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05/29/2023
Suppressing Instability in a Vlasov-Poisson System by an External Electric Field Through Constrained Optimization
Fusion energy offers the potential for the generation of clean, safe, an...
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05/06/2023
Differential-Equation Constrained Optimization With Stochasticity
Most inverse problems from physical sciences are formulated as PDE-const...
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04/19/2023
Generative Modeling of Time-Dependent Densities via Optimal Transport and Projection Pursuit
Motivated by the computational difficulties incurred by popular deep lea...
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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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09/25