Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of partial differential equations. Depending on whether the available data is scattered in space-time or arranged in fixed temporal snapshots, we introduce two main classes of algorithms, namely continuous time and discrete time models. The effectiveness of our approach is demonstrated using a wide range of benchmark problems in mathematical physics, including conservation laws, incompressible fluid flow, and the propagation of nonlinear shallow-water waves.
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UNVERDICTED 8roles
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A novel teacher-student ensemble of physics-informed deep learning models improves traffic state estimation under varying speed limit conditions by using a classifier to select appropriate physics-constrained models.
A generative solver separates data-driven prior learning from inference-time enforcement of conservation laws using martingale-regularized score matching and physics-informed sampling for stable field reconstruction.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
A physics-informed neural network method is developed to approximate controls for nonlinear PDEs, including convergence analysis and numerical experiments demonstrating good performance.
PINNs are applied in a proof-of-concept to mitigate attacks on liquid pump controllers in water distribution networks by incorporating physical flow laws into network training.
A physics-informed neural network merges sparse LBM data with Navier-Stokes equations to predict unsteady flows in fractal-rough microchannels at 150-200 times lower data cost.
A comprehensive review of deep learning techniques for computational mechanics, including LSTM for constitutive modeling, PINNs for PDE solving, optimizers, and kernel methods.
citing papers explorer
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Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
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Physics-Informed Teacher-Student Ensemble Learning for Traffic State Estimation with a Varying Speed Limit Scenario
A novel teacher-student ensemble of physics-informed deep learning models improves traffic state estimation under varying speed limit conditions by using a classifier to select appropriate physics-constrained models.
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Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
A generative solver separates data-driven prior learning from inference-time enforcement of conservation laws using martingale-regularized score matching and physics-informed sampling for stable field reconstruction.
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Bayesian Reasoning for Physics Informed Neural Networks
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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Computational Control of Nonlinear Partial Differential Equations Using Machine Learning
A physics-informed neural network method is developed to approximate controls for nonlinear PDEs, including convergence analysis and numerical experiments demonstrating good performance.
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Physics-Informed Neural Networks for Securing Water Distribution Systems
PINNs are applied in a proof-of-concept to mitigate attacks on liquid pump controllers in water distribution networks by incorporating physical flow laws into network training.
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Amalgamation of Physics-Informed Neural Network and LBM for the Prediction of Unsteady Fluid Flows in Fractal-Rough Microchannels
A physics-informed neural network merges sparse LBM data with Navier-Stokes equations to predict unsteady flows in fractal-rough microchannels at 150-200 times lower data cost.
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Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics
A comprehensive review of deep learning techniques for computational mechanics, including LSTM for constitutive modeling, PINNs for PDE solving, optimizers, and kernel methods.