In silico experimentation is the way of the future: Computing enables engineering designers to explore new ideas beyond what is possible in physical experiments. But simulating complex physics is computationally expensive — just a single simulation can take days on a supercomputer, making it practically impossible for a designer to fully explore the high-dimensional space of design options. Reduced-order models address this challenge, giving a rapid simulation capability while retaining predictive power. Operator Inference is a non-intrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. I will discuss recent advances in embedding additional structure in Operator Inference models, including a nested formulation that exploits the inherent hierarchy within the reduced space and a block-structured formulation that reflects the structure of a multiphysics system. Incorporating this extra structure improves both the conditioning of the learning problem and the effectiveness of the learned reduced models.
Joint work with Nicole Aretz, Anirban Chaudhuri and Benjamin Zastrow.
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