Physics-Informed Neural ODE for Non-Euclidean Dynamics
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Solution Overview
Problem
Current machine learning approaches for learning dynamics in complex electro-mechanical systems require access to higher-order derivatives and make restrictive assumptions about energy conservation, making them impractical for real-world applications, and lack integration of physics-based priors in control policy design.
Innovation Solution
A physics-informed machine learning system using neural ODE solvers that learns structured dynamics with embedded non-Euclidean coordinates, incorporating a feeder neural network to estimate ODEs from time series data and a neural ODE solver to synthesize controllers, enabling efficient learning and control of systems with translational and rotational motions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If physics-based machine learning approaches (Lagrangian/Hamiltonian mechanics) are used to learn dynamics, then model accuracy and energy conservation are improved, but the requirement for higher-order derivatives and restrictive assumptions make the system impractical for real-world applications
Solution Approach 1:
The patent extracts and removes the problematic higher-order derivative requirements from the physics-based learning framework. By formulating the learning objective to depend only on first-order derivatives and using neural network approximations that avoid higher-order computations, the method retains the accuracy benefits of physics-based approaches while eliminating the practical implementation barriers.
Solution Approach 2:
The patent changes the parameterization approach by introducing latent space representations and neural network approximators that transform the dynamics learning problem. Instead of directly computing higher-order derivatives of physical quantities, the method learns latent dynamics models that inherently capture the system behavior without requiring explicit higher-order derivative computations.
2Adaptability or versatility
If neural networks are used to identify control policies without physics-based priors, then flexibility in control design is improved, but the lack of physics integration reduces control effectiveness and safety assurances
Solution Approach 1:
The patent merges neural network flexibility with physics-based reliability by integrating both approaches into a unified framework. The method combines neural network policy optimization with physics-informed dynamics models, allowing the system to leverage the adaptability of data-driven methods while maintaining the safety and effectiveness guarantees of physics-based control through embedded physical constraints and energy conservation principles.
Data Source
AI summary
System and method for synthesizing a controller for a dynamical system includes a feeder neural network trained to estimate an ordinary differential equation (ODE) from time series training data (X) of a trajectory having embedded angular data and configured to learn dynamics of a physical system by encoding a generalization of a Hamiltonian representation of the dynamics using a constant external control term (u). A neural ODE solver receives the estimate of the ODE from the feeder neural network and synthesizes a controller to control the system to track a reference configuration.