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Relevant bibliographies by topics / Physics-informed Machine Learning

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Academic literature on the topic 'Physics-informed Machine Learning'

Author: Grafiati

Published: 6 September 2023

Last updated: 1 March 2025

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Journal articles on the topic "Physics-informed Machine Learning"

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Xypakis, Emmanouil, Valeria deTurris, Fabrizio Gala, Giancarlo Ruocco, and Marco Leonetti. "Physics-informed machine learning for microscopy." EPJ Web of Conferences 266 (2022): 04007. http://dx.doi.org/10.1051/epjconf/202226604007.

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We developed a physics-informed deep neural network architecture able to achieve signal to noise ratio improvements starting from low exposure noisy data. Our model is based on the nature of the photon detection process characterized by a Poisson probability distribution which we included in the training loss function. Our approach surpasses previous algorithms performance for microscopy data, moreover, the generality of the physical concepts employed here, makes it readily exportable to any imaging context.

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Pateras, Joseph, Pratip Rana, and Preetam Ghosh. "A Taxonomic Survey of Physics-Informed Machine Learning." Applied Sciences 13, no. 12 (June 7, 2023): 6892. http://dx.doi.org/10.3390/app13126892.

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Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning.

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Karimpouli, Sadegh, and Pejman Tahmasebi. "Physics informed machine learning: Seismic wave equation." Geoscience Frontiers 11, no. 6 (November 2020): 1993–2001. http://dx.doi.org/10.1016/j.gsf.2020.07.007.

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Barmparis, G. D., and G. P. Tsironis. "Discovering nonlinear resonances through physics-informed machine learning." Journal of the Optical Society of America B 38, no. 9 (August 2, 2021): C120. http://dx.doi.org/10.1364/josab.430206.

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Pilania, G., K. J. McClellan, C. R. Stanek, and B. P. Uberuaga. "Physics-informed machine learning for inorganic scintillator discovery." Journal of Chemical Physics 148, no. 24 (June 28, 2018): 241729. http://dx.doi.org/10.1063/1.5025819.

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Lagomarsino-Oneto, Daniele, Giacomo Meanti, Nicolò Pagliana, Alessandro Verri, Andrea Mazzino, Lorenzo Rosasco, and Agnese Seminara. "Physics informed machine learning for wind speed prediction." Energy 268 (April 2023): 126628. http://dx.doi.org/10.1016/j.energy.2023.126628.

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Tóth, Máté, Adam Brown, Elizabeth Cross, Timothy Rogers, and Neil D. Sims. "Resource-efficient machining through physics-informed machine learning." Procedia CIRP 117 (2023): 347–52. http://dx.doi.org/10.1016/j.procir.2023.03.059.

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Kapoor, Taniya, Hongrui Wang, Alfredo Núñez, and Rolf Dollevoet. "Physics-informed machine learning for moving load problems." Journal of Physics: Conference Series 2647, no. 15 (June 1, 2024): 152003. http://dx.doi.org/10.1088/1742-6596/2647/15/152003.

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Abstract This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and aim to predict the deflection of beams and the magnitude of the loads. The mathematical representation of the moving load considered involves a Dirac delta function, to capture the effect of the load moving across the structure. Approximating the Dirac delta function with PINNs is challenging because of its instantaneous change of output at a single point, causing difficulty in the convergence of the loss function. We propose to approximate the Dirac delta function with a Gaussian function. The incorporated Gaussian function physical equations are used in the physics-informed neural architecture to simulate beam deflections and to predict the magnitude of the load. Numerical results show that PIML is an effective method for simulating the forward and inverse problems for the considered model of a moving load.

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Behtash, Mohammad, Sourav Das, Sina Navidi, Abhishek Sarkar, Pranav Shrotriya, and Chao Hu. "Physics-Informed Machine Learning for Battery Capacity Forecasting." ECS Meeting Abstracts MA2024-01, no. 2 (August 9, 2024): 210. http://dx.doi.org/10.1149/ma2024-012210mtgabs.

