58 citations · 117 across the 17 of their papers we have counts for
20 papers
An optimal Petrov-Galerkin framework for operator networks
Philip Charles, Deep Ray, Yue Yu +7
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect…
Graph Laplacian-based Bayesian Multi-fidelity Modeling
Orazio Pinti, Jeremy M. Budd, Franca Hoffmann +1
We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Lapl…
A dimension-reduced variational approach for solving physics-based inverse problems using generative adversarial network priors and normalizing flows
Agnimitra Dasgupta, Dhruv V Patel, Deep Ray +2
We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posteri…
Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts
Bryan Shaddy, Deep Ray, Angel Farguell +7
Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in u…
Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penalty
Deep Ray, Javier Murgoitio-Esandi, Agnimitra Dasgupta +1
The solution of probabilistic inverse problems for which the corresponding forward problem is constrained by physical principles is challenging. This is especially true if the dime…
A few-shot graph Laplacian-based approach for improving the accuracy of low-fidelity data
Orazio Pinti, Assad A. Oberai
Low-fidelity data is typically inexpensive to generate but inaccurate. On the other hand, high-fidelity data is accurate but expensive to obtain. Multi-fidelity methods use a small…
Building a Fuel Moisture Model for the Coupled Fire-Atmosphere Model WRF-SFIRE from Data: From Kalman Filters to Recurrent Neural Networks
J. Mandel, J. Hirschi, A. K. Kochanski +6
The current fuel moisture content (FMC) subsystems in WRF-SFIRE and its workflow system WRFx use a time-lag differential equation model with assimilation of data from FMC sensors o…
Deep Learning and Computational Physics (Lecture Notes)
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. They should be accessible to a typical engineering gradua…
Variationally Mimetic Operator Networks
Dhruv Patel, Deep Ray, Michael R. A. Abdelmalik +2
In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input fu…
The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems
Deep Ray, Harisankar Ramaswamy, Dhruv V. Patel +1
In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems. The generator…
Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors
Dhruv V Patel, Deep Ray, Assad A Oberai
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One…
The Effect of Super-spreader Events in Epidemics
Harisankar Ramaswamy, Assad A Oberai, Mitul Luhar +1
The spread of infectious epidemics is often accelerated by super-spreader events. Understanding their effect is important, particularly in the context of standard epidemiological m…
A comprehensive spatial-temporal infection model
Harisankar Ramaswamy, Assad A Oberai, Yannis C Yortsos
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for trans…
Benchmarking features from different radiomics toolkits / toolboxes using Image Biomarkers Standardization Initiative
Mingxi Lei, Bino Varghese, Darryl Hwang +6
There is no consensus regarding the radiomic feature terminology, the underlying mathematics, or their implementation. This creates a scenario where features extracted using differ…
GAN-based Priors for Quantifying Uncertainty
Dhruv V. Patel, Assad A. Oberai
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. De…
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Franca Hoffmann, Bamdad Hosseini, Assad A. Oberai +1
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a cen…
Bayesian Inference with Generative Adversarial Network Priors
Dhruv Patel, Assad A Oberai
Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical m…
Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation
Olalekan A. Babaniyi, Assad A. Oberai, Paul E. Barbone
We consider the problem of estimating the vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by appli…
A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics
David Sondak, John N. Shadid, Assad A. Oberai +3
New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulat…
Variational multiscale analysis: the fine-scale Green's function for stochastic partial differential equations
Jayanth Jagalur-Mohan, Onkar Sahni, Alireza Doostan +1
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating acc…