Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control

Abstract

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.

Published as a Conference Paper at ICLR 2020

Cited by in corpus (44)

• A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic
• Deep learning of thermodynamics-aware reduced-order models from data
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics
• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
• Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems
• OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
• Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning
• LieTransformer: Equivariant self-attention for Lie Groups
• Differentiable Molecular Simulations for Control and Learning
• Symplectic Learning for Hamiltonian Neural Networks
• Forecasting Sequential Data using Consistent Koopman Autoencoders
• Neural Canonical Transformation with Symplectic Flows
• Symplectic integration of learned Hamiltonian systems
• Learning Neural Event Functions for Ordinary Differential Equations
• Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
• Linearly Constrained Neural Networks
• LagNetViP: A Lagrangian Neural Network for Video Prediction
• Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
• Locally-symplectic neural networks for learning volume-preserving dynamics
• MALI: A memory efficient and reverse accurate integrator for Neural ODEs
• Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework
• Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling
• Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators
• Learning Potentials of Quantum Systems using Deep Neural Networks
• Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models
• Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control
• Continuous-Time Model-Based Reinforcement Learning
• Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features
• SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
• Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data
• "Hey, that's not an ODE": Faster ODE Adjoints via Seminorms
• Nested Mixture of Experts: Cooperative and Competitive Learning of Hybrid Dynamical System
• A Differential Game Theoretic Neural Optimizer for Training Residual Networks
• Time-Reversal Symmetric ODE Network
• Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control
• Reversible and irreversible bracket-based dynamics for deep graph neural networks
• Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational $N$-body Problem
• SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision
• Enhancing Human-Machine Teaming for Medical Prognosis Through Neural Ordinary Differential Equations (NODEs)
• Nonseparable Symplectic Neural Networks
• Towards Conditional Generation of Minimal Action Potential Pathways for Molecular Dynamics
• NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
• Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features
• No Need for Interactions: Robust Model-Based Imitation Learning using Neural ODE