Статті в журналах: "Differentiable model"

1

Putra, Roni Tri. "Model Epidemi Seir dengan Insidensi Standar." Jurnal Ilmiah Poli Rekayasa 12, no. 1 (October 14, 2016): 73. http://dx.doi.org/10.30630/jipr.12.1.37.

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In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with standard incidence. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.

2

Putra, Roni Tri, Sukatik, and Sri Nita. "Kestabilan Model Epidemi SEIR Dengan Laju Insidensi." Jurnal Ilmiah Poli Rekayasa 10, no. 2 (April 14, 2015): 74. http://dx.doi.org/10.30630/jipr.10.2.77.

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In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.

3

Putra, Roni Tri, and Quinoza Guvil. "Kestabilan Model Epidemi Dengan Laju Insidensi Jenuh." Jurnal Ilmiah Poli Rekayasa 13, no. 1 (October 16, 2017): 43. http://dx.doi.org/10.30630/jipr.13.1.64.

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In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with saturated incidence. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.

4

Szidarovsky, Ferenc, and Koji Okuguchi. "A non-differentiable input-output model." Mathematical Social Sciences 18, no. 2 (October 1989): 187–90. http://dx.doi.org/10.1016/0165-4896(89)90044-9.

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5

Putra, Roni Tri. "Analisis Eksistensi dan Ketunggalan Solusi Model Epidemi SEIR." Jurnal Ilmiah Poli Rekayasa 10, no. 1 (October 15, 2014): 65. http://dx.doi.org/10.30630/jipr.10.1.58.

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In this paper, it will be studied existence and uniqueness solution of equilibrium points for a SEIR model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.

6

Cho, Jin Seo, and Halbert White. "DIRECTIONALLY DIFFERENTIABLE ECONOMETRIC MODELS." Econometric Theory 34, no. 5 (August 22, 2017): 1101–31. http://dx.doi.org/10.1017/s0266466617000354.

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The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.

7

Swietojanski, Pawel, and Steve Renals. "Differentiable Pooling for Unsupervised Acoustic Model Adaptation." IEEE/ACM Transactions on Audio, Speech, and Language Processing 24, no. 10 (October 2016): 1773–84. http://dx.doi.org/10.1109/taslp.2016.2584700.

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8

Agop, M., O. Niculescu, A. Timofte, L. Bibire, A. S. Ghenadi, A. Nicuta, C. Nejneru, and G. V. Munceleanu. "Non-Differentiable Mechanical Model and Its Implications." International Journal of Theoretical Physics 49, no. 7 (April 9, 2010): 1489–506. http://dx.doi.org/10.1007/s10773-010-0330-5.

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9

Shi, Peng, Guoyan Huang, Hongdou He, Guyu Zhao, Xiaobing Hao, and Yifang Huang. "Few-shot regression with differentiable reference model." Information Sciences 658 (February 2024): 120010. http://dx.doi.org/10.1016/j.ins.2023.120010.

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Rokhlin, Dmitry B., and Anatoly Usov. "Rational taxation in an open access fishery model." Archives of Control Sciences 27, no. 1 (March 1, 2017): 5–27. http://dx.doi.org/10.1515/acsc-2017-0001.

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Abstract We consider a model of fishery management, where n agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the maximization of the discounted cooperative revenue, then the biomass stabilizes at the level, defined by the well known “golden rule”. We show that for independent myopic harvesting agents such optimal (or ε-optimal) cooperative behavior can be stimulated by the proportional tax, depending on the resource stock, and equal to the marginal value function of the cooperative problem. To implement this taxation scheme we prove that the mentioned value function is strictly concave and continuously differentiable, although the instantaneous individual revenues may be neither concave nor differentiable.

11

CIORUŢA, Bogdan. "REGARDING A CONTINUOUSLY DIFFERENTIABLE FRICTION MODEL USED FOR CONTROL OF DYNAMIC SYSTEMS DESIGN." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 19, no. 1 (July 31, 2017): 393–400. http://dx.doi.org/10.19062/2247-3173.2017.19.1.49.

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12

Ziane, Djelloul, Mountassir Hamdi Cherif, Dumitru Baleanu, and Kacem Belghaba. "Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets." Fractal and Fractional 4, no. 1 (February 9, 2020): 5. http://dx.doi.org/10.3390/fractalfract4010005.

