to maximize the average pressure recovery factor for two inlet boundary conditions with different swirl, corresponding to different operating modes of the hydraulic turbine. Polynomial response surfaces and radial basis neural networks are used as surrogates, while a hybrid formulation of the NSGA-IIa evolutionary algorithm and a ϵ-constraint strategy is applied to construct the Pareto front from the two surrogates. The proposed optimization framework drastically reduces the computational load of the problem, compared to solely utilizing an evolutionary algorithm. For the present problem, the radial basis neural networks are more accurate near the Pareto front while the response surface performs better in regions away from it. By using a local resampling updating scheme the fidelity of both surrogates is improved, especially near the Pareto front. The optimal design yields larger wall angles, nonaxisymmetrical shapes, and delay in wall separation, resulting in 14.4% and 8.9% improvement, respectively, for the two inlet boundary conditions.

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Hue, Keat Yung, Jin Hau Lew, Maung Maung Myo Thant, Omar K. Matar, Paul F. Luckham i Erich A. Müller. "Molecular Dynamics Simulation of Polyacrylamide Adsorption on Calcite". Molecules 28, nr 17 (31.08.2023): 6367. http://dx.doi.org/10.3390/molecules28176367.

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In poorly consolidated carbonate rock reservoirs, solids production risk, which can lead to increased environmental waste, can be mitigated by injecting formation-strengthening chemicals. Classical atomistic molecular dynamics (MD) simulation is employed to model the interaction of polyacrylamide-based polymer additives with a calcite structure, which is the main component of carbonate formations. Amongst the possible calcite crystal planes employed as surrogates of reservoir rocks, the (1 0 4) plane is shown to be the most suitable surrogate for assessing the interactions with chemicals due to its stability and more realistic representation of carbonate structure. The molecular conformation and binding energies of pure polyacrylamide (PAM), hydrolysed polyacrylamide in neutral form (HPAM), hydrolysed polyacrylamide with 33% charge density (HPAM 33%) and sulfonated polyacrylamide with 33% charge density (SPAM 33%) are assessed to determine the adsorption characteristics onto calcite surfaces. An adsorption-free energy analysis, using an enhanced umbrella sampling method, is applied to evaluate the chemical adsorption performance. The interaction energy analysis shows that the polyacrylamide-based polymers display favourable interactions with the calcite structure. This is attributed to the electrostatic attraction between the amide and carboxyl functional groups with the calcite. Simulations confirm that HPAM33% has a lower free energy than other polymers, presumably due to the presence of the acrylate monomer in ionised form. The superior chemical adsorption performance of HPAM33% agrees with Atomic Force Microscopy experiments reported herein.

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Wenink, Robert, Martin van der Eijk, Neil Yorke-Smith i Peter Wellens. "Multi-fidelity Kriging extrapolation together with CFD for the design of the cross-section of a falling lifeboat". International Shipbuilding Progress 70, nr 2 (22.12.2023): 115–50. http://dx.doi.org/10.3233/isp-230013.

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Surrogate modelling techniques such as Kriging are a popular means for cheaply emulating the response of expensive Computational Fluid Dynamics (CFD) simulations. These surrogate models are often used for exploring a parameterised design space and identifying optimal designs. Multi-fidelity Kriging extends the methodology to incorporate data of variable accuracy and costs to create a more effective surrogate. This work recognises that the grid convergence property of CFD solvers is currently an unused source of information and presents a novel method that, by leveraging the data structure implied by grid convergence, could further improve the performance of the surrogate model and the corresponding optimisation process. Grid convergence states that the simulation solution converges to the true simulation solution as the numerical grid is refined. The proposed method is tested with realistic multi-fidelity data acquired with CFD simulations. The performance of the surrogate model is comparable to an existing method, and likely more robust. More research is needed to explore the full potential of the proposed method. Code has been made available online at https://github.com/robertwenink/MFK-Extrapolation.

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Ma, Xiaopeng, Jinsheng Zhao, Desheng Zhou, Kai Zhang i Yapeng Tian. "Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs". Mathematics 12, nr 5 (2.03.2024): 754. http://dx.doi.org/10.3390/math12050754.

