Learning To Solve Differential Equation Constrained Optimization Problems

TL;DR

This paper presents a learning-based method combining neural differential equations and proxy optimization to efficiently solve differential equation constrained optimization problems with high accuracy and real-time capabilities.

Contribution

It introduces a dual-network architecture that approximates control strategies and solves DEs simultaneously, improving efficiency and accuracy over existing methods.

Findings

Achieves up to 25 times more precise results than traditional methods.

Ensures full compliance with dynamic constraints in energy and finance problems.

Operates in near real-time for complex DE-constrained optimization tasks.

Abstract

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control strategies must be determined for systems governed by ordinary or stochastic differential equations. Despite its significance, the computational challenges associated with these problems have limited their practical use. To address these limitations, this paper introduces a learning-based approach to DE-constrained optimization that combines techniques from proxy optimization and neural differential equations. The proposed approach uses a dual-network architecture, with one approximating the control strategies, focusing on steady-state constraints, and another solving the associated DEs. This combination enables the approximation of optimal strategies while accounting for dynamic constraints in near real-time. Experiments across problems in energy optimization and finance modeling show that this method provides full compliance with dynamic constraints and it produces results up to 25 times more precise than other methods which do not explicitly model the system's dynamic equations.