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

• URL: http://arxiv.org/abs/2111.00998v2
• Date: Thu, 4 Nov 2021 15:16:22 GMT
• Title: PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning
• Authors: Robert Stephany, Christopher Earls
• Abstract summary: We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a principled sparse regression algorithm. We successfully identify the Heat, Burgers, and Korteweg-De Vries equations with remarkable consistency. Our approach is unprecedentedly robust to both sparsity and noise and is, therefore, applicable to real-world observational data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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