Abstract
AbstractIdentifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems.
Funder
National Science Foundation
United States Department of Defense | United States Army | U.S. Army Research, Development and Engineering Command | Army Research Office
United States Department of Defense | Defense Advanced Research Projects Agency
United States Department of Defense | United States Air Force | AFMC | Air Force Research Laboratory
United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research
U.S. Department of Defense, National Defense Science & Engineering Graduate Fellowship
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy
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