Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
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Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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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Universal Differential Equations for Scientific Machine Learning
Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
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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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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.