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The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative operator are taken in the local fractional sense. Two examples have been presented showing the effectiveness of this method in solving this model on Cantor sets.

13

Robitzsch, Alexander. "L0 and Lp Loss Functions in Model-Robust Estimation of Structural Equation Models." Psych 5, no. 4 (October 20, 2023): 1122–39. http://dx.doi.org/10.3390/psych5040075.

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The Lp loss function has been used for model-robust estimation of structural equation models based on robustly fitting moments. This article addresses the choice of the tuning parameter ε that appears in the differentiable approximations of the nondifferentiable Lp loss functions. Moreover, model-robust estimation based on the Lp loss function is compared with a recently proposed differentiable approximation of the L0 loss function and a direct minimization of a smoothed version of the Bayesian information criterion in regularized estimation. It turned out in a simulation study that the L0 loss function slightly outperformed the Lp loss function in terms of bias and root mean square error. Furthermore, standard errors of the model-robust SEM estimators were analytically derived and exhibited satisfactory coverage rates.

14

Chianese, Marco, Adam Coogan, Paul Hofma, Sydney Otten, and Christoph Weniger. "Differentiable strong lensing: uniting gravity and neural nets through differentiable probabilistic programming." Monthly Notices of the Royal Astronomical Society 496, no. 1 (May 28, 2020): 381–93. http://dx.doi.org/10.1093/mnras/staa1477.

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ABSTRACT Since upcoming telescopes will observe thousands of strong lensing systems, creating fully automated analysis pipelines for these images becomes increasingly important. In this work, we make a step towards that direction by developing the first end-to-end differentiable strong lensing pipeline. Our approach leverages and combines three important computer science developments: (i) convolutional neural networks (CNNs), (ii) efficient gradient-based sampling techniques, and (iii) deep probabilistic programming languages. The latter automatize parameter inference and enable the combination of generative deep neural networks and physics components in a single model. In the current work, we demonstrate that it is possible to combine a CNN trained on galaxy images as a source model with a fully differentiable and exact implementation of gravitational lensing physics in a single probabilistic model. This does away with hyperparameter tuning for the source model, enables the simultaneous optimization of nearly 100 source and lens parameters with gradient-based methods, and allows the use of efficient gradient-based posterior sampling techniques. These features make this automated inference pipeline potentially suitable for processing a large amount of data. By analysing mock lensing systems with different signal-to-noise ratios, we show that lensing parameters are reconstructed with per cent-level accuracy. More generally, we consider this work as one of the first steps in establishing differentiable probabilistic programming techniques in the particle astrophysics community, which have the potential to significantly accelerate and improve many complex data analysis tasks.

15

Piergiovanni, AJ, Anelia Angelova, and Michael S. Ryoo. "Differentiable Grammars for Videos." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (April 3, 2020): 11874–81. http://dx.doi.org/10.1609/aaai.v34i07.6861.

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This paper proposes a novel algorithm which learns a formal regular grammar from real-world continuous data, such as videos. Learning latent terminals, non-terminals, and production rules directly from continuous data allows the construction of a generative model capturing sequential structures with multiple possibilities. Our model is fully differentiable, and provides easily interpretable results which are important in order to understand the learned structures. It outperforms the state-of-the-art on several challenging datasets and is more accurate for forecasting future activities in videos. We plan to open-source the code.1

16

E. Álvarez, Enrique, and Julieta Ferrario. "Robust Differentiable Functionals for the Additive Hazards Model." Open Journal of Statistics 05, no. 06 (2015): 631–44. http://dx.doi.org/10.4236/ojs.2015.56064.

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17

Shen, Siyuan, Yin Yang, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, and Kun Zhou. "High-order differentiable autoencoder for nonlinear model reduction." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–15. http://dx.doi.org/10.1145/3476576.3476620.

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18

Shen, Siyuan, Yin Yang, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, and Kun Zhou. "High-order differentiable autoencoder for nonlinear model reduction." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–15. http://dx.doi.org/10.1145/3450626.3459754.

