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08/15/2023
On the nature of the boundary resonance error in numerical homogenization and its reduction
Numerical homogenization of multiscale equations typically requires taki...
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02/08/2023
Adaptive State-Dependent Diffusion for Derivative-Free Optimization
This paper develops and analyzes a stochastic derivative-free optimizati...
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01/26/2023
Neural Inverse Operators for Solving PDE Inverse Problems
A large class of inverse problems for PDEs are only well-defined as mapp...
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04/12/2022
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization
We propose a new stochastic gradient descent algorithm for finding the g...
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01/23/2022
A Generalized Weighted Optimization Method for Computational Learning and Inversion
The generalization capacity of various machine learning models exhibits ...
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01/31/2020
Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping
Full waveform inversion (FWI) is today a standard process for the invers...
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10/15/2019
Numerical multiscale methods and effective boundary conditions
We develop numerical multiscale methods for viscous boundary layer flow....
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09/02/2019
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
In this work, we review the connection between the subjects of homogeniz...
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05/20/2019