Search Results for author: Michael Penwarden

Found 7 papers, 2 papers with code

Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics

no code implementations16 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.

Physics-informed machine learning

Neural Operator Learning for Ultrasound Tomography Inversion

1 code implementation6 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).

Operator learning

Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils

no code implementations2 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.

regression

A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs

no code implementations26 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

Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)

no code implementations25 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.

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