Mathematics Colloquia and Seminars

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Description

In this talk, I will discuss the disruptive potential for machine learning algorithms to accelerate and even automate scientific computing tasks.  I will focus on nanophotonic technologies as a model system for analysis, though the methods can ultimately generalize to other domains of scientific computing.  First, I will first discuss how physics-augmented deep networks can be trained to serve as surrogate PDE solvers and preconditioners capable of solving Maxwell’s equations at large scales, high accuracy, and fast speeds.  Second, I will discuss how these solvers can be utilized in high-speed freeform optimization algorithms, including a newly proposed population-based optimization algorithm that utilizes the training of generative deep networks with physical solvers.  Third, I will then discuss how concepts in computer vision and neuro-rendering can streamline freeform design within experimental fabrication pipelines. Finally, I will discuss our efforts in utilizing a multi-agentic approach to engage human-AI collaboration to perform practical nanophotonic design tasks.  We anticipate that these concepts will impact how academic and industrial researchers approach innovation and design in the field.