用神经网络联合求解微分方程约束的优化问题，提速且更准。
Learning To Solve Differential Equation Constrained Optimization Problems
- 双网络架构：一网学控制策略，一网解微分方程。
- 动态约束完全满足，精度比不建模方程的方法高25倍。
- 适合能源、金融等需精确动态建模的优化场景。
微分方程（DE）约束优化在能源系统、航空航天、生态学和金融等领域至关重要，需为受常微分或随机微分方程支配的系统寻找最优配置或控制策略。尽管意义重大，其计算复杂性限制了实际应用。本文提出一种基于学习的DE约束优化方法，融合代理优化与神经微分方程技术。采用双网络架构：一个网络近似控制策略并关注稳态约束，另一个网络求解相关微分方程。该组合可在近实时条件下逼近最优策略，并同时满足动态约束。在能源优化与金融建模问题上的实验表明，该方法能完全遵守动态约束，结果精度最高可达未显式建模系统动态方程方法的25倍。
原文摘要 · Abstract (English)
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.
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