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04/10/2023
An autoencoder compression approach for accelerating large-scale inverse problems
PDE-constrained inverse problems are some of the most challenging and co...
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04/07/2023
Unified hp-HDG Frameworks for Friedrichs' PDE systems
This work proposes a unified hp-adaptivity framework for hybridized disc...
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01/03/2023
On Unifying Randomized Methods For Inverse Problems
This work unifies the analysis of various randomized methods for solving...
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12/20/2022
Use of mobile phone sensing data to estimate residence and mobility times in urban patches during the COVID-19 epidemic: The case of the 2020 outbreak in Hermosillo, Mexico
It is often necessary to introduce the main characteristics of populatio...
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11/13/2022
Layerwise Sparsifying Training and Sequential Learning Strategy for Neural Architecture Adaptation
This work presents a two-stage framework for progressively developing ne...
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08/09/2022
A Model-Constrained Tangent Manifold Learning Approach for Dynamical Systems
Real time accurate solutions of large scale complex dynamical systems ar...
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03/14/2022
Probabilistic Constrained Bayesion Inversion for Transpiration Cooling
To enable safe operations in applications such as rocket combustion cham...
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12/30/2021
A Unified and Constructive Framework for the Universality of Neural Networks
One of the reasons why many neural networks are capable of replicating c...
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05/25/2021
Model-Constrained Deep Learning Approaches for Inverse Problems
Deep Learning (DL), in particular deep neural networks (DNN), by design ...
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05/02/2021
Bridging and Improving Theoretical and Computational Electric Impedance Tomography via Data Completion
In computational PDE-based inverse problems, a finite amount of data is ...
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12/14/2020
A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD
We present a scalable block preconditioning strategy for the trace syste...
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11/02/2020
A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations
We propose an Exponential DG approach for numerically solving partial di...
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03/23/2020
Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Hessian operators arising in inverse problems governed by partial differ...
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12/17/2019
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models
Inverse problems are pervasive mathematical methods in inferring knowled...
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12/05/2019
Solving Forward and Inverse Problems Using Autoencoders
This work develops a model-aware autoencoder networks as a new method fo...
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09/20/2019
Sequential Ensemble Transform for Bayesian Inverse Problems
We present the Sequential Ensemble Transform (SET) method, a new approac...
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03/26/2019
A Multilevel Approach for Trace System in HDG Discretizations
We propose a multilevel approach for trace systems resulting from hybrid...
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08/21/2018
A Hybridized Discontinuous Galerkin Method for A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures
We develop a high-order hybridized discontinuous Galerkin (HDG) method f...
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11/07/2017