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

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.