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19

González-Olivares, E., E. Sáez, E. Stange, and I. Szántó. "Topological Description of a Non-Differentiable Bioeconomics Model." Rocky Mountain Journal of Mathematics 35, no. 4 (August 2005): 1133–55. http://dx.doi.org/10.1216/rmjm/1181069680.

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20

Roșu, Iulian Alin, Marius Mihai Cazacu, and Maricel Agop. "Multifractal Model of Atmospheric Turbulence Applied to Elastic Lidar Data." Atmosphere 12, no. 2 (February 6, 2021): 226. http://dx.doi.org/10.3390/atmos12020226.

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This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title “On a Multifractal Approach of Turbulent Atmosphere Dynamics”.

21

Du, Tao, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, and Wojciech Matusik. "DiffPD: Differentiable Projective Dynamics." ACM Transactions on Graphics 41, no. 2 (April 30, 2022): 1–21. http://dx.doi.org/10.1145/3490168.

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We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit timestepping schemes require tiny timesteps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics ( PD ), we present Differentiable Projective Dynamics ( DiffPD ), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4–19 times faster compared with the standard Newton’s method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a reality-to-simulation ( real-to-sim ) example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

22

Guo, Yingjia. "The stability of the positive solution for a fractional SIR model." International Journal of Biomathematics 10, no. 01 (November 15, 2016): 1750014. http://dx.doi.org/10.1142/s1793524517500140.

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In order to deal with non-differentiable functions, a modification of the Riemann–Liouville definition is recently proposed which appears to provide a framework for a fractional calculus which is quite parallel with classical calculus. Based on these new results, we study on the fractional SIR model in this paper. First, we give the general solution of the fractional differential equation. And then a unique global positive solution of the SIR model is obtained. Furthermore, we get the Lyapunov stability theory. By using this stability theory, the asymptotic stability of the positive solution is analyzed.

23

Prediger, Lukas, Niki Loppi, Samuel Kaski, and Antti Honkela. "d3p - A Python Package for Differentially-Private Probabilistic Programming." Proceedings on Privacy Enhancing Technologies 2022, no. 2 (March 3, 2022): 407–25. http://dx.doi.org/10.2478/popets-2022-0052.

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Abstract We present d3p, a software package designed to help fielding runtime efficient widely-applicable Bayesian inference under differential privacy guarantees. d3p achieves general applicability to a wide range of probabilistic modelling problems by implementing the differentially private variational inference algorithm, allowing users to fit any parametric probabilistic model with a differentiable density function. d3p adopts the probabilistic programming paradigm as a powerful way for the user to flexibly define such models. We demonstrate the use of our software on a hierarchical logistic regression example, showing the expressiveness of the modelling approach as well as the ease of running the parameter inference. We also perform an empirical evaluation of the runtime of the private inference on a complex model and find a ~10 fold speed-up compared to an implementation using TensorFlow Privacy.

24

Tian, Pinzhuo, Zhangkai Wu, Lei Qi, Lei Wang, Yinghuan Shi, and Yang Gao. "Differentiable Meta-Learning Model for Few-Shot Semantic Segmentation." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (April 3, 2020): 12087–94. http://dx.doi.org/10.1609/aaai.v34i07.6887.

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To address the annotation scarcity issue in some cases of semantic segmentation, there have been a few attempts to develop the segmentation model in the few-shot learning paradigm. However, most existing methods only focus on the traditional 1-way segmentation setting (i.e., one image only contains a single object). This is far away from practical semantic segmentation tasks where the K-way setting (K > 1) is usually required by performing the accurate multi-object segmentation. To deal with this issue, we formulate the few-shot semantic segmentation task as a learning-based pixel classification problem, and propose a novel framework called MetaSegNet based on meta-learning. In MetaSegNet, an architecture of embedding module consisting of the global and local feature branches is developed to extract the appropriate meta-knowledge for the few-shot segmentation. Moreover, we incorporate a linear model into MetaSegNet as a base learner to directly predict the label of each pixel for the multi-object segmentation. Furthermore, our MetaSegNet can be trained by the episodic training mechanism in an end-to-end manner from scratch. Experiments on two popular semantic segmentation datasets, i.e., PASCAL VOC and COCO, reveal the effectiveness of the proposed MetaSegNet in the K-way few-shot semantic segmentation task.