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Batteries, recognized as effective energy storage solutions, are considered the main facilitators of the world-wide transition towards clean and renewable energy sources. Among different types of batteries, lithium-ion (Li-ion) variants offer higher energy densities and relatively longer life spans when compared to other types. Nonetheless, a primary concern with these batteries is their lifetime. Batteries undergo various degradation mechanisms under storage and use, significantly impacting their lifespan. To this end, it is crucial to predict the degradation and lifetime of Li-ion batteries under given conditions. Researchers use three main methodologies to perform battery health diagnostics and to predict the lifetime of batteries. One approach revolves around using mechanistic, first-principle electrochemical models, also known as physics-based models. If equipped with proper thermodynamic theories, such models can show promising capabilities; however, holistic degradation prediction with these models is still challenging due to the computational complexities and the multitude of parameters that need to be fine-tuned in this approach. The other common strategy is to use empirical models to predict battery degradation. These models generally entail fewer parameters to be identified and are computationally less intensive to solve. Nonetheless, empirical models can suffer from the accuracy point-of-view as they are constrained to predict degradation trends introduced by certain degradation modes. Another common technique in battery life prediction is to utilize purely data-driven methods, such as machine learning (ML) algorithms, which also have shown promising results in the literature on rapid health predictions. However, these methods require large volumes of experimental data for training and testing ML models to ensure accuracy. In addition, data-driven methods are likely to extrapolate poorly to conditions beyond their training data and are indifferent towards the underlying degradation mechanisms. Recently, physics-informed machine learning (PI-ML) methods have garnered significant attention. They integrate physics-based or empirical models (developed based on physics) with a data-driven approach and allow one to train ML models on a smaller set of experimental data. To the best of the authors’ knowledge, the performance comparison between first-principle and empirical models when integrated within PI-ML remains unclear. Therefore, in this work, we aim to compare these two models when applied to prognostics (capacity forecasting and remaining useful life prediction) of a set of Li-ion batteries. To perform this study, we generate aging data for 40 Li-ion coin cells cycled under randomized conditions. Each cell undergoes a three-step charging stage followed by a two-step discharge stage. After obtaining the aging data, we will develop two PI-ML models, one equipped with a physics-based model and another with a set of empirical models. Both PI-ML models in this work will follow the sequential integration approach, where the training data for the final PI-ML model come from both experimental and computational data, the latter of which are obtained from the physics-based or empirical models. The parameters for the physics-based and empirical models are identified from another set of experimental data. Finally, the PI-ML models will be tested with experimental data obtained at different cycling conditions. The data flow for the sequential architecture of PI-ML is shown in the attached figure. This comparative study will help identify the performance of physics-based and empirical models when integrated into PI-ML. The main performance metric considered in this work is each model’s ability to extrapolate beyond the experimental training data set, hence aiding the final PI-ML model in generalizing to conditions not covered by its experimental training data set. Figure 1

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Mandl, Luis, Somdatta Goswami, Lena Lambers, and Tim Ricken. "Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning." Computer Methods in Applied Mechanics and Engineering 434 (February 2025): 117586. http://dx.doi.org/10.1016/j.cma.2024.117586.

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Dissertations / Theses on the topic "Physics-informed Machine Learning"

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Mack, Jonas. "Physics Informed Machine Learning of Nonlinear Partial Differential Equations." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-441275.

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Wu, Jinlong. "Predictive Turbulence Modeling with Bayesian Inference and Physics-Informed Machine Learning." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/85129.

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Reynolds-Averaged Navier-Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high-fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled.
Ph. D.
Reynolds-Averaged Navier–Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled.

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Cedergren, Linnéa. "Physics-informed Neural Networks for Biopharma Applications." Thesis, Umeå universitet, Institutionen för fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-185423.

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Physics-Informed Neural Networks (PINNs) are hybrid models that incorporate differential equations into the training of neural networks, with the aim of bringing the best of both worlds. This project used a mathematical model describing a Continuous Stirred-Tank Reactor (CSTR), to test two possible applications of PINNs. The first type of PINN was trained to predict an unknown reaction rate law, based only on the differential equation and a time series of the reactor state. The resulting model was used inside a multi-step solver to simulate the system state over time. The results showed that the PINN could accurately model the behaviour of the missing physics also for new initial conditions. However, the model suffered from extrapolation error when tested on a larger reactor, with a much lower reaction rate. Comparisons between using a numerical derivative or automatic differentiation in the loss equation, indicated that the latter had a higher robustness to noise. Thus, it is likely the best choice for real applications. A second type of PINN was trained to forecast the system state one-step-ahead based on previous states and other known model parameters. An ordinary feed-forward neural network with an equal architecture was used as baseline. The second type of PINN did not outperform the baseline network. Further studies are needed to conclude if or when physics-informed loss should be used in autoregressive applications.

