SymFlux: deep symbolic regression of Hamiltonian vector fields
This work addresses the problem of automated symbolic regression in Hamiltonian mechanics for researchers in physics and machine learning, but it appears incremental as it builds on existing deep learning methods with a new dataset.
The authors tackled the problem of identifying Hamiltonian functions from vector fields using a deep learning framework called SymFlux, which achieved accurate symbolic expression recovery, advancing automated discovery in Hamiltonian mechanics.
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.