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Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints
Marc Finzi · Ke Alexander Wang · Andrew Wilson

Thu Dec 10 07:00 AM -- 07:10 AM (PST) @ Orals & Spotlights: Deep Learning
in Orals & Spotlights Track 28: Deep Learning »
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian of a system rather than the differential equations directly. While these methods encode the constraints of the systems using generalized coordinates, we show that embedding the system into Cartesian coordinates and enforcing the constraints explicitly with Lagrange multipliers dramatically simplifies the learning problem. We introduce a series of challenging chaotic and extended-body systems, including systems with $N$-pendulums, spring coupling, magnetic fields, rigid rotors, and gyroscopes, to push the limits of current approaches. Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency.

Author Information

Marc Finzi (New York University)
Ke Alexander Wang (Stanford University)
Andrew Wilson (New York University)
Andrew Wilson

I am a professor of machine learning at New York University.

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