Collaborative Research: Learning and Distributional Feedback Control for Fabrication of Advanced Materials

这笔赠款将支持促进科学知识的研究，以及能够制造先进材料的算法的设计。这反过来将催化可扩展和经济上可行的精密制造，为技术进步和国家繁荣做出贡献。具有所需质量的可扩展和高成本效益的先进材料的制造越来越依赖于在分子尺度上预测和控制过程的能力。这种分子过程的例子包括对制造具有高达亚纳米精度的独特光学、电学和机械性能的材料至关重要的自组装过程，或者无缺陷制造多层膜的成核和生长过程。虽然基于模型的分子过程控制是公认的能够制造先进材料的方法，但现有的方法可能不适合使用有限的计算资源进行实时实施，特别是考虑到分子过程的快速和不确定的动力学。因此，仍然迫切需要实现控制分子过程的状态变量分布的快速非平衡成形，以实现先进材料的无缺陷和可扩展制造。基于物理的在线学习和反馈控制框架，基于随机控制和机器学习的最新理论和算法突破，将能够在物理约束下实时地对系统状态的分布进行最优反馈控制。除了对机器学习、控制和制造产生深远的科学影响外，该项目还将展示精确控制分布的潜力，这些分布将服务于许多新兴的工程应用--从控制神经元群体到群体引导和概率运动规划。除了促进加州大学圣克鲁斯分校和加州大学伯克利分校之间的合作研究，这项研究还将导致大量的教育和推广活动。该项目的关键科学价值在于为分子过程带来创新的系统理论和基于学习的分布式控制方法，这些过程由表现出高度非线性和不确定动力学的多维偏微分方程模型控制。这项工作包括在线学习分子过程的复杂动力学，并通过实时反馈以最小能量关闭回路，对有限时间范围内的布居分布进行最优控制。与现有的最先进技术相反，这项研究不会对动力学或分布形状进行任何参数近似。相反，它将利用潜在的非线性方程的结构特性来学习和在线适应动态宏观特征，并合成反馈。该项目将提供计算基准和一个开源的数值工具箱，以提供对现有最先进技术所取得的改进的量化演示。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will support research that will advance the scientific knowledge as well as the design of algorithms to enable the fabrication of advanced materials. This will in turn catalyze scalable and economically viable precision manufacturing contributing to the advancement of technology, and national prosperity. Scalable and cost-effective manufacturing of advanced materials with desired quality increasingly relies on the ability to predict and control processes at the molecular scale. Examples of such molecular processes include self-assembly processes that are central to the manufacturing of materials that have unique optical, electrical, and mechanical properties with up to subnanometer precision, or nucleation and growth processes in defect-free manufacturing of multi-layer films. While model-based control of molecular processes is well-recognized for enabling fabrication of advanced materials, existing approaches may not be amenable to real-time implementations with modest computational resources, especially given the fast and uncertain dynamics of the molecular processes. Thus, there remains a critical need to achieve fast non-equilibrium shaping of the distribution of state variables governing molecular processes, towards defect-free and scalable manufacturing of advanced materials. The physics-based online learning and feedback control framework, grounded on recent theoretical and algorithmic breakthroughs in stochastic control and machine learning, will enable optimal feedback control of the distributions of system states in real-time subject to the physical constraints. In addition to its far-reaching scientific impact cross-cutting machine learning, control and manufacturing, the project will also demonstrate the potential for precise control of distributions that will serve many emerging engineering applications--from controlling neuronal populations to swarm guidance and probabilistic motion planning. Besides fostering collaborative research between UC Santa Cruz and UC Berkeley, the research will lead to a multitude of educational and outreach activities.The project’s key scientific merit lies in bringing innovative systems-theoretic and learning-based distributional control approaches for molecular processes governed by multidimensional partial differential equation models that exhibit highly nonlinear and uncertain dynamics. The effort includes online learning of the complex dynamics of molecular processes and closing the loop with minimum energy optimal control of the population distribution over a finite time horizon via real-time feedback. Contrary to the existing state-of-the-art, the research will not make any parametric approximation of the dynamics or of the distributional shapes. Instead, it will exploit the structural properties of the underlying nonlinear equations for learning and online adaptation of the dynamic macroscopic features, and to synthesize feedback. The project will deliver computational benchmarks and an open source numerical toolbox to provide a quantitative demonstration of the improvements achieved over the existing state-of-the-art.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.