PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning

11/01/2021
by   Robert Stephany, et al.
98

PDE discovery shows promise for uncovering predictive models for complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a principled sparse regression algorithm to identify the hidden dynamics that govern a system's response. The first network learns the system response function, while the second learns a hidden PDE which drives the system's evolution. We then use a parameter-free sparse regression algorithm to extract a human-readable form of the hidden PDE from the second network. We implement our approach in an open-source library called PDE-READ. Our approach successfully identifies the Heat, Burgers, and Korteweg-De Vries equations with remarkable consistency. We demonstrate that our approach is unprecedentedly robust to both sparsity and noise and is, therefore, applicable to real-world observational data.

READ FULL TEXT

page 12

page 14

page 16

page 17

page 18

page 19

page 21

page 30

research
12/09/2022

PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Data

In this paper, we introduce PDE-LEARN, a novel PDE discovery algorithm t...
research
12/09/2022

A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data

Given ample experimental data from a system governed by differential equ...
research
08/05/2021

Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data

Scientific machine learning has been successfully applied to inverse pro...
research
06/26/2022

Noise-aware Physics-informed Machine Learning for Robust PDE Discovery

This work is concerned with discovering the governing partial differenti...
research
06/09/2021

Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

Partial differential equations (PDEs) are concise and understandable rep...
research
07/17/2019

Stability selection enables robust learning of partial differential equations from limited noisy data

We present a statistical learning framework for robust identification of...
research
06/11/2020

Robust PDE Identification from Noisy Data

We propose robust methods to identify underlying Partial Differential Eq...

Please sign up or login with your details

Forgot password? Click here to reset