1 code implementation • 8 Dec 2023 • Vivek Oommen, Khemraj Shukla, Saaketh Desai, Remi Dingreville, George Em Karniadakis
This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism that enables accurate extrapolation and efficient time-to-solution predictions of the dynamics.
no code implementations • 22 Oct 2023 • Khemraj Shukla, Yeonjong Shin
The probability distribution of the random vector determines the statistical properties of RFG.
1 code implementation • 29 Sep 2023 • Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla, George Em Karniadakis
The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification.
1 code implementation • 23 Jul 2023 • Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi
We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach.
no code implementations • 18 Jul 2023 • Elham Kiyani, Mahdi Kooshkbaghi, Khemraj Shukla, Rahul Babu Koneru, Zhen Li, Luis Bravo, Anindya Ghoshal, George Em Karniadakis, Mikko Karttunen
Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression.
no code implementations • 27 Jun 2023 • Varun Kumar, Leonard Gleyzer, Adar Kahana, Khemraj Shukla, George Em Karniadakis
To demonstrate the flow of the MyCrunchGPT, and create an infrastructure that can facilitate a broader vision, we built a webapp based guided user interface, that includes options for a comprehensive summary report.
no code implementations • 18 May 2023 • Elham Kiyani, Khemraj Shukla, George Em Karniadakis, Mikko Karttunen
In addition, symbolic regression is employed to determine the closed form of the unknown part of the equation from the data, and the results confirm the accuracy of the X-PINNs based approach.
no code implementations • 7 Feb 2023 • Aniruddha Bora, Khemraj Shukla, Shixuan Zhang, Bryce Harrop, Ruby Leung, George Em Karniadakis
In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet).
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 • 16 May 2022 • Khemraj Shukla, Mengjia Xu, Nathaniel Trask, George Em Karniadakis
For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs).
BIG-bench Machine Learning Physics-informed machine learning
no code implementations • 11 Apr 2022 • Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Remi Dingreville, George Em Karniadakis
We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space.
no code implementations • 7 May 2020 • Khemraj Shukla, Patricio Clark Di Leoni, James Blackshire, Daniel Sparkman, George Em. Karniadakis
The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry.