Physics-informed Machine Learning (Φ-ML) Meets Engineering Webinar

Thursday 9 Feb 2023, 13:00 → 14:00 UTC

Learning physics-based reduced-order models from data using quadratic manifolds

Abstract: The rapidly increasing demand for computer simulations of complex physical, chemical, and other processes places a significant burden on the shoulders of computational scientists and engineers. Despite the remarkable rise of available computer resources and computing technologies, the need for model order reduction to cope with these complex problems is an ever-present reality. Reduced-order models are imperative in making computationally tractable outer-loop applications that require simulating systems for many scenarios with different parameters and under varying inputs. They require that one numerically solves the differential equations describing the physical system of interest in low-dimensional reduced spaces, in contrast to the original full-order models. However, traditional model reduction techniques often fail to identify a low-dimensional linear subspace for approximating the solution to many physics-based simulations. In this talk I will propose a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.

Speaker: Dr Rudy Geelen

ZOOM link: https://turing-uk.zoom.us/j/93206223969?pwd=ZzJGQ0t6Z24xa2VYNGRKU3E0d1hEZz09

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