用神经网络控制复杂系统，实现精准动态调控
Control of dynamical systems with neural networks
- 用神经网络参数化控制输入，适配连续与离散系统
- 结合自动微分优化控制策略，解决难解的动态调控问题
- 适用于生物、工程、医学等多领域复杂系统控制
控制问题广泛存在于科学与工业应用中，目标是将动态系统从初始状态引导至期望的目标状态。深度学习与自动微分的进展使这些方法在控制任务中日益实用。本文探讨使用神经网络及现代机器学习库对离散时间与连续时间系统、确定性与随机动力学中的控制输入进行参数化。对于连续时间系统，神经微分方程（neural ODEs）提供了一种有效的控制输入建模方式；对于离散时间系统，我们展示了如何利用自动微分实现自定义控制输入参数化并进行优化。所提方法为计算密集或解析不可解的控制任务提供了实用解决方案，适用于生物、工程、物理和医学等多个领域的真实复杂场景。
原文摘要 · Abstract (English)
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation have made applying these methods to control problems increasingly practical. In this paper, we examine the use of neural networks and modern machine-learning libraries to parameterize control inputs across discrete-time and continuous-time systems, as well as deterministic and stochastic dynamics. We highlight applications in multiple domains, including biology, engineering, physics, and medicine. For continuous-time dynamical systems, neural ordinary differential equations (neural ODEs) offer a useful approach to parameterizing control inputs. For discrete-time systems, we show how custom control-input parameterizations can be implemented and optimized using automatic-differentiation methods. Overall, the methods presented provide practical solutions for control tasks that are computationally demanding or analytically intractable, making them valuable for complex real-world applications.
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