用双网络架构解带参数微分代数方程的多任务优化问题
Double Coupling Architecture and Training Method for Optimization Problems of Differential Algebraic Equations with Parameters
- 构建双神经网络解耦约束与目标函数
- 引入松弛变量保证解等价性，理论可证明
- 遗传算法提升训练效率，支持实时响应需求
仿真建模在产品开发中至关重要，常以复杂的非线性微分代数方程表示。日益多样化的功能需求推动多任务优化成为核心挑战。本文提出一种双物理信息神经网络架构，用于解耦参数化微分代数方程优化中的约束与目标函数。理论分析表明，引入具有全局误差界的新松弛变量，可确保网络解与原优化问题解等价。结合遗传算法增强的训练框架，显著提升物理信息神经网络的训练精度与效率，避免重复求解微分代数方程。该方法支持单次训练实现多任务目标泛化，保持对产品需求的实时响应能力。
原文摘要 · Abstract (English)
Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The growing diversity of product requirements demands multi-task optimization, a key challenge in simulation modeling research. A dual physics-informed neural network architecture has been proposed to decouple constraints and objective functions in parametric differential algebraic equation optimization problems. Theoretical analysis shows that introducing a relaxation variable with a global error bound ensures solution equivalence between the network and optimization problem. A genetic algorithm-enhanced training framework for physics-informed neural networks improves training precision and efficiency, avoiding redundant solving of differential algebraic equations. This approach enables generalization for multi-task objectives with a single, training maintaining real-time responsiveness to product requirements.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。