SymFlux: deep symbolic regression of Hamiltonian vector fields

TL;DR

SymFlux is a deep learning framework that uses hybrid CNN-LSTM models to perform symbolic regression, accurately recovering Hamiltonian functions from vector fields, thereby advancing automated discovery in Hamiltonian mechanics.

Contribution

The paper introduces SymFlux, a novel hybrid CNN-LSTM architecture for symbolic regression of Hamiltonian functions from vector fields, with new datasets for training and validation.

Findings

Successfully recovers symbolic Hamiltonian expressions

Demonstrates high accuracy on newly developed datasets

Advances automated discovery in Hamiltonian mechanics

Abstract

We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM architectures to learn and output the symbolic mathematical expression of the underlying Hamiltonian. Training and validation are conducted on newly developed datasets of Hamiltonian vector fields, a key contribution of this work. Our results demonstrate the model's effectiveness in accurately recovering these symbolic expressions, advancing automated discovery in Hamiltonian mechanics.