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Inverse modeling can estimate uncertain parameters in subsurface reservoirs and provide reliable numerical models for reservoir development and management. The traditional simulation-based inversion method usually requires numerous numerical simulations, which is time-consuming. Recently, deep learning-based surrogate models have been widely studied as an alternative to numerical simulation, which can significantly improve the solving efficiency of inversion. However, for reservoirs with complex fracture distribution, constructing the surrogate model of numerical simulation presents a significant challenge. In this work, we present a deep graph learning-based surrogate model for inverse modeling of fractured reservoirs. Specifically, the proposed surrogate model integrates the graph attention mechanisms to extract features of fracture network in reservoirs. The graph learning can retain the discrete characteristics and structural information of the fracture network. The extracted features are subsequently integrated with a multi-layer recurrent neural network model to predict the production dynamics of wells. A surrogate-based inverse modeling workflow is then developed by combining the surrogate model with the differential evolutionary algorithm. Numerical studies performed on a synthetic naturally fractured reservoir model with multi-scale fractures illustrate the performance of the proposed methods. The results demonstrate that the proposed surrogate model exhibits promising generalization performance of production prediction. Compared with tens of thousands of numerical simulations required by the simulation-based inverse modeling method, the proposed surrogate-based method only requires 1000 to 1500 numerical simulations, and the solution efficiency can be improved by ten times.

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Martin, Tim, Anne Koch i Frank Allgöwer. "Data-driven surrogate models for LTI systems via saddle-point dynamics". IFAC-PapersOnLine 53, nr 2 (2020): 953–58. http://dx.doi.org/10.1016/j.ifacol.2020.12.1261.

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Rasheed, Abdur, Shubham Sharma, Prasenjit Kabi, Abhishek Saha, Swetaprovo Chaudhuri i Saptarshi Basu. "Precipitation dynamics of surrogate respiratory sessile droplets leading to possible fomites". Journal of Colloid and Interface Science 600 (październik 2021): 1–13. http://dx.doi.org/10.1016/j.jcis.2021.04.128.

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Eichinger, Matthias, Alexander Heinlein i Axel Klawonn. "Surrogate convolutional neural network models for steady computational fluid dynamics simulations". ETNA - Electronic Transactions on Numerical Analysis 56 (2022): 235–55. http://dx.doi.org/10.1553/etna_vol56s235.

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Sharma, Shubham, Siddhant Jain, Abhishek Saha i Saptarshi Basu. "Evaporation dynamics of a surrogate respiratory droplet in a vortical environment". Journal of Colloid and Interface Science 623 (październik 2022): 541–51. http://dx.doi.org/10.1016/j.jcis.2022.05.061.

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Taylor, Paul G., Michael Small, Kwee-Yum Lee, Raul Landeo, Damien M. O’Meara i Emma L. Millett. "A Surrogate Technique for Investigating Deterministic Dynamics in Discrete Human Movement". Motor Control 20, nr 4 (październik 2016): 459–70. http://dx.doi.org/10.1123/mc.2015-0043.

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Loy, Y. Y., G. P. Rangaiah i S. Lakshminarayanan. "Surrogate modelling for enhancing consequence analysis based on computational fluid dynamics". Journal of Loss Prevention in the Process Industries 48 (lipiec 2017): 173–85. http://dx.doi.org/10.1016/j.jlp.2017.04.027.

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Tuan, Nguyen Hung, Le Xuan Huynh i Pham Hoang Anh. "A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure". Vietnam Journal of Mechanics 37, nr 1 (27.02.2015): 17–27. http://dx.doi.org/10.15625/0866-7136/37/1/3923.

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This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. In the design of the surrogate model, complete quadratic polynomials are selected with all fuzzy variables are transformed to standardized fuzzy variables. This methodology allows accurate determination of the fuzzy dynamic outputs, which is the major issue in response surface based techniques. The effectiveness of the proposed fuzzy finite element algorithm is illustrated through a numerical analysis of a linear two-storey shear frame structure.