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Wang, Jianxun. "Physics-Informed, Data-Driven Framework for Model-Form Uncertainty Estimation and Reduction in RANS Simulations." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77035.

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Computational fluid dynamics (CFD) has been widely used to simulate turbulent flows. Although an increased availability of computational resources has enabled high-fidelity simulations (e.g. large eddy simulation and direct numerical simulation) of turbulent flows, the Reynolds-Averaged Navier-Stokes (RANS) equations based models are still the dominant tools for industrial applications. However, the predictive capability of RANS models is limited by potential inaccuracies driven by hypotheses in the Reynolds stress closure. With the ever-increasing use of RANS simulations in mission-critical applications, the estimation and reduction of model-form uncertainties in RANS models have attracted attention in the turbulence modeling community. In this work, I focus on estimating uncertainties stemming from the RANS turbulence closure and calibrating discrepancies in the modeled Reynolds stresses to improve the predictive capability of RANS models. Both on-line and off-line data are utilized to achieve this goal. The main contributions of this dissertation can be summarized as follows: First, a physics-based, data-driven Bayesian framework is developed for estimating and reducing model-form uncertainties in RANS simulations. An iterative ensemble Kalman method is employed to assimilate sparse on-line measurement data and empirical prior knowledge for a full-field inversion. The merits of incorporating prior knowledge and physical constraints in calibrating RANS model discrepancies are demonstrated and discussed. Second, a random matrix theoretic framework is proposed for estimating model-form uncertainties in RANS simulations. Maximum entropy principle is employed to identify the probability distribution that satisfies given constraints but without introducing artificial information. Objective prior perturbations of RANS-predicted Reynolds stresses in physical projections are provided based on comparisons between physics-based and random matrix theoretic approaches. Finally, a physics-informed, machine learning framework towards predictive RANS turbulence modeling is proposed. The functional forms of model discrepancies with respect to mean flow features are extracted from the off-line database of closely related flows based on machine learning algorithms. The RANS-modeled Reynolds stresses of prediction flows can be significantly improved by the trained discrepancy function, which is an important step towards the predictive turbulence modeling.
Ph. D.

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Quattromini, Michele. "Graph Neural Networks for fluid mechanics : data-assimilation and optimization." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPAST161.

