23-000003470 Deep Uncertainty Quantification in Multiscale and Multi-Physics Systems
Abstract
Modeling a wide range of physical processes relies on solving complex partial differential equation (PDE) systems. Example applications include predicting crack propagation in underwater vehicles or controlling dissipated heat in microprocessors that are cooled with turbulent flows. While significant advancements have been made in solving such PDEs, existing technologies are prohibitively expensive. The costs are especially high in the case of #stochastic# PDEs because a large number of simulations are required to characterize the effects of uncertainties on the solution. These high costs reduce engineers efficiency in solving inverse problems, building digital twins, or designing systems that must perform robustly in uncertain environments.To reduce computational costs, this proposal develops deep learning (DL) models that rapidly solve stochastic PDE systems. Our DL models have three novel features that distinguish them from existing approaches which solve PDEs via DL: (1) they are#transferable# which means they can readily model different processes that share the same governing equations, (2) they are #scalable# and hence can solve PDEs on large domains while resolving small-scale details, and (3) they are #probabilistic by construction# which means they can efficiently learn from scarce data and provide probabilistic predictions without using expensive sampling-based techniques. Compared to traditional solvers such as the finite element method, these features will provide the capability to predict the solution of stochastic PDEs with at least 2 orders of magnitude speedups and less than 2% loss in accuracy. By embedding our deep neural networks (DNNs) in multiscale or multi-physicssimulations, the computational savings will be even more.Upon successful completion, our contributions will enable on-the-fly emulation of a wide range of stochastic PDE systems on arbitrary domains via #pre-trained# DNNs. Hence, we expect to eliminate long training times while increasing accuracy and scalability. Additionally, we will leverage our approach to answer fundamental questions in engineering applications on multi-scale modeling of metallic alloys and thermofluidic heat control.To achieve real-time and robust performance, we design geometry-aware learning algorithms and leverage the well-established mathematics of domain decomposition methods that uniquely exploit parallel computing on heterogeneous machines that have multiple GPUs and CPUs. Additionally, to emulate multi-physics processes under uncertainty, we train multiple DNNs to learn each physics and then couple their predictions to solve the underlying stochastic PDE system. We expect our contributions to provide a sustainable platform for studying PDE-governed engineeredsystems. Therefore, we will develop the tools that ensure timely adoption and rapid maintenance. We will also provide scaling guidelines to estimate the required computational power for reaching desired levels of accuracy.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 15, 2023
- Source ID
- N000142312485
Entities
People
- Ramin Baghgar Bostanabad
Organizations
- Office of Naval Research
- United States Navy
- University of California, Irvine