[Paper Review] Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning

Yaofeng Desmond Zhong, Biswadip Dey+1 more|arXiv (Cornell University)|Feb 20, 2020

Model Reduction and Neural Networks21 references33 citations

TL;DR

Dissipative SymODEN extends SymODEN by incorporating energy dissipation and external inputs through port-Hamiltonian dynamics, enabling physics-informed learning of non-conservative systems with improved accuracy and interpretability.

ABSTRACT

In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.

Motivation & Objective

• Motivate learning accurate dynamics of physical systems with dissipation from observed trajectories.
• Incorporate energy dissipation and external inputs into a Hamiltonian-based learning framework.
• Provide a structured neural network architecture that reveals inertia, dissipation, and potential energy.

Proposed method

• Use port-Hamiltonian dynamics with a dissipation term to model non-conservative systems.
• Represent inverse mass matrix, potential energy, input matrix, and dissipation matrix with neural nets.
• Define Hamiltonian H as (1/2)p^T M^{-1}(q) p + V(q) and compute dynamics via structured RHS as in (5) and (6).
• Handle embedded angle data with an angle-aware formulation that uses (cos q, sin q, qdot, u) as state representation.
• Enforce positive semi-definiteness of D and positive definiteness of M^{-1} via Cholesky-factor parameterizations.
• Train with Neural ODE using differentiable solvers and use a constant input u during training to learn the RHS.

Experimental results

Research questions

• RQ1 Can dissipation-aware, Hamiltonian-based priors improve prediction accuracy for systems with energy losses?
• RQ2 How does an explicit dissipation term affect generalization and data efficiency in learning dynamics?
• RQ3 What physical insights (inertia, potential energy, dissipation) can be extracted from the learned model to support energy-based control?
• RQ4 How does angle data embedding impact learning quality for rotational systems?

Key findings

• Dissipative SymODEN achieves higher accuracy with fewer parameters than baseline variants across tasks.
• Including dissipation improves prediction and generalization over the original SymODEN which lacks dissipation.
• Angle-aware embedding yields better learning of the dissipation term and aligns learned dynamics with ground truth.
• Unstructured Dissipative SymODEN underperforms compared to the structured Dissipative SymODEN due to weaker inductive biases.
• The learned components (e.g., M^{-1}, V, g, D) provide interpretable physical insights relevant to energy-based control methods.