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Cette thèse de doctorat explore l'application des réseaux de neurones en graphes (GNN) dans le domaine de la dynamique des fluides numérique (CFD), avec un accent particulier sur l'assimilation de données et l'optimisation. Le travail est structuré en trois parties principales: assimilation de données pour les équations de Navier-Stokes moyennées à la Reynolds (RANS) basée sur des modèles GNN; assimilation de données augmentée par les GNN avec des contraintes physiques imposées par la méthode adjointe; optimisation des systèmes fluides par des techniques d'apprentissage automatique (ML).Dans la première partie, la thèse examine le potentiel des GNN pour contourner les modèles de fermeture traditionnels, qui nécessitent souvent une calibration manuelle et sont sujets à des inexactitudes. En exploitant des données de simulation à haute fidélité, les GNN sont entraînés à apprendre directement les quantités non résolues de l'écoulement, offrant ainsi un cadre plus flexible pour le problème de fermeture des équations RANS. Cette approche élimine le besoin de modèles de fermeture calibrés manuellement, fournissant une alternative généralisée et basée sur les données. De plus, dans cette première partie, une étude approfondie de l'impact de la quantité de données sur les performances des GNN est réalisée, avec la conception d'une stratégie d'Active Learning pour sélectionner les données les plus informatives parmi celles disponibles. Sur la base de ces résultats, la deuxième partie de la thèse aborde un défi critique souvent rencontré par les modèles d'apprentissage automatique : l'absence de garantie de cohérence physique dans leurs prédictions. Afin de garantir que les GNN non seulement minimisent les erreurs, mais produisent également des résultats physiquement valides, cette partie intègre des contraintes physiques directement dans le processus d'entraînement des GNN. En incorporant les principes clés de la mécanique des fluides dans le cadre de l'apprentissage automatique, le modèle produit des prédictions à la fois fiables et cohérentes avec les lois physiques sous-jacentes, améliorant ainsi son applicabilité aux problèmes réels. Dans la troisième partie, la thèse démontre l'application des GNN pour optimiser les systèmes de dynamique des fluides, avec un accent particulier sur la conception des éoliennes. Ici, les GNN sont utilisés comme modèles de substitution, permettant des prédictions rapides de diverses configurations de conception sans avoir besoin de réaliser une simulation CFD complète à chaque itération. Cette approche accélère considérablement le processus de conception et montre le potentiel de l'optimisation basée sur l'apprentissage automatique dans le cadre de la CFD, permettant une exploration plus efficace des espaces de conception et une convergence plus rapide vers des solutions optimales. Sur le plan méthodologique, la thèse introduit une architecture GNN sur mesure spécifiquement adaptée aux applications CFD. Contrairement aux réseaux de neurones traditionnels, les GNN sont intrinsèquement capables de gérer des données de maillage non structurées, ce qui est courant dans les problèmes de mécanique des fluides impliquant des géométries irrégulières et des domaines d'écoulement complexes. À cette fin, la thèse présente une interface en deux parties entre les solveurs de la méthode des éléments finis (FEM) et l'architecture GNN. Cette interface transforme les champs vectoriels FEM en tenseurs numériques pouvant être traités efficacement par le réseau neuronal, permettant ainsi l'échange de données entre l'environnement de simulation et le modèle d'apprentissage
This PhD thesis investigates the application of Graph Neural Networks (GNNs) in the field of Computational Fluid Dynamics (CFD), with a focus on data-assimilation and optimization. The work is structured into three main parts: data-assimilation for Reynolds-Averaged Navier-Stokes (RANS) equations based on GNN models; data-assimilation augmented by GNN and adjoint-based enforced physical constraint; fluid systems optimization by ML techniques. In the first part, the thesis explores the potential of GNNs to bypass traditional closure models, which often require manual calibration and are prone to inaccuracies. By leveraging high-fidelity simulation data, GNNs are trained to directly learn the unresolved flow quantities, offering a more flexible framework for the RANS closure problem. This approach eliminates the need for manually tuned closure models, providing a generalized and data-driven alternative. Moreover, in this first part, a comprehensive study of the impact of data quantity on GNN performance is conducted, designing an Active Learning strategy to select the most informative data among those available. Building on these results, the second part of the thesis addresses a critical challenge often faced by ML models: the lack of guaranteed physical consistency in their predictions. To ensure that the GNNs not only minimize errors but also produce physically valid results, this part integrates physical constraints directly into the GNN training process. By embedding key fluid mechanics principles into the machine learning framework, the model produces predictions that are both reliable and consistent with the underlying physical laws, enhancing its applicability to real-world problems. In the third part, the thesis demonstrates the application of GNNs to optimize fluid dynamics systems, with a particular focus on wind turbine design. Here, GNNs are employed as surrogate models, enabling rapid predictions of various design configurations without the need for performing a full CFD simulation at each iteration. This approach significantly accelerates the design process and demonstrates the potential of ML-driven optimization in CFD workflows, allowing for more efficient exploration of design spaces and faster convergence toward optimal solutions. On the methodology side, the thesis introduces a custom GNN architecture specifically tailored for CFD applications. Unlike traditional neural networks, GNNs are inherently capable of handling unstructured mesh data, which is common in fluid mechanics problems involving irregular geometries and complex flow domains. To this end, the thesis presents a two-fold interface between Finite Element Method (FEM) solvers and the GNN architecture. This interface transforms FEM vector fields into numerical tensors that can be efficiently processed by the neural network, allowing data exchange between the simulation environment and the learning model

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Rautela, Mahindra Singh. "Hybrid Physics-Data Driven Models for the Solution of Mechanics Based Inverse Problems." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6123.

