no code implementations • 16 Feb 2024 • Michael Penwarden, Houman Owhadi, Robert M. Kirby
This topic encompasses a broad array of methods and models aimed at solving a single or a collection of PDE problems, called multitask learning.
1 code implementation • 6 Apr 2023 • Haocheng Dai, Michael Penwarden, Robert M. Kirby, Sarang Joshi
Neural operator learning as a means of mapping between complex function spaces has garnered significant attention in the field of computational science and engineering (CS&E).
1 code implementation • 28 Feb 2023 • Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, Robert M. Kirby
This problem is also found in, and in some sense more difficult, with domain decomposition strategies such as temporal decomposition using XPINNs.
no code implementations • 2 Feb 2023 • Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.
no code implementations • 23 Oct 2022 • Shibo Li, Michael Penwarden, Yiming Xu, Conor Tillinghast, Akil Narayan, Robert M. Kirby, Shandian Zhe
However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions.
no code implementations • 26 Oct 2021 • Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world.
BIG-bench Machine Learning Physics-informed machine learning +1
no code implementations • 25 Jun 2021 • Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences.