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Title

On the influence of over-parameterization in manifold based surrogates
and deep neural operators

On the influence of over-parameterization in manifold based surrogates and deep neural operators

9 March 2022

Katiana Kontolati

Michael D. Shields

George Karniadakis

ArXiv (abs)PDF HTML

Papers citing "On the influence of over-parameterization in manifold based surrogates and deep neural operators"

15 / 15 papers shown

Title
Polynomial Chaos Expansion for Operator Learning Himanshu Sharma Lukás Novák Michael D. Shields AI4CE 8 1 0 28 Aug 2025
Basis-to-Basis Operator Learning Using Function Encoders Tyler Ingebrand Adam J. Thorpe Somdatta Goswami Krishna Kumar Ufuk Topcu 119 8 0 30 Sep 2024
Efficient Training of Deep Neural Operator Networks via Randomized Sampling Sharmila Karumuri Lori Graham-Brady Somdatta Goswami 117 3 0 20 Sep 2024
Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification Jungho Kim Sang-ri Yi Ziqi Wang 107 7 0 07 Feb 2024
Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification Dimitris G. Giovanis Dimitrios Loukrezis Ioannis G. Kevrekidis Michael D. Shields 128 5 0 30 Jan 2024
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology Qingsong Xu Yilei Shi Jonathan Bamber Ye Tuo Ralf Ludwig Xiao Xiang Zhu AI4CE 255 10 0 08 Oct 2023
LNO: Laplace Neural Operator for Solving Differential Equations Qianying Cao S. Goswami George Karniadakis 133 52 0 19 Mar 2023
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils K. Shukla Vivek Oommen Ahmad Peyvan Michael Penwarden L. Bravo A. Ghoshal Robert M. Kirby George Karniadakis 141 22 0 02 Feb 2023
Physics-constrained 3D Convolutional Neural Networks for Electrodynamics A. Scheinker R. Pokharel 74 15 0 31 Jan 2023
Neural Operator: Is data all you need to model the world? An insight into the impact of Physics Informed Machine Learning Hrishikesh Viswanath Md Ashiqur Rahman Abhijeet Vyas Andrey Shor Beatriz Medeiros Stephanie Hernandez S. Prameela Aniket Bera PINN AI4CE 172 6 0 30 Jan 2023
Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications Zhongkai Hao Songming Liu Yichi Zhang Chengyang Ying Yao Feng Hang Su Jun Zhu PINN AI4CE 195 114 0 15 Nov 2022
Physics-Informed Deep Neural Operator Networks S. Goswami Aniruddha Bora Yue Yu George Karniadakis PINN AI4CE 177 128 0 08 Jul 2022
Deep transfer operator learning for partial differential equations under conditional shift S. Goswami Katiana Kontolati Michael D. Shields George Karniadakis 168 119 0 20 Apr 2022
A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems Katiana Kontolati Dimitrios Loukrezis D. D. Giovanis Lohit Vandanapu Michael D. Shields 146 47 0 09 Feb 2022
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 285 489 0 06 Nov 2021