Knowledge-Based Learning of Nonlinear Dynamics and Chaos
- URL: http://arxiv.org/abs/2010.03415v4
- Date: Thu, 2 Dec 2021 15:52:24 GMT
- Title: Knowledge-Based Learning of Nonlinear Dynamics and Chaos
- Authors: Tom Z. Jiahao, M. Ani Hsieh, Eric Forgoston
- Abstract summary: We present a universal learning framework for extracting predictive models from nonlinear systems based on observations.
Our framework can readily incorporate first principle knowledge because it naturally models nonlinear systems as continuous-time systems.
- Score: 3.673994921516517
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Extracting predictive models from nonlinear systems is a central task in
scientific machine learning. One key problem is the reconciliation between
modern data-driven approaches and first principles. Despite rapid advances in
machine learning techniques, embedding domain knowledge into data-driven models
remains a challenge. In this work, we present a universal learning framework
for extracting predictive models from nonlinear systems based on observations.
Our framework can readily incorporate first principle knowledge because it
naturally models nonlinear systems as continuous-time systems. This both
improves the extracted models' extrapolation power and reduces the amount of
data needed for training. In addition, our framework has the advantages of
robustness to observational noise and applicability to irregularly sampled
data. We demonstrate the effectiveness of our scheme by learning predictive
models for a wide variety of systems including a stiff Van der Pol oscillator,
the Lorenz system, and the Kuramoto-Sivashinsky equation. For the Lorenz
system, different types of domain knowledge are incorporated to demonstrate the
strength of knowledge embedding in data-driven system identification.
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