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Fu, Chao, Zhaoli Zheng, Weidong Zhu, Zhongliang Xie, Weiyang Qin i Kuan Lu. "Nonlinear dynamics of discontinuous uncertain oscillators with unilateral constraints". Chaos: An Interdisciplinary Journal of Nonlinear Science 32, nr 12 (grudzień 2022): 123112. http://dx.doi.org/10.1063/5.0125365.

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Nonlinear dynamics of discontinuous oscillators with unilateral constraints and non-random parametric uncertainties are investigated. Nonlinear oscillators considering single- and double-sided constraints are carefully constructed to exhibit rich bifurcations, such as period-doubling and Neimark–Sacker bifurcations. In deterministic amplitude–frequency responses, both hardening and softening effects are induced by non-smooth contact-type nonlinearities. Stabilities of the solutions are determined by the shooting method and the monodromy matrix. To effectively quantify the behaviors of nonlinear oscillators in the presence of parametric uncertainties, a non-intrusive surrogate function aided by arc-length ratio interpolation is constructed. Simulation results demonstrate variabilities of nonlinear responses under different non-random uncertainties. Moreover, an accuracy verification is provided to verify the effectiveness of the non-intrusive uncertainty propagation method. It is found that the surrogate function in combination with the arc-length ratio technique has high accuracy and evolutions of turning points are captured satisfactorily regardless of complex interactions of nonlinearities and uncertainties. The findings and methodologies reported are meaningful to general nonlinear systems having complex motions, paving the road for more in-depth investigations into uncertain nonlinear dynamics.

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Wang, Gang, Yiming Zhou, Chunjie Wang, Shengpeng Ma i Jianzhong Ding. "Multi-objective Optimization for the Base Lattice Structure of a Small Space Sampling Return Capsule". Journal of Physics: Conference Series 2658, nr 1 (1.12.2023): 012003. http://dx.doi.org/10.1088/1742-6596/2658/1/012003.

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Abstract The space sample-return mission capsule will bear a large landing impact at the moment of landing, so the return capsule structure is required to be the lightest under the premise of ensuring the safety of equipment and sampling samples. In view of the small size, compact layout and high lightweight requirements of the space sample-return mission module, the base lattice structure made of additive materials can achieve better comprehensive performance of landing impact resistance. In this paper, design of experiments (DOE) and surrogate model are used to carry out parameter sensitivity analysis and multi-objective optimization for the base lattice structure of small return capsule landing impact for space sampling. First, the parametric model of the large base lattice of the landing impact dynamics of the return capsule was established. Then, the Latin Hypercube Sampling (LHS) method was used to carry out sensitivity analysis of the lattice structure parameters and identify key factors. Finally, the response surface model was constructed, and the genetic algorithm was used to optimize the lattice structure parameters. The optimal design was obtained. By comparison with the dynamics analysis model, the results of the surrogate model are basically consistent with the dynamic analysis results.

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Hirata, Yoshito, Masanori Shiro i José M. Amigó. "Surrogate Data Preserving All the Properties of Ordinal Patterns up to a Certain Length". Entropy 21, nr 7 (22.07.2019): 713. http://dx.doi.org/10.3390/e21070713.

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We propose a method for generating surrogate data that preserves all the properties of ordinal patterns up to a certain length, such as the numbers of allowed/forbidden ordinal patterns and transition likelihoods from ordinal patterns into others. The null hypothesis is that the details of the underlying dynamics do not matter beyond the refinements of ordinal patterns finer than a predefined length. The proposed surrogate data help construct a test of determinism that is free from the common linearity assumption for a null-hypothesis.

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Mukhopadhyay, Satabhisa, Tathagata Dasgupta, Angelene Berwick, Elizabeth Walsh, Andrew Hanby, Rebecca Millican-Slater, Michele Cummings i Nicolas M. Orsi. "Automated H&E whole slide image surrogate Ki67 index prediction and prognostic value across breast cancer subtypes." Journal of Clinical Oncology 40, nr 16_suppl (1.06.2022): e12518-e12518. http://dx.doi.org/10.1200/jco.2022.40.16_suppl.e12518.