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Inverse problems pose a significant challenge as they aim to estimate the causal factors that result in a measured response. However, the responses are often truncated, partially available, and corrupted by measurement noise, rendering the problems ill-posed, and may have multiple or no solutions. Solving such problems using regularization transforms them into a family of well-posed functions. While physics-based models are interpretable, they operate under approximations and assumptions. Data-driven models such as machine learning and deep learning have shown promise in solving mechanics-based inverse problems, but they lack robustness, convergence, and generalization when operating under partial information, compromising the interpretability and explainability of their predictions. To overcome these challenges, hybrid physics-data-driven models can be formulated by integrating prior knowledge of physical laws, expert knowledge, spatial invariances, empirically validated rules, etc., acting as a regularizing agent to select a more feasible solution space. This approach improves prediction accuracy, robustness, generalization, interpretability, and explainability of the data-driven models. In this dissertation, we propose various physics-data-driven models to solve inverse problems related to engineering mechanics by integrating prior knowledge and its representation into a data-driven pipeline at different stages. We have used these hybrid models to solve six different inverse problems, such as leakage estimation of a pressurized habitat, estimating dispersion relations of a waveguide, structural damage identification, filtering temperature effects in guided waves, material property prediction, and guided wave generation and material design. The dissertation presents a detailed overview of inverse problems, definitions of the six inverse problems, and the motivation behind using hybrid models for their solution. Six different hybrid models, such as adaptive model calibration, physics-informed neural networks, inverse deep surrogate, deep latent variable, and unsupervised representation learning models, are formulated, and arranged on different levels of a pyramid, showing the trade-off between autonomy and explainability. All these new methods are designed with practical implementation in mind. The first model uses an adaptive real-time calibration framework to estimate the severity of leaks in a pressurized deep space habitat before they become a threat to the crew and habitat. The second model utilizes a physics-informed neural network to estimate the speed of wave propagation in a waveguide from limited experimental observations. The third model uses deep surrogate models to solve structural damage identification and material property prediction problems. The fourth model proposes a domain knowledge-based data augmentation scheme for ultrasonic guided waves-based damage identification. The fifth model uses unsupervised feature learning to solve guided waves-based structural anomaly detection and filtering the temperature effects on guided waves. The final model employs a deep latent variable model for structural anomaly detection, guided wave generation, and material design problems. Overall, the thesis demonstrates the effectiveness of hybrid models that combine prior knowledge with machine learning techniques to address a wide range of inverse problems. These models offer faster, more accurate, and more automated solutions to these problems than traditional methods.

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Yadav, Sangeeta. "Data Driven Stabilization Schemes for Singularly Perturbed Differential Equations." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6095.

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This thesis presents a novel way of leveraging Artificial Neural Network (ANN) to aid conventional numerical techniques for solving Singularly Perturbed Differential Equation (SPDE). SPDEs are challenging to solve with conventional numerical techniques such as Finite Element Methods (FEM) due to the presence of boundary and interior layers. Often the standard numerical solution shows spurious oscillations in the vicinity of these layers. Stabilization techniques are often employed to eliminate these spurious oscillations in the numerical solution. The accuracy of the stabilization technique depends on a user-chosen stabilization parameter whose optimal value is challenging to find. A few formulas for the stabilization parameter exist in the literature, but none extends well for high-dimensional and complex problems. In order to solve this challenge, we have developed the following ANN-based techniques for predicting this stabilization parameter: 1) SPDE-Net: As a proof of concept, we have developed an ANN called SPDE-Net for one-dimensional SPDEs. In the proposed method, we predict the stabilization parameter for the Streamline Upwind Petrov Galerkin (SUPG) stabilization technique. The prediction task is modelled as a regression problem using equation coefficients and domain parameters as inputs to the neural network. Three training strategies have been proposed, i.e. supervised learning, L 2-Error minimization (global) and L2-Error minimization (local). The proposed method outperforms existing state-of-the-art ANN-based partial differential equations (PDE) solvers, such as Physics Informed Neural Networks (PINNs). 2) AI-stab FEM With an aim for extending SPDE-Net for two-dimensional problems, we have also developed an optimization scheme using another Neural Network called AI-stab FEM and showed its utility in solving higher-dimensional problems. Unlike SPDE-Net, it minimizes the equation residual along with the crosswind derivative term and can be classified as an unsupervised method. We have shown that the proposed approach yields stable solutions for several two-dimensional benchmark problems while being more accurate than other contemporary ANN-based PDE solvers such as PINNs and Variational Neural Networks for the Solution of Partial Differential Equations (VarNet) 3) SPDE-ConvNet In the last phase of the thesis, we attempt to predict a cell-wise stabilization parameter to treat the interior/boundary layer regions adequately by developing an oscillations-aware neural network. We present SPDE-ConvNet, Convolutional Neural Network (CNN), for predicting the local (cell-wise) stabilization parameter. For the network training, we feed the gradient of the Galerkin solution, which is an indirect metric for representing oscillations in the numerical solution, along with the equation coefficients, to the network. It obtains a cell-wise stabilization parameter while sharing the network parameters among all the cells for an equation. Similar to AI-stab FEM, this technique outperforms PINNs and VarNet. We conclude the thesis with suggestions for future work that can leverage our current understanding of data-driven stabilization schemes for SPDEs to develop and improve the next-generation neural network-based numerical solvers for SPDEs.

