Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems

Understand

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.