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Deep Learning for Efficient Modeling of High-Dimensional Spatiotemporal Physics
Arvind Mohan, Los Alamos National Laboratory
Several research problems in physical sciences are exceptionally complex and high-dimensional, exhibiting spatio-temporal dynamics, non-linearity, and chaos. In an era when vast quantities of such scientific data are generated, building practical, physics-driven reduced-order models (ROM) of such phenomena is crucial. While deep neural networks for spatio-temporal data have shown considerable promise, they face severe computational bottlenecks in learning extremely high-dimensional datasets, often with greater than 10^9 degrees of freedom. These application-agnostic networks may also lack physical constraints and interpretability that is desired in scientific ROMs. We'll present our efforts in leveraging the strong mathematical and physical foundations underlying wavelet theory with the learning capacity of deep neural nets. We'll demonstrate computationally efficient, partially interpretable learning with some embedded physics constraints for modeling large scientific datasets.