25

Vishniakou, Ivan, and Johannes D. Seelig. "Differentiable model-based adaptive optics for two-photon microscopy." Optics Express 29, no. 14 (June 23, 2021): 21418. http://dx.doi.org/10.1364/oe.424344.

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26

Fursov, Ivan, Alexey Zaytsev, Pavel Burnyshev, Ekaterina Dmitrieva, Nikita Klyuchnikov, Andrey Kravchenko, Ekaterina Artemova, Evgenia Komleva, and Evgeny Burnaev. "A Differentiable Language Model Adversarial Attack on Text Classifiers." IEEE Access 10 (2022): 17966–76. http://dx.doi.org/10.1109/access.2022.3148413.

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27

MATSUMOTO, Hiroyuki, and Hisami OHISHI. "Higher order spectral analysis in continuously differentiable friction model." Proceedings of the Dynamics & Design Conference 2018 (2018): 152. http://dx.doi.org/10.1299/jsmedmc.2018.152.

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28

Mezey, Paul G. "The differentiable manifold model of quantum-chemical reaction networks." International Journal of Quantum Chemistry 24, S17 (July 9, 2009): 137–52. http://dx.doi.org/10.1002/qua.560240815.

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29

Akhare, Deepak, Tengfei Luo, and Jian-Xun Wang. "Physics-integrated neural differentiable (PiNDiff) model for composites manufacturing." Computer Methods in Applied Mechanics and Engineering 406 (March 2023): 115902. http://dx.doi.org/10.1016/j.cma.2023.115902.

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30

Tesloianu, Nicolae Dan, Lucian Dobreci, Vlad Ghizdovat, Andrei Zala, Adrian Valentin Cotirlet, Alina Gavrilut, Maricel Agop, et al. "Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions." Entropy 23, no. 4 (April 9, 2021): 444. http://dx.doi.org/10.3390/e23040444.

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By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data.

31

Geng, Chenhua, Hong-Ye Hu, and Yijian Zou. "Differentiable programming of isometric tensor networks." Machine Learning: Science and Technology 3, no. 1 (January 21, 2022): 015020. http://dx.doi.org/10.1088/2632-2153/ac48a2.

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Abstract Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been generalized to tensor network optimizations. Here, we extend the differentiable programming to tensor networks with isometric constraints with applications to multiscale entanglement renormalization ansatz (MERA) and tensor network renormalization (TNR). By introducing several gradient-based optimization methods for the isometric tensor network and comparing with Evenbly–Vidal method, we show that auto-differentiation has a better performance for both stability and accuracy. We numerically tested our methods on 1D critical quantum Ising spin chain and 2D classical Ising model. We calculate the ground state energy for the 1D quantum model and internal energy for the classical model, and scaling dimensions of scaling operators and find they all agree with the theory well.

32

Shi, Zhi Guang, and Wei Huo. "Robust Tracking for BLDCM System Based on Unknown Differentiable Deadzone Nonlinearity." Applied Mechanics and Materials 313-314 (March 2013): 530–34. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.530.

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In this paper, trajectory tracking control of the brushless DC motor system (BLDCMS) with parameter unknown deadzone nonlinearity and viscous friction is investigated. Firstly, a global differential homeomorphism based on the recently established differentiable deadzone model is developed to linearize BLDCMS. Then, a model reference robust controller is presented to suppress the uncertainties. Finally, uniformly ultimate boundedness of the closed-loop system is proved and simulation results show validity of the proposed controller.

33

Son, Sanghyun, Yi-Ling Qiao, Jason Sewall, and Ming C. Lin. "Differentiable Hybrid Traffic Simulation." ACM Transactions on Graphics 41, no. 6 (November 30, 2022): 1–10. http://dx.doi.org/10.1145/3550454.3555492.

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We introduce a novel differentiable hybrid traffic simulator , which simulates traffic using a hybrid model of both macroscopic and microscopic models and can be directly integrated into a neural network for traffic control and flow optimization. This is the first differentiable traffic simulator for macroscopic and hybrid models that can compute gradients for traffic states across time steps and inhomogeneous lanes. To compute the gradient flow between two types of traffic models in a hybrid framework, we present a novel intermediate conversion component that bridges the lanes in a differentiable manner as well. We also show that we can use analytical gradients to accelerate the overall process and enhance scalability. Thanks to these gradients, our simulator can provide more efficient and scalable solutions for complex learning and control problems posed in traffic engineering than other existing algorithms. Refer to https://sites.google.com/umd.edu/diff-hybrid-traffic-sim for our project.

