Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit\n Constraints

Abstract

Reasoning about the physical world requires models that are endowed with the\nright inductive biases to learn the underlying dynamics. Recent works improve\ngeneralization for predicting trajectories by learning the Hamiltonian or\nLagrangian of a system rather than the differential equations directly. While\nthese methods encode the constraints of the systems using generalized\ncoordinates, we show that embedding the system into Cartesian coordinates and\nenforcing the constraints explicitly with Lagrange multipliers dramatically\nsimplifies the learning problem. We introduce a series of challenging chaotic\nand extended-body systems, including systems with N-pendulums, spring coupling,\nmagnetic fields, rigid rotors, and gyroscopes, to push the limits of current\napproaches. Our experiments show that Cartesian coordinates with explicit\nconstraints lead to a 100x improvement in accuracy and data efficiency.\n