Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems

• URL: http://arxiv.org/abs/2209.01521v1
• Date: Sun, 4 Sep 2022 03:17:40 GMT
• Title: Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems
• Authors: Daniel M. DiPietro, Bo Zhu
• Abstract summary: Symplectically Integrated Symbolic Regression (SISR) is a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to probabilistically sample Hamiltonian symbolic expressions.
• Score: 11.39873640706974
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integration scheme; prediction performance is used to train the LSTM-RNN to generate increasingly better functions via a risk-seeking policy gradients approach. Employing these techniques, we extract correct governing equations from oscillator, pendulum, two-body, and three-body gravitational systems with noisy and extremely small datasets.

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