Automatic Decoupling and Index-aware Model-Order Reduction for Nonlinear Differential-Algebraic Equations

TL;DR

This paper introduces an index-aware model-order reduction method for nonlinear differential-algebraic equations, enabling efficient simulation of complex systems like gas pipeline networks without linearization.

Contribution

It extends index-aware reduction techniques to nonlinear DAE systems, allowing automatic decoupling and application of standard reduction methods without linearization.

Findings

Effective reduction of gas flow models in pipelines.

Maintains accuracy while reducing computational cost.

Compatible with standard numerical integration schemes.

Abstract

We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for example, in the spatial discretization of the gas flow in pipeline networks. In practice, mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and system size. Model-order reduction aims to eliminate this problem by generating reduced-order models that have lower computational cost to simulate, yet accurately represent the original large-scale system behavior. However, direct reduction and simulation of nonlinear differential-algebraic equations is difficult due to hidden constraints which affect the choice of numerical integration methods and model-order reduction techniques. We propose an extension of index-aware model-order reduction methods to nonlinear differential-algebraic equations without any kind of linearization. The proposed model-order reduction approach involves automatic decoupling of nonlinear differential-algebraic equations into nonlinear ordinary differential equations and algebraic equations. This allows applying standard model-order reduction techniques to both parts without worrying about the index. The same procedure can also be used to simulate nonlinear differential-algebraic equations using standard integration schemes. We illustrate the performance of our proposed method for nonlinear differential-algebraic equations arising from gas flow models in pipeline networks.