学习用于相互作用活性粒子控制的连续介质级闭合关系
Learning Continuum-level Closures For Control of Interacting Active Particles
AI总结：
针对活性物质群难以操控的问题，提出基于通用微分方程的学习框架，从智能体模拟中学习连续介质闭合关系，嵌入模型预测控制实现对活性粒子动力学的精准调控。
摘要：
活性物质群——即能够自组装、运送微观货物或赋予材料动态特性的自驱动粒子集合体——仍然难以操控。在拥挤系统中，追踪或控制单个智能体极具挑战，因此控制策略需作用于粒子密度等宏观场。然而，由于智能体间的相互作用，预测密度的演化过程十分困难。对于基于模型的反馈控制方法（如模型预测控制MPC）而言，快速、准确且可微的模型至关重要。精细的基于智能体的模拟速度过慢，因此需要粗粒度的连续介质模型。但构建准确的闭合关系——即表达未解析微观状态（如智能体位置）对连续介质动力学影响的近似关系——对活性物质群来说是一大难题。我们提出了一种面向控制的学习框架，可从智能体模拟中学习连续介质闭合关系，并以可控外场作用下的活性布朗粒子为例进行了验证。我们的通用微分方程（UDE）框架将连续介质表示为平流-扩散方程。神经算子学习平流项，为自驱动、相互作用和外场响应等微观效应提供闭合关系。这种UDE方法将通用函数逼近器嵌入微分方程，在直接从数据中学习复杂动力学的同时，确保符合物理定律（如守恒律）。我们将该学习得到的连续介质模型嵌入MPC，以实现对智能体模拟的精准控制。我们通过动态交换两组粒子的密度，以及同时控制粒子密度和平均通量使其遵循指定的正弦分布，验证了该框架的性能。这些结果凸显了该框架在控制复杂活性物质动力学方面的潜力。
英文摘要：
Active matter swarms -- collectives of self-propelled particles that could self-assemble, ferry microscopic cargo, or endow materials with dynamic properties -- remain hard to steer. In crowded systems, tracking or controlling individual agents becomes challenging, so strategies should operate on macroscopic fields like particle density. Yet predicting how density evolves is difficult due to inter-agent interactions. For model-based feedback control methods -- like Model Predictive Control (MPC) -- fast, accurate, and differentiable models are crucial. Detailed agent-based simulations are too slow, necessitating coarse-grained continuum models. However, constructing accurate closures -- approximations expressing the effect of unresolved microscopic states (e.g., agent positions) on continuum dynamics -- is challenging for active matter swarms. We present a learning-for-control framework that learns continuum closures from agent simulations, demonstrated with active Brownian particles under a controllable external field. Our Universal Differential Equation (UDE) framework represents the continuum as an advection-diffusion equation. A neural operator learns the advection term, providing closure relations for microscopic effects like self-propulsion, interactions, and external field responses. This UDE approach, embedding universal function approximators in differential equations, ensures adherence to physical laws (e.g., conservation) while learning complex dynamics directly from data. We embed this learned continuum model into MPC for precise agent simulation control. We demonstrate this framework's capabilities by dynamically exchanging particle densities between two groups, and simultaneously controlling particle density and mean flux to follow a prescribed sinusoidal profile. These results highlight the framework's potential to control complex active matter dynamics.
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