Prof. Benjamin Peherstorfer from the Courant Institute of Mathematical Sciences speaking in the UW Data-driven methods in science and engineering seminar on Nov. 19, 2021.
Sign up for notifications of future talks: mailman11.u.wa...
Abstract: Latent dynamics of transport-dominated phenomena such as described by hyperbolic conservation laws typically exhibit nonlinear structures that make traditional model reduction in low-dimensional subspaces inefficient. In this presentation, we propose numerical time integration methods that propagate forward in time nonlinear parametrizations such as deep neural networks that can efficiently describe the latent dynamics of transport-dominated problems. The parameters are learned by integrating systems of differential equations given by the physics of the problem. This is different to collocation methods that fit the parameters by minimizing the residual based on samples from the space and time domain. Numerical results demonstrate that the proposed approach requires few degrees of freedom to accurately describe and predict transport-dominated dynamics. Furthermore, the approach is compatible with adaptive sampling schemes to efficiently approximate high-dimensional problems with spatially local features.
5 окт 2024
