Incorporating Additive Separability into Hamiltonian Neural Networks for Regression and Interpretation

Hamiltonian neural networks are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton’s equations. A recent observation is that incorporating a second-order bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose three separable Hamiltonian neural networks that incorporate additive separability within Hamiltonian neural networks using observational, learning and inductive biases. We show that the proposed models are more effective than a Hamiltonian neural network at regressing a vector field, and have the capability to interpret the kinetic and potential energy of the system.