34

Díaz-Avalos, Josué D. "A positively invariant attracting set for a predator-prey model with a non-differentiable functional response." Selecciones Matemáticas 9, no. 02 (November 30, 2022): 234–42. http://dx.doi.org/10.17268/sel.mat.2022.02.02.

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Fan, Xiaolong, Maoguo Gong, Yue Wu, Zedong Tang, and Jieyi Liu. "Neural Gaussian Similarity Modeling for Differential Graph Structure Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 11 (March 24, 2024): 11919–26. http://dx.doi.org/10.1609/aaai.v38i11.29078.

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Graph Structure Learning (GSL) has demonstrated considerable potential in the analysis of graph-unknown non-Euclidean data across a wide range of domains. However, constructing an end-to-end graph structure learning model poses a challenge due to the impediment of gradient flow caused by the nearest neighbor sampling strategy. In this paper, we construct a differential graph structure learning model by replacing the non-differentiable nearest neighbor sampling with a differentiable sampling using the reparameterization trick. Under this framework, we argue that the act of sampling nearest neighbors may not invariably be essential, particularly in instances where node features exhibit a significant degree of similarity. To alleviate this issue, the bell-shaped Gaussian Similarity (GauSim) modeling is proposed to sample non-nearest neighbors. To adaptively model the similarity, we further propose Neural Gaussian Similarity (NeuralGauSim) with learnable parameters featuring flexible sampling behaviors. In addition, we develop a scalable method by transferring the large-scale graph to the transition graph to significantly reduce the complexity. Experimental results demonstrate the effectiveness of the proposed methods.

36

Koch, Benjamin, and Ignacio Reyes. "Differentiable-path integrals in quantum mechanics." International Journal of Geometric Methods in Modern Physics 12, no. 09 (October 2015): 1550100. http://dx.doi.org/10.1142/s0219887815501005.

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A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of Cα, by only allowing paths which possess at least α derivatives. The method introduces two external parameters, and induces the appearance of a particular time scale ϵD such that for time intervals longer than ϵD the model behaves as usual quantum mechanics. However, for time scales smaller than ϵD, modifications to standard formulation of quantum theory occur. This restriction renders convergent some quantities which are usually divergent in the time-continuum limit ϵ → 0. We illustrate the model by computing several meaningful physical quantities such as the mean square velocity 〈v2〉, the canonical commutator, the Schrödinger equation and the energy levels of the harmonic oscillator. It is shown that an adequate choice of the parameters introduced makes the evolution unitary.

37

Kuo, Chao-Hung, Jia-Wei Chen, Yi Yang, Yu-Hao Lan, Shao-Wei Lu, Ching-Fu Wang, Yu-Chun Lo, et al. "A Differentiable Dynamic Model for Musculoskeletal Simulation and Exoskeleton Control." Biosensors 12, no. 5 (May 9, 2022): 312. http://dx.doi.org/10.3390/bios12050312.

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An exoskeleton, a wearable device, was designed based on the user’s physical and cognitive interactions. The control of the exoskeleton uses biomedical signals reflecting the user intention as input, and its algorithm is calculated as an output to make the movement smooth. However, the process of transforming the input of biomedical signals, such as electromyography (EMG), into the output of adjusting the torque and angle of the exoskeleton is limited by a finite time lag and precision of trajectory prediction, which result in a mismatch between the subject and exoskeleton. Here, we propose an EMG-based single-joint exoskeleton system by merging a differentiable continuous system with a dynamic musculoskeletal model. The parameters of each muscle contraction were calculated and applied to the rigid exoskeleton system to predict the precise trajectory. The results revealed accurate torque and angle prediction for the knee exoskeleton and good performance of assistance during movement. Our method outperformed other models regarding the rate of convergence and execution time. In conclusion, a differentiable continuous system merged with a dynamic musculoskeletal model supported the effective and accurate performance of an exoskeleton controlled by EMG signals.

