
Physics Informed Deep Learning (Part I): Datadriven Solutions of Nonlinear Partial Differential Equations
We introduce physics informed neural networks  neural networks that ar...
11/28/2017 ∙ by Maziar Raissi, et al. ∙ 0 ∙ shareread it

Deeplearning PDEs with unlabeled data and hardwiring physics laws
Providing fast and accurate solutions to partial differential equations ...
04/13/2019 ∙ by S. Mohammad H. Hashemi, et al. ∙ 0 ∙ shareread it

Stability selection enables robust learning of partial differential equations from limited noisy data
We present a statistical learning framework for robust identification of...
07/17/2019 ∙ by Suryanarayana Maddu, et al. ∙ 0 ∙ shareread it

Discovery of Physics from Data: Universal Laws and Discrepancy Models
Machine learning (ML) and artificial intelligence (AI) algorithms are no...
06/19/2019 ∙ by Brian de Silva, et al. ∙ 4 ∙ shareread it

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling TimeDependent Data
We propose a neural network based approach for extracting models from dy...
08/08/2019 ∙ by Yifan Sun, et al. ∙ 29 ∙ shareread it

Learning in Modal Space: Solving TimeDependent Stochastic PDEs Using PhysicsInformed Neural Networks
One of the open problems in scientific computing is the longtime integr...
05/03/2019 ∙ by Dongkun Zhang, et al. ∙ 6 ∙ shareread it

Datadriven discovery of PDEs in complex datasets
Many processes in science and engineering can be described by partial di...
08/31/2018 ∙ by Jens Berg, et al. ∙ 12 ∙ shareread it
Physics Informed Deep Learning (Part II): Datadriven Discovery of Nonlinear Partial Differential Equations
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 twopart treatise, we focus on the problem of datadriven discovery of partial differential equations. Depending on whether the available data is scattered in spacetime 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 shallowwater waves.
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