Dirac interconnected neural networks find modular physical systems without simplification
Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction
Machine Learning
Summary
Real-world physical systems are made of connected parts, but it’s hard for computers to learn their behavior if they assume the system is simplified or if the connections are known ahead of time. The authors created a neural network approach called DINEs that learns both the parts and how they connect directly from data, without simplifying the system. This lets them study and combine parts separately or together, even if some parts are not fully visible. Their tests show this works on complex physical systems where older methods struggle.
What this means in practice
- •For robotics engineers: Model complex robots as sets of interconnected components without simplifying their physical constraints, enabling better modular design and control.
- •For energy system modelers: Create modular models of physical energy networks that maintain algebraic constraints, improving analysis of interdependent components without full system reduction.
Authors
Reiho Li, Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura, Takashi Matsubara
Abstract
Deep learning has shown remarkable success in the data-driven modeling of dynamical systems. Much of its success is attributed not to the flexibility of neural networks but to inductive biases based on physical prior knowledge, such as energy conservation and symplecticity. However, existing methods do not fully exploit the fact that real-world physical systems are interconnections of components. Some methods require the interconnection to be known a priori, while others assume the system to be reducible to an ordinary differential equation (ODE) and learn only the reduced ODE, discarding the algebraic constraints imposed by the interconnection. Here, we propose Dirac-interconnected neural elements (DINEs), a neural network model that represents a physical system as a differential-algebraic equation (DAE), whose algebraic constraints are given by a Dirac structure in kernel representation. With DINEs, we simultaneously identify from data the interconnection among the components as a Dirac structure and learn the characteristics of the components as neural networks. This allows us to keep the learned subsystems in unreduced form and isolate or compose them to make a new system without retraining. Moreover, DINEs can handle partially observable systems. Experimental results demonstrate these capabilities on physical systems beyond the reach of existing methods.