Applied Interdisciplinary Mathematics (AIM) Seminar

A data-driven model can be built to accurately accelerate computationally expensive physical simulations, which is essential in multi-query problems, such as inverse problem, uncertainty quantification, design optimization, and optimal control. In this talk, two types of data-driven model order reduction techniques will be discussed, i.e., the black-box approach that incorporates only data and the physics-constrained approach that incorporates the first principle as well as data. The advantages and disadvantages of each method will be discussed. Several recent developments of generalizable and robust data-driven physics-constrained reduced order models will be demonstrated for various physical simulations as well. For example, a hyper-reduced time-windowing reduced order model overcomes the difficulty of advection-dominated shock propagation phenomenon, achieving a speed-up of O(20~100) with a relative error much less than 1% for Lagrangian hydrodynamics problems, such as 3D Sedov blast problem, 3D triple point problem, 3D Taylor-Green vortex problem, 2D Gresho vortex problem, and 2D Rayleigh-Taylor instability problem. The nonlinear manifold reduced order model also overcomes the challenges posed by the problems with Kolmogorov's width decaying slowly by representing the solution field with a compact neural network decoder, i.e., nonlinear manifold. The space-time reduced order model accelerates a large-scale particle Boltzmann transport simulation by a factor of 2,700 with a relative error less than 1%. Furthermore, successful application of these reduced order models for mate-material lattice-structure design optimization problems will be presented. Finally, the library for reduced order models, i.e., libROM ( https://www.librom.net), and its webpage and several YouTube tutorial videos will be introduced, which is useful for education as well as research purpose.
Speaker(s): Youngsoo Choi (LLNL)