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Vishniakou, Ivan, and Johannes D. Seelig. "Differentiable model-based adaptive optics with transmitted and reflected light." Optics Express 28, no. 18 (August 21, 2020): 26436. http://dx.doi.org/10.1364/oe.403487.

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Fenn, T. D., M. J. Schnieders, and A. T. Brunger. "A smooth and differentiable bulk-solvent model for macromolecular diffraction." Acta Crystallographica Section D Biological Crystallography 66, no. 9 (August 13, 2010): 1024–31. http://dx.doi.org/10.1107/s0907444910031045.

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Inclusion of low-resolution data in macromolecular crystallography requires a model for the bulk solvent. Previous methods have used a binary mask to accomplish this, which has proven to be very effective, but the mask is discontinuous at the solute–solvent boundary (i.e. the mask value jumps from zero to one) and is not differentiable with respect to atomic parameters. Here, two algorithms are introduced for computing bulk-solvent models using either a polynomial switch or a smoothly thresholded product of Gaussians, and both models are shown to be efficient and differentiable with respect to atomic coordinates. These alternative bulk-solvent models offer algorithmic improvements, while showing similar agreement of the model with the observed amplitudes relative to the binary model as monitored using R, R free and differences between experimental and model phases. As with the standard solvent models, the alternative models improve the agreement primarily with lower resolution (>6 Å) data versus no bulk solvent. The models are easily implemented into crystallographic software packages and can be used as a general method for bulk-solvent correction in macromolecular crystallography.

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Stuyck, Tuur, and Hsiao-yu Chen. "DiffXPBD." Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, no. 3 (August 16, 2023): 1–14. http://dx.doi.org/10.1145/3606923.

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We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic cloth and volumetric material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.

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Li, Peng, Zhiyi Chen, Xu Chu, and Kexin Rong. "DiffPrep: Differentiable Data Preprocessing Pipeline Search for Learning over Tabular Data." Proceedings of the ACM on Management of Data 1, no. 2 (June 13, 2023): 1–26. http://dx.doi.org/10.1145/3589328.

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Data preprocessing is a crucial step in the machine learning process that transforms raw data into a more usable format for downstream ML models. However, it can be costly and time-consuming, often requiring the expertise of domain experts. Existing automated machine learning (AutoML) frameworks claim to automate data preprocessing. However, they often use a restricted search space of data preprocessing pipelines which limits the potential performance gains, and they are often too slow as they require training the ML model multiple times. In this paper, we propose DiffPrep, a method that can automatically and efficiently search for a data preprocessing pipeline for a given tabular dataset and a differentiable ML model such that the performance of the ML model is maximized. We formalize the problem of data preprocessing pipeline search as a bi-level optimization problem. To solve this problem efficiently, we transform and relax the discrete, non-differential search space into a continuous and differentiable one, which allows us to perform the pipeline search using gradient descent with training the ML model only once. Our experiments show that DiffPrep achieves the best test accuracy on 15 out of the 18 real-world datasets evaluated and improves the model's test accuracy by up to 6.6 percentage points.

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Prihandono, Bayu, Mariatul Kiftiah, and Yudhi Yudhi. "Existence and Uniqueness in the Linearised One and Two-dimensional Problem of Partial Differential Equations With Variational Method." Jurnal Matematika UNAND 11, no. 3 (July 30, 2022): 141. http://dx.doi.org/10.25077/jmua.11.3.141-158.2022.

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The classical solution and the strong solution of a partial differential equation problem are continuously differentiable solutions. This solution has a derivative for a continuous infinity level. However, not all problems of partial differential equations can be easily obtained by strong solutions. Even the existence of a solution requires in-depth investigation. The variational formulation method can qualitatively analyze a single solution to a partial differential equation problem. This study provides an alternative method in analyzing the problem model of partial differential equations analytically. In this research, we will examine the partial differential equation modelling built from fluid dynamics modelling.

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Opipari, Anthony, Jana Pavlasek, Chao Chen, Shoutian Wang, Karthik Desingh, and Odest Chadwicke Jenkins. "DNBP: Differentiable Nonparametric Belief Propagation." ACM / IMS Journal of Data Science 1, no. 1 (January 16, 2024): 1–24. http://dx.doi.org/10.1145/3592762.

