Hamiltonian Graph Networks with ODE Integrators

By Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, Peter W. Battaglia. 2019

195 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence

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Citations in the corpus

Learning to Simulate Complex Physics with Graph Networks (2020, background): “, “interaction networks”, can learn to simulate rigid body, mass-spring, n-body, and robotic control systems (Battaglia et al., 2016; Chang et al., 2016; SanchezGonzalez et al., 2018; Mrowca et al., 2018; Li et al., 2019; Sanchez-Gonzalez et al., 2019), as well as non-physical systems, such as multi”
Isometric Transformation Invariant and Equivariant Graph Convolutional Networks (2020, background): “Several related studies, including those by Sanchez-Gonzalez et al. (2018; 2019); Alet et al. (2019) were focused on applying GNNs to learn physical simulations.”
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data (2020, background): “, 2016), Hamiltonian ODE graph networks (HOGN) (Sanchez-Gonzalez et al., 2019), and our own LieConv architecture on predicting the motion of point particles connected by springs as described in (Sanchez-Gonzalez et al.”
Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, methodology): “Here, we introduce the “Flattened Hamiltonian Graph Network,” or “FlatHGN”, which uses eq.”
Lagrangian Neural Networks (2020, result): “This is similar to the Hamiltonian Graph Network of Sanchez-Gonzalez et al. (2019), or more speciﬁcally, the Flattened Hamiltonian Graph Network of Cranmer et al. (2020).”
Graph neural networks in particle physics (2020, background): “Much work on GNs has focused on learning physical simulation [36–38, 43 ], similar Recently GNs have been extended by adding inductive biases derived from physics, adjusting their architectures to be consistent with Hamiltonian [44] and Lagrangian mechanics [45], which can improve performance and ge”
GRAND: Graph Neural Diffusion (2021, methodology): “Finally, Sanchez-Gonzalez et al. (2019) used graph-based ODEs to generate physics simulations.”
A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection (2023, background): “…posed by physical constraints, promising performance has been achieved thanks to the incorporation of inductive biases from known physical laws [190], [191] and architectures that maintain the symmetries of the underlying system, such as equivariance to rotations and translations [189], [192],…”
Continuous-in-Depth Neural Networks (2020, background): “Due to their popularity, there is a rich body of work that aims to explain “why” shortcut connections between layers enables the training of very deep NNs [73, 4, 29, 48, 51, 44].”