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Model-constrained deep learning approaches for inverse problems
Deep Learning (DL), in particular deep neural networks (DNN), by design is purely data-driven and in general does not require physics. …
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Unified hp-HDG Frameworks for Friedrichs PDE systems
This work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial …
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Multi-patch epidemic models with partial mobility, residency, and demography
The emergence and re-emergence of infectious diseases has been a global cause of concern in the past few decades. Previous research in …
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A Model-Constrained Tangent Manifold Learning Approach for Dynamical Systems
Real time accurate solutions of large scale complex dynamical systems are in critical need for control, optimization, uncertainty …
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A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD
We present a scalable block preconditioning strategy for the trace system coming from the high-order hybridized discontinuous Galerkin …
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An autoencoder compression approach for accelerating large-scale inverse problems
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science …
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On unifying randomized methods for inverse problems
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by …
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TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems
Deep Learning (DL), in particular deep neural networks (DNN), by default is purely data-driven and in general does not require physics. …
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A Unified and Constructive Framework for the Universality of Neural Networks
One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal property. …
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Bridging and Improving Theoretical and Computational Electrical Impedance Tomography via Data Completion
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to …
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