论文标题
部分可观测时空混沌系统的无模型预测
Optimization-Informed Neural Networks
论文作者
论文摘要
解决受限的非线性优化问题（CNLP）是一个长期存在的问题，例如在各个领域，例如经济学，计算机科学和工程。我们提出了优化信息的神经网络（OINN），这是一种解决CNLP的深度学习方法。通过神经动力学优化方法，首先将CNLP重新构成涉及普通微分方程（ODE）系统的初始值问题（IVP）。然后将神经网络模型用作该IVP的近似解决方案，终点是对CNLP的预测。我们提出了一种新颖的培训算法，该算法指示该模型在培训期间保持最佳预测。简而言之，Oinn将CNLP转变为神经网络训练问题。通过这样做，我们只能基于深度学习基础架构解决CNLP，而无需使用标准优化求解器或数值集成求解器。通过经典问题的集合，例如变异不平等，非线性互补问题和标准CNLP来证明所提出的方法的有效性。
Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep learning approach to solve CNLPs. By neurodynamic optimization methods, a CNLP is first reformulated as an initial value problem (IVP) involving an ordinary differential equation (ODE) system. A neural network model is then used as an approximate solution for this IVP, with the endpoint being the prediction to the CNLP. We propose a novel training algorithm that directs the model to hold the best prediction during training. In a nutshell, OINN transforms a CNLP into a neural network training problem. By doing so, we can solve CNLPs based on deep learning infrastructure only, without using standard optimization solvers or numerical integration solvers. The effectiveness of the proposed approach is demonstrated through a collection of classical problems, e.g., variational inequalities, nonlinear complementary problems, and standard CNLPs.
