MINDS Seminar on Machine Learning | Advancing model reduction techniques: deep learning approaches for homogenization and reduc

Abstract: This presentation introduces the application of deep learning approaches in two model reduction techniques. The first part focuses on homogenization of multiscale elliptic equations. Multiscale equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). We develop a physics-informed neural networks (PINNs) algorithm to estimate the G-limits from the multiscale solution data. Unlike the traditional approaches, our approach does not rely on the periodicity assumption or the known multiscale coefficient during the learning stage. The second part of the presentation introduces a reduced order modeling for parameterized dynamical systems. Our proposed algorithm leverages autoencoders to capture the latent representation of high-dimensional full-order model data. Additionally, we employ the GENERIC formalism informed neural networks (GFINNs) to learn the dynamics of the latent variables. By training these neural networks simultaneously, we achieve efficient and accurate reduced order models for parameterized dynamical systems.

<online>

https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09