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08/23/2023
On-Manifold Projected Gradient Descent
This work provides a computable, direct, and mathematically rigorous app...
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07/05/2023
GNEP Based Dynamic Segmentation and Motion Estimation for Neuromorphic Imaging
This paper explores the application of event-based cameras in the domain...
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06/28/2023
Randomized Reduced Basis Methods for Parameterized Fractional Elliptic PDEs
This paper is interested in developing reduced order models (ROMs) for r...
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05/16/2023
A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Method
Empirical interpolation method (EIM) is a well-known technique to effici...
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03/27/2023
Adjoint-based Determination of Weaknesses in Structures
An adjoint-based procedure to determine weaknesses, or, more generally t...
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01/20/2023
State-constrained Optimization Problems under Uncertainty: A Tensor Train Approach
We propose an algorithm to solve optimization problems constrained by pa...
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12/22/2022
Analysis of a sinc-Galerkin Method for the Fractional Laplacian
We provide the convergence analysis for a sinc-Galerkin method to solve ...
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11/30/2022
Neural Network Representation of Time Integrators
Deep neural network (DNN) architectures are constructed that are the exa...
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09/29/2022
Boundary control of time-harmonic eddy current equations
Motivated by various applications, this article develops the notion of b...
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08/24/2022
Nonlocal Bounded Variations with Applications
Motivated by problems where jumps across lower dimensional subsets and s...
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05/09/2022
Efficient algorithms for Bayesian Inverse Problems with Whittle–Matérn Priors
This paper tackles efficient methods for Bayesian inverse problems with ...
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04/18/2022
An Optimal Time Variable Learning Framework for Deep Neural Networks
Feature propagation in Deep Neural Networks (DNNs) can be associated to ...
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03/15/2022
NINNs: Nudging Induced Neural Networks
New algorithms called nudging induced neural networks (NINNs), to contro...
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02/17/2022
A Deterministic Pathogen Transmission Model Based on High-Fidelity Physics
A deterministic pathogen transmission model based on high-fidelity physi...
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11/22/2021
Data Assimilation with Deep Neural Nets Informed by Nudging
The nudging data assimilation algorithm is a powerful tool used to forec...
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11/09/2021
TTRISK: Tensor Train Decomposition Algorithm for Risk Averse Optimization
This article develops a new algorithm named TTRISK to solve high-dimensi...
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06/24/2021
Optimal Control, Numerics, and Applications of Fractional PDEs
This article provides a brief review of recent developments on two nonlo...
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06/23/2021
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
In this paper, we consider non-diffusive variational problems with mixed...
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04/20/2021
Approximation of fractional harmonic maps
This paper addresses the approximation of fractional harmonic maps. Besi...
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04/03/2021
Convergence Analysis of the Rank-Restricted Soft SVD Algorithm
The soft SVD is a robust matrix decomposition algorithm and a key compon...
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04/01/2021
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Chemically reacting flows are common in engineering, such as hypersonic ...
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02/08/2021
Novel Deep neural networks for solving Bayesian statistical inverse
We consider the simulation of Bayesian statistical inverse problems gove...
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10/27/2020
A Note on Multigrid Preconditioning for Fractional PDE-Constrained Optimization Problems
In this note we present a multigrid preconditioning method for solving q...
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10/13/2020
Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis
Fueled by many applications in random processes, imaging science, geophy...
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06/23/2020
Detailed Simulation of Viral Propagation In The Built Environment
A summary is given of the mechanical characteristics of virus contaminan...
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04/20/2020
Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case
This paper considers optimal control of fractional parabolic PDEs with b...
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04/01/2020
Fractional Deep Neural Network via Constrained Optimization
This paper introduces a novel algorithmic framework for a deep neural ne...
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12/10/2019
Moreau-Yosida Regularization for Optimal Control of Fractional Elliptic Problems with State and Control Constraints
Recently the authors have studied a state and control constrained optima...
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12/06/2019
Revisiting Calderon's Problem
A finite element code for heat conduction, together with an adjoint solv...
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11/28/2019
Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs
Given only a collection of points sampled from a Riemannian manifold emb...
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10/31/2019
Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
We study the controllability to trajectories, under positivity constrain...
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10/16/2019
Convergence of solutions of discrete semi-linear space-time fractional evolution equations
Let (-Δ)_c^s be the realization of the fractional Laplace operator on th...
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07/22/2019
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
In this work we consider a generalized bilevel optimization framework fo...
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07/02/2019
Adaptive particle-based approximations of the Gibbs posterior for inverse problems
In this work, we adopt a general framework based on the Gibbs posterior ...
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02/13/2019
Fractional Operators Applied to Geophysical Electromagnetics
A growing body of applied mathematics literature in recent years has foc...
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05/16/2018