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e12518 Background: Despite its purported prognostic significance in breast cancer, Ki67 index assessment remains poorly standardized and features high discordance rates amongst pathologists. Moreover, its clinical utility is presently confined to low stage, ER+/HER2- tumors in determining the advisability of adjuvant chemotherapy. Unfortunately, established cut-offs limit its utility to tumors with either high or low Ki67 index extremes. While Ki67 is a marker of actively dividing cells, it fails to capture the detail of cell cycle phase and dynamics which could be informative in terms of prognosis and tumor sensitivity to specific therapies (e.g. CDK4/6 inhibitors). This study therefore developed two novel indices as surrogates of (i) Ki67 index and (ii) quiescent cell population load (QPL). Methods: Breast cancer (comprising evenly distributed hormone receptor/HER2 status cases) H&E slides ( n = 79 cases/108 slides) were digitized on an Aperio DT3 scanner, and used to extract surrogate Ki67 and QPL indices. Sections were also stained for Ki67 by immunohistochemistry (IHC) using a clinically validated assay and digitized. Whole slide image (WSI) tumor Ki67 counts were performed on QuPath and used to validate the surrogate Ki67 index (Cohen’s kappa score). Indices (i) and (ii) were related to progression free survival (PFS). Survival analyses were performed using Kaplan-Meier (KM; with median cut-off) and Cox Proportional Hazards (as a continuous variable) models. Results: The surrogate Ki67 index showed good concordance with IHC scores (kappa = 0.76; 95%CI 0.61-0.91; P< 0.00001). However, this surrogate index performed better as a prognostic indicator of PFS compared to conventional Ki67 IHC (KM P = 0.048; HR = 1.35, P = 0.015 vs. KM P = 0.70; HR = 1.23, P = 0.08). Prognostically, the QPL index outperformed both Ki67 indices (KM P = 0.03; HR = 3.22, P = 0.001). Conclusions: We have developed two novel surrogate indices of Ki67 and QPL that can be readily automated to analyze H&E breast cancer WSIs. Our results show that both outperformed conventional Ki67 IHC evaluation in terms of prognostication, applied across molecular subtypes, improved informativeness of mid-range Ki67 index calls, and could potentially have predictive merit in selecting patients for cell cycle targeted therapies such as CDK4/6 inhibitors.

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Brusentseva, S. V., A. V. Glushkov, Ya I. Lepikh i V. B. Ternovsky. "NONLINEAR DYNAMICS OF RELATIVISTIC BACKWARD-WAVE TUBE IN AUTOMODULATION AND CHAOTIC REGIME WITH ACCOUNTING THE EFFECTS WAVES REFLECTION, SPACE CHARGE FIELD AND DISSIPATION". Photoelectronics, nr 25 (26.12.2016): 102–8. http://dx.doi.org/10.18524/0235-2435.2016.25.157636.

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It has been performed quantitative modelling, analysis of dynamics relativistic backward-wave tube (RBWT) with accounting relativistic effects, dissipation, a presence of space charge etc. There are computed the temporal dependences of the normalized field amplitudes in a wide range of variation of the controlling parameters which are characteristic for distributed relativistic electron-waved selfvibrational systems: electric length of an interaction space N, bifurcation parameter L and relativistic factor γ0. The computed temporal dependence of the field amplitude is in a good agreement with theoretical data by Ryskin-Titov regarding the RBWT dynamics with accounting the reflection effect, but without accounting dissipation effect and space charge field influence etc. The analysis techniques including multi-fractal approach, methods of correlation integral, false nearest neighbour, Lyapunov exponent’s, surrogate data, is applied analysis of numerical parameters of chaotic dynamics of RBWT. There are computed the dynamic and topological invariants of the RBWT dynamics in automodulation, chaotic regimes, correlation dimensions values), embedding, Kaplan-York dimensions, LE(+,+) Kolmogorov entropy.

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