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Book chapters on the topic "Physics-informed Machine Learning"

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Neuer, Marcus J. "Physics-Informed Learning." In Machine Learning for Engineers, 173–208. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. http://dx.doi.org/10.1007/978-3-662-69995-9_6.

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Braga-Neto, Ulisses. "Physics-Informed Machine Learning." In Fundamentals of Pattern Recognition and Machine Learning, 293–324. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-60950-3_12.

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Wang, Sifan, and Paris Perdikaris. "Adaptive Training Strategies for Physics-Informed Neural Networks." In Knowledge-Guided Machine Learning, 133–60. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003143376-6.

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Sun, Alexander Y., Hongkyu Yoon, Chung-Yan Shih, and Zhi Zhong. "Applications of Physics-Informed Scientific Machine Learning in Subsurface Science: A Survey." In Knowledge-Guided Machine Learning, 111–32. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003143376-5.

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Cross, Elizabeth J., S. J. Gibson, M. R. Jones, D. J. Pitchforth, S. Zhang, and T. J. Rogers. "Physics-Informed Machine Learning for Structural Health Monitoring." In Structural Integrity, 347–67. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81716-9_17.

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Mo, Zhaobin, Yongjie Fu, Daran Xu, and Xuan Di. "TrafficFlowGAN: Physics-Informed Flow Based Generative Adversarial Network for Uncertainty Quantification." In Machine Learning and Knowledge Discovery in Databases, 323–39. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-26409-2_20.

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Oh, Dong Keun. "Pure Physics-Informed Echo State Network of ODE Solution Replicator." In Artificial Neural Networks and Machine Learning – ICANN 2023, 225–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-44201-8_19.

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Uhrich, Benjamin, Martin Schäfer, Oliver Theile, and Erhard Rahm. "Using Physics-Informed Machine Learning to Optimize 3D Printing Processes." In Progress in Digital and Physical Manufacturing, 206–21. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-33890-8_18.

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Sankaran, Sathish, and Hardik Zalavadia. "Hybrid Data-Driven and Physics-Informed Reservoir Modeling for Unconventional Reservoirs." In Machine Learning Applications in Subsurface Energy Resource Management, 143–64. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003207009-12.

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Martín-González, Elena, Ebraham Alskaf, Amedeo Chiribiri, Pablo Casaseca-de-la-Higuera, Carlos Alberola-López, Rita G. Nunes, and Teresa Correia. "Physics-Informed Self-supervised Deep Learning Reconstruction for Accelerated First-Pass Perfusion Cardiac MRI." In Machine Learning for Medical Image Reconstruction, 86–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-88552-6_9.

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Conference papers on the topic "Physics-informed Machine Learning"

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Osorio Quero, Carlos Alexander, and Jose Martinez-Carranza. "Physics-Informed Machine Learning for UAV Control." In 2024 21st International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 1–6. IEEE, 2024. https://doi.org/10.1109/cce62852.2024.10770871.

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Zhu, Shijie, Hao Li, Yejie Jiang, and Yingjun Deng. "Inner Defect Detection via Physics-Informed Machine Learning." In 2024 6th International Conference on System Reliability and Safety Engineering (SRSE), 212–16. IEEE, 2024. https://doi.org/10.1109/srse63568.2024.10772527.

