B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
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TLDR
Compared with PINNs, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting and dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty.About:
This article is published in Journal of Computational Physics.The article was published on 2021-01-15 and is currently open access. It has received 410 citations till now. The article focuses on the topics: Uncertainty quantification & Dropout (neural networks).read more
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Journal ArticleDOI
Physics-informed machine learning
TL;DR: Some of the prevailing trends in embedding physics into machine learning are reviewed, some of the current capabilities and limitations are presented and diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems are discussed.
Posted Content
When and why PINNs fail to train: A neural tangent kernel perspective
TL;DR: A novel gradient descent algorithm is proposed that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error and a series of numerical experiments are performed to verify the correctness of the theory and the practical effectiveness of the proposed algorithms.
Journal ArticleDOI
Physics-Informed Neural Networks for Heat Transfer Problems
TL;DR: In this paper, physics-informed neural networks (PINNs) have been applied to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods.
Journal ArticleDOI
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
TL;DR: A general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials is formulated.
Posted Content
Integrating Physics-Based Modeling with Machine Learning: A Survey
TL;DR: An overview of techniques to integrate machine learning with physics-based modeling and classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint is provided.
References
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Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
TL;DR: This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Dropout as a Bayesian approximation: representing model uncertainty in deep learning
Yarin Gal,Zoubin Ghahramani +1 more
TL;DR: A new theoretical framework is developed casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes, which mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy.