[01072] Data-Driven Methods in Scientific Machine Learning
Session Date & Time :
01072 (1/2) : 4D (Aug.24, 15:30-17:10)
01072 (2/2) : 4E (Aug.24, 17:40-19:20)
Type : Proposal of Minisymposium
Abstract : The ample availability of data for scientific problems, in addition to developments in hardware and software for machine and deep learning have changed the way mathematicians approach problems, particularly those in numerical analysis and scientific computing. Rather than relying strictly on the physics of the problem at hand for modeling and computing, data-driven methods incorporate observational data to inform their solutions. This session focuses on significant advances in data-driven methods and machine learning for a variety of problems in scientific computing, including but not limited to: function approximation, inverse problems, dynamical systems, dimensionality reduction, and generally scientific machine learning.
Tan Bui-Thanh (Oden Institute, University of Texas)
Dongbin Xiu (The Ohio State University)
Victor Churchill (Trinity College / Ohio State University)
Talks in Minisymposium :
[05116] Acceleration of multiscale solvers via adjoint operator learning
Author(s) :
Emanuel Eld Ström (KTH Royal Institute of Technology)
Ozan Öktem (KTH Royal Institute of Technology)
Anna-Karin Tornberg (KTH Royal Institute of Technology)
Abstract : We leverage recent advances in operator learning to accelerate multiscale solvers for laminar fluid flow over a rough boundary. We focus on the HMM method, which involves formulating the problem through a coupled system of microscopic and macroscopic subproblems. Solving microscopic problems can be viewed as a nonlinear operator mapping from the space of micro domains to the solution space. Our main contribution is to use an FNO-type architecture to perform this mapping.
