Constrained Neural Ordinary Differential Equations with Stability Guarantees

TL;DR

This paper introduces a method for modeling neural ODEs with stability guarantees using implicit eigenvalue constraints and barrier methods, enhancing safety and performance in engineering applications.

Contribution

It presents a novel approach to incorporate stability and inequality constraints into neural ODEs, improving their reliability for engineering modeling and control.

Findings

Stable neural ODE layers derived from eigenvalue constraints

Barrier methods effectively handle inequality constraints

High prediction accuracy on open-loop simulations

Abstract

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches require domain expertise and are often difficult to tune or adapt to new systems. In this paper, we show how to model discrete ordinary differential equations (ODE) with algebraic nonlinearities as deep neural networks with varying degrees of prior knowledge. We derive the stability guarantees of the network layers based on the implicit constraints imposed on the weight's eigenvalues. Moreover, we show how to use barrier methods to generically handle additional inequality constraints. We demonstrate the prediction accuracy of learned neural ODEs evaluated on open-loop simulations compared to ground truth dynamics with bi-linear terms.