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We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the probabilistic factors of a graphical model. In this work, we replace each crafted factor with a differentiable neural network, enabling the factors to be learned using an efficient optimization routine from labeled data. By combining differentiable neural networks with an efficient belief propagation algorithm, our method learns to maintain a set of marginal posterior samples using end-to-end training. We evaluate our differentiable nonparametric belief propagation (DNBP) method on a set of articulated pose tracking tasks and compare performance with learned baselines. Results from these experiments demonstrate the effectiveness of using learned factors for tracking and suggest the practical advantage over hand-crafted approaches. The project webpage is available at: https://progress.eecs.umich.edu/projects/dnbp/ .

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Lim, Hyoungjin, Gwonsoo Che, Wonyeol Lee, and Hongseok Yang. "Differentiable Algorithm for Marginalising Changepoints." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4828–35. http://dx.doi.org/10.1609/aaai.v34i04.5918.

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We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables other than changepoints. Also, it runs in time O(mn) where n is the number of time steps and m the number of changepoints, an improvement over a naive marginalisation method with O(nm) time complexity. We derive the algorithm by identifying quantities related to this marginalisation problem, showing that these quantities satisfy recursive relationships, and transforming the relationships to an algorithm via dynamic programming. Since our algorithm is differentiable, it can be applied to convert a model non-differentiable due to changepoints to a differentiable one, so that the resulting models can be analysed using gradient-based inference or learning techniques. We empirically show the effectiveness of our algorithm in this application by tackling the posterior inference problem on synthetic and real-world data.

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Zaika, Yu V., and I. A. Chernov. "Nonlinear dynamical boundary-value problem of hydrogen thermal desorption." International Journal of Mathematics and Mathematical Sciences 2003, no. 23 (2003): 1447–63. http://dx.doi.org/10.1155/s0161171203203288.

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The nonlinear boundary-value problem for the diffusion equation, which models gas interaction with solids, is considered. The model includes diffusion and the sorption/desorption processes on the surface, which leads to dynamical nonlinear boundary conditions. The boundary-value problem is reduced to an integro-differential equation of a special kind; existence and uniqueness of the classical (differentiable) solution theorems are proved. The results of numerical experiments are presented.

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PARVATE, ABHAY, and A. D. GANGAL. "CALCULUS ON FRACTAL SUBSETS OF REAL LINE — II: CONJUGACY WITH ORDINARY CALCULUS." Fractals 19, no. 03 (September 2011): 271–90. http://dx.doi.org/10.1142/s0218348x11005440.

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Calculus on fractals, or Fα-calculus, developed in a previous paper, is a calculus based fractals F ⊂ R, and involves Fα-integral and Fα-derivative of orders α, 0 < α ≤ 1, where α is the dimension of F. The Fα-integral is suitable for integrating functions with fractal support of dimension α, while the Fα-derivative enables us to differentiate functions like the Cantor staircase. Several results in Fα-calculus are analogous to corresponding results in ordinary calculus, such as the Leibniz rule, fundamental theorems, etc. The functions like the Cantor staircase function occur naturally as solutions of Fα-differential equations. Hence the latter can be used to model processes involving fractal space or time, which in particular include a class of dynamical systems exhibiting sublinear behaviour. In this paper we show that, as operators, the Fα-integral and Fα-derivative are conjugate to the Riemann integral and ordinary derivative respectively. This is accomplished by constructing a map ψ which takes Fα-integrable functions to Riemann integrable functions, such that the corresponding integrals on appropriate intervals have equal values. Under suitable conditions, a restriction of ψ also takes Fα-differentiable functions to ordinarily differentiable functions such that their values at appropriate points are equal. Further, this conjugacy is generalized to one between Sobolev spaces in ordinary calculus and Fα-calculus. This conjugacy is useful, among other things, to find solutions to Fα-differential equations: they can be mapped to ordinary differential equations, and the solutions of the latter can be transformed back to get those of the former. This is illustrated with a few examples.

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Romero-Ordoñez, Marco, Jhelly Pérez-Núñez, and Luis Vásquez-Serpa. "Qualitative analysis and simulations of a ratio-dependent May-Holling-Tanner predator-prey model with an alternative food source for the predator." Selecciones Matemáticas 9, no. 01 (June 30, 2022): 196–209. http://dx.doi.org/10.17268/sel.mat.2022.01.17.