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Farlessyost, William, and Shweta Singh. "Improving Mechanistic Model Accuracy with Machine Learning Informed Physics." In Foundations of Computer-Aided Process Design, 275–82. Hamilton, Canada: PSE Press, 2024. http://dx.doi.org/10.69997/sct.121371.

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Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while maintaining interpretability of the underlying mechanistic framework. This work demonstrates the potential for machine learning techniques like SINDy to aid simple mechanistic models in scale-specific predictive accuracy.

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Sampath, Akila, Omar Faruque, Azim Khan, Vandana Janeja, and Jianwu Wang. "Physics-Informed Machine Learning for Sea Ice Thickness Prediction." In 2024 IEEE International Conference on Knowledge Graph (ICKG), 325–33. IEEE, 2024. https://doi.org/10.1109/ickg63256.2024.00048.

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Banna, Fayad Ali, Jean-Philippe Colombier, Rémi Emonet, and Marc Sebban. "Physics-Informed Machine Learning for Better Understanding Laser-Matter Interaction." In 2024 IEEE 36th International Conference on Tools with Artificial Intelligence (ICTAI), 199–205. IEEE, 2024. https://doi.org/10.1109/ictai62512.2024.00037.

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Bardi De Fourtou, Gautier, Edward Chow, and Thomas Lu. "Digital Twin and Physics Informed Machine Learning for Rover Motion Simulation." In IAF Space Exploration Symposium, Held at the 75th International Astronautical Congress (IAC 2024), 2049–55. Paris, France: International Astronautical Federation (IAF), 2024. https://doi.org/10.52202/078357-0234.

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Hu, Borong, Wei Mu, Hui Zhu, Ameer Janabi, Xufu Ren, Daohui Li, Jiayu Li, Yunlei Jiang, and Teng Long. "Digital Twin of Power Modules based on Physics Informed Machine Learning." In 2024 IEEE Energy Conversion Congress and Exposition (ECCE), 1718–22. IEEE, 2024. https://doi.org/10.1109/ecce55643.2024.10861878.

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Maruyama, Takashi, Daisuke Etou, Toshio Kamiya, Francesco Alesiani, and Makoto Takamoto. "Generalized Precise Orbit Prediction of LEO Satellites via Physics Informed Machine Learning." In IAF Astrodynamics Symposium, Held at the 75th International Astronautical Congress (IAC 2024), 1562–69. Paris, France: International Astronautical Federation (IAF), 2024. https://doi.org/10.52202/078368-0135.

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Rahnemoonfar, Maryam, and Benjamin Zalatan. "Physics-informed Machine Learning for Deep Ice Layer Tracing in SAR images." In IGARSS 2024 - 2024 IEEE International Geoscience and Remote Sensing Symposium, 6938–42. IEEE, 2024. http://dx.doi.org/10.1109/igarss53475.2024.10641831.

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Tai, Tsenjung, Kenta Senzaki, and Masato Toda. "Cross-Orbital SAR Change Detection With A Physics-Informed Machine Learning Approach." In IGARSS 2024 - 2024 IEEE International Geoscience and Remote Sensing Symposium, 8844–47. IEEE, 2024. http://dx.doi.org/10.1109/igarss53475.2024.10641587.

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Reports on the topic "Physics-informed Machine Learning"

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Martinez, Carianne, Jessica Jones, Drew Levin, Nathaniel Trask, and Patrick Finley. Physics-Informed Machine Learning for Epidemiological Models. Office of Scientific and Technical Information (OSTI), October 2020. http://dx.doi.org/10.2172/1706217.

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Wang, Jianxun, Jinlong Wu, Julia Ling, Gianluca Iaccarino, and Heng Xiao. Physics-Informed Machine Learning for Predictive Turbulence Modeling: Towards a Complete Framework. Office of Scientific and Technical Information (OSTI), September 2016. http://dx.doi.org/10.2172/1562229.

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Bailey Bond, Robert, Pu Ren, James Fong, Hao Sun, and Jerome F. Hajjar. Physics-informed Machine Learning Framework for Seismic Fragility Analysis of Steel Structures. Northeastern University, August 2024. http://dx.doi.org/10.17760/d20680141.

