Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control

By Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty. 2019

341 citations recorded by the source corpus.

In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistical and Nonlinear Physics

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Citations in the corpus

Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “The Hamiltonian operator in physics is the primary tool for modeling the time evolution of systems with conserved quantities, but until recently the formalism had not been integrated with NNs. Greydanus et al. [112] design a NN architecture that naturally learns and respects energy conservation and ”
Continuous-in-Depth Neural Networks (2020, background): “In recent literature, so-called Neural ODEs have attracted attention in both the ML and the physical sciences communities [11, 66, 16, 87, 85, 20].”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “A recent direction also relating to conserved or invariant quantities is the incorporation of the Hamiltonian operator into NNs [54, 98, 249, 299].”
Universal Differential Equations for Scientific Machine Learning (2020, methodology): “The data efficiency of PINNs has been shown to further improve when encoding structural assumptions like energy conservation by directly modeling the Hamiltonian [14, 15].”