Paper Info
Title
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations.
Abstract
We put forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time. Specifically, we approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks. The first network acts as a prior on the unknown solution and essentially enables us to avoid numerical differentiations which are inherently ill-conditioned and unstable. The second network represents the nonlinear dynamics and helps us distill the mechanisms that govern the evolution of a given spatiotemporal data-set. We test the effectiveness of our approach for several benchmark problems spanning a number of scientific domains and demonstrate how the proposed framework can help us accurately learn the underlying dynamics and forecast future states of the system. In particular, we study the Burgers', Korteweg-de Vries (KdV), Kuramoto-Sivashinsky, nonlinear Schrodinger, and Navier-Stokes equations.
Year
Venue
Keywords
2018
JOURNAL OF MACHINE LEARNING RESEARCH
Systems Identification,Data-driven Scientific Discovery,Physics Informed Machine Learning,Predictive Modeling,Nonlinear Dynamics,Big Data
DocType
Volume
Issue
Journal
19
1
ISSN
Citations 
PageRank 
1532-4435
16
0.71
References 
Authors
13
1
Name
Order
Citations
PageRank
Maziar Raissi117111.29