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The seismic assessment of structures is a critical step to increase community resilience under earthquake hazards. This research aims to develop a Physics-reinforced Machine Learning (PrML) paradigm for metamodeling of nonlinear structures under seismic hazards using artificial intelligence. Structural metamodeling, a reduced-fidelity surrogate model to a more complex structural model, enables more efficient performance-based design and analysis, optimizing structural designs and ease the computational effort for reliability fragility analysis, leading to globally efficient designs while maintaining required levels of accuracy. The growing availability of high-performance computing has improved this analysis by providing the ability to evaluate higher order numerical models. However, more complex models of the seismic response of various civil structures demand increasing amounts of computing power. In addition, computational cost greatly increases with numerous iterations to account for optimization and stochastic loading (e.g., Monte Carlo simulations or Incremental Dynamic Analysis). To address the large computational burden, simpler models are desired for seismic assessment with fragility analysis. Physics reinforced Machine Learning integrates physics knowledge (e.g., scientific principles, laws of physics) into the traditional machine learning architectures, offering physically bounded, interpretable models that require less data than traditional methods. This research introduces a PrML framework to develop fragility curves using the combination of neural networks of domain knowledge. The first aim involves clustering and selecting ground motions for nonlinear response analysis of archetype buildings, ensuring that selected ground motions will include as few ground motions as possible while still expressing all the key representative events the structure will probabilistically experience in its lifetime. The second aim constructs structural PrML metamodels to capture the nonlinear behavior of these buildings utilizing the nonlinear Equation of Motion (EOM). Embedding physical principles, like the general form of the EOM, into the learning process will inform the system to stay within known physical bounds, resulting in interpretable results, robust inferencing, and the capability of dealing with incomplete and scarce data. The third and final aim applies the metamodels to probabilistic seismic response prediction, fragility analysis, and seismic performance factor development. The efficiency and accuracy of this approach are evaluated against existing physics-based fragility analysis methods.

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Ullrich, Paul, Tapio Schneider, and Da Yang. Physics-Informed Machine Learning from Observations for Clouds, Convection, and Precipitation Parameterizations and Analysis. Office of Scientific and Technical Information (OSTI), April 2021. http://dx.doi.org/10.2172/1769762.

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Ghanshyam, Pilania, Kenneth James McClellan, Christopher Richard Stanek, and Blas P. Uberuaga. Physics-Informed Machine Learning for Discovery and Optimization of Materials: A Case Study of Scintillators. Office of Scientific and Technical Information (OSTI), August 2018. http://dx.doi.org/10.2172/1463529.

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Bao, Jie, Chao Wang, Zhijie Xu, and Brian J. Koeppel. Physics-Informed Machine Learning with Application to Solid Oxide Fuel Cell System Modeling and Optimization. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1569289.

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Moran, Samuel, Kyle Johnson, W. Saul, Albert To, and Basil Paudel. Compensating for Sintering Distortion in Additively Manufactured Shaped Charge Liners using Physics-Informed Machine Learning. Office of Scientific and Technical Information (OSTI), September 2023. http://dx.doi.org/10.2172/2430184.

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Perdikaris, Paris. Probabilistic data fusion and physics-informed machine learning: A new paradigm for modeling under uncertainty, and its application to accelerating the discovery of new materials. Office of Scientific and Technical Information (OSTI), April 2024. http://dx.doi.org/10.2172/2339512.

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Fan, Jiwen, Zhangshuan Hou, Paul O'Gorman, Jessika Trancik, John Allen, Peeyush Kumar, Ranveer Chandra, Jingyu Wang, and Lai-Yung Leung. Develop a weather-aware climate model to understand and predict extremes and associated power outages and renewable energy shortageswith uncertainty-aware and physics-informed machine learning. Office of Scientific and Technical Information (OSTI), April 2021. http://dx.doi.org/10.2172/1769695.

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Fan, Tiffany, Nathaniel Trask, Marta D'Elia, and Eric Darve. PhILMs: Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems. Office of Scientific and Technical Information (OSTI), February 2024. https://doi.org/10.2172/2305747.

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