no code implementations • 21 Mar 2024 • Philip Charles, Deep Ray

In the present work, we propose a variant of the SP-WENO, termed as Deep Sign-Preserving WENO (DSP-WENO), where a neural network is trained to learn the WENO weighting strategy.

no code implementations • 5 Sep 2023 • Bryan Shaddy, Deep Ray, Angel Farguell, Valentina Calaza, Jan Mandel, James Haley, Kyle Hilburn, Derek V. Mallia, Adam Kochanski, Assad Oberai

The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections.

no code implementations • 27 Aug 2023 • Deep Ray, Souvik Roy

We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography.

no code implementations • 8 Jun 2023 • Deep Ray, Javier Murgoitio-Esandi, Agnimitra Dasgupta, Assad A. Oberai

The cWGAN developed in this work differs from earlier versions in that its critic is required to be 1-Lipschitz with respect to both the inferred and the measurement vectors and not just the former.

no code implementations • 3 Jan 2023 • Deep Ray, Orazio Pinti, Assad A. Oberai

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California.

no code implementations • 26 Sep 2022 • Dhruv Patel, Deep Ray, Michael R. A. Abdelmalik, Thomas J. R. Hughes, Assad A. Oberai

The application of the VarMiON to a canonical elliptic PDE and a nonlinear PDE reveals that for approximately the same number of network parameters, on average the VarMiON incurs smaller errors than a standard DeepONet and a recently proposed multiple-input operator network (MIONet).

no code implementations • 15 Feb 2022 • Deep Ray, Harisankar Ramaswamy, Dhruv V. Patel, Assad A. Oberai

In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems.

no code implementations • NeurIPS Workshop Deep_Invers 2021 • Deep Ray, Dhruv V Patel, Harisankar Ramaswamy, Assad Oberai

In this work, we propose a conditional generative adversarial network (cGAN) to sample from the posterior of physics-based Bayesian inference problems.

no code implementations • 6 Jul 2021 • Dhruv V Patel, Deep Ray, Assad A Oberai

Specifically, we demonstrate how using the approximate distribution learned by a Generative Adversarial Network (GAN) as a prior in a Bayesian update and reformulating the resulting inference problem in the low-dimensional latent space of the GAN, enables the efficient solution of large-scale Bayesian inverse problems.

no code implementations • 23 Oct 2020 • Dhruv V Patel, Deep Ray, Harisankar Ramaswamy, Assad Oberai

Generative adversarial networks (GANs) have found multiple applications in the solution of inverse problems in science and engineering.

4 code implementations • 13 Aug 2020 • Kjetil O. Lye, Siddhartha Mishra, Deep Ray, Praveen Chandrasekhar

We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems.

no code implementations • 13 Dec 2019 • Tim De Ryck, Siddhartha Mishra, Deep Ray

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions.

no code implementations • 29 Apr 2019 • Jim Magiera, Deep Ray, Jan S. Hesthaven, Christian Rohde

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates.

3 code implementations • 7 Mar 2019 • Kjetil O. Lye, Siddhartha Mishra, Deep Ray

Under the assumption that the underlying neural networks generalize well, we prove that the deep learning MC and QMC algorithms are guaranteed to be faster than the baseline (quasi-) Monte Carlo methods.

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