2019

Hamiltonian Graph Networks with ODE Integrators

Sanchez-Gonzalez, Alvaro, Bapst, Victor, Cranmer, Kyle et al.

Understand

We introduce an approach for imposing physically informed inductive biases in learned simulation models.

  • We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states, and a Hamiltonian as an internal representation.
  • We find that our approach outperforms baselines without these biases in terms of predictive accuracy, energy accuracy, and zero-shot generalization to time-step sizes and integrator orders not experienced during training.
  • This advances the state-of-the-art of learned simulation, and in principle is applicable beyond physical domains.

Built on

  • Hamiltonian neural networks

    Original

    Sam Greydanus, Misko Dzamba, and Jason Yosinski · 1906

    Earlier work this paper cites.

  • Latent odes for irregularly-sampled time series

    Original

    Yulia Rubanova, Ricky T. Q. Chen, and David Duvenaud · 1907

    Earlier work this paper cites.

  • A symplectic integration algorithm for separable hamiltonian functions

    J Candy and W Rozmus · 1991

    Earlier work this paper cites.

  • Computational Science Stack Exchange, 2015

    Test of 3rd-order vs 4th-order symplectic integrator with strange result · 2015

    Earlier work this paper cites.

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