Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems
This addresses the challenge of discovering physical laws from limited data for researchers in physics and machine learning, representing a novel method rather than an incremental improvement.
The paper tackles the problem of learning physical governing equations from noisy and small datasets by introducing Symplectically Integrated Symbolic Regression (SISR), which uses deep symbolic regression with symplectic neural networks and a fourth-order symplectic integration scheme, successfully extracting correct equations for systems like oscillators, pendulums, and gravitational bodies.
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.