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In this work, a May-Holling-Tanner ratio-dependent predator-prey model is studied with an alternative food source for the predator, described by a two-dimensional system of ordinary differential equations. We study the existence and uniqueness of the solutions of the mentioned above system. In addition, the boundedness and positivity of these solutions are analyzed and we establish conditions for the local stability of a simplified model, through a differentiable equivalence. Likewise, the Python programming language is used to perform the simulations using the Runge-Kutta numerical method of order four with the aim of showing the different cases of qualitative analysis.

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Al-Mohanna, Salam Mohammed Ghazi, and Yong-Hui Xia. "Fear Effect on a Predator–Prey Model with Non-Differential Fractional Functional Response." Fractal and Fractional 7, no. 4 (April 4, 2023): 312. http://dx.doi.org/10.3390/fractalfract7040312.

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In this paper, we study the factor of the fear effect in a predator–prey model with prey refuge and a non-differentiable fractional functional response due to the group defense. Since the functional response is non-differentiable, the dynamics of this system are considerably different from the dynamics of a classical predator–prey system. The persistence, the stability and the existence of the steady states are investigated. We examine the Hopf bifurcation at the unique positive equilibrium. Direct Hopf bifurcation is studied via the central manifold theorem. When the value of the fear factor decreases and is less than a threshold κH, the limit cycle appears, and it disappears through a loop of heteroclinic orbits when the value of the fear factor is equal to a value κhet.

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Wang, Ying, Jasper Verheul, Sang-Hoon Yeo, Nima Khademi Kalantari, and Shinjiro Sueda. "Differentiable Simulation of Inertial Musculotendons." ACM Transactions on Graphics 41, no. 6 (November 30, 2022): 1–11. http://dx.doi.org/10.1145/3550454.3555490.

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We propose a simple and practical approach for incorporating the effects of muscle inertia, which has been ignored by previous musculoskeletal simulators in both graphics and biomechanics. We approximate the inertia of the muscle by assuming that muscle mass is distributed along the centerline of the muscle. We express the motion of the musculotendons in terms of the motion of the skeletal joints using a chain of Jacobians, so that at the top level, only the reduced degrees of freedom of the skeleton are used to completely drive both bones and musculotendons. Our approach can handle all commonly used musculotendon path types, including those with multiple path points and wrapping surfaces. For muscle paths involving wrapping surfaces, we use neural networks to model the Jacobians, trained using existing wrapping surface libraries, which allows us to effectively handle the Jacobian discontinuities that occur when musculotendon paths collide with wrapping surfaces. We demonstrate support for higher-order time integrators, complex joints, inverse dynamics, Hill-type muscle models, and differentiability. In the limit, as the muscle mass is reduced to zero, our approach gracefully degrades to traditional simulators without support for muscle inertia. Finally, it is possible to mix and match inertial and non-inertial musculotendons, depending on the application.

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Wu, Jiaxian, Yue Lin, and Dehui Lu. "DR-Occluder: Generating Occluders Using Differentiable Rendering." ACM Transactions on Graphics 42, no. 6 (December 5, 2023): 1–14. http://dx.doi.org/10.1145/3618346.

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The target of the occluder is to use very few faces to maintain similar occlusion properties of the original 3D model. In this paper, we present DR-Occluder, a novel coarse-to-fine framework for occluder generation that leverages differentiable rendering to optimize a triangle set to an occluder. Unlike prior work, which has not utilized differentiable rendering for this task, our approach provides the ability to optimize a 3D shape to defined targets. Given a 3D model as input, our method first projects it to silhouette images, which are then processed by a convolution network to output a group of vertex offsets. These offsets are used to transform a group of distributed triangles into a preliminary occluder, which is further optimized by differentiable rendering. Finally, triangles whose area is smaller than a threshold are removed to obtain the final occluder. Our extensive experiments demonstrate that DR-Occluder significantly outperforms state-of-the-art methods in terms of occlusion quality. Furthermore, we compare the performance of our method with other approaches in a commercial engine, providing compelling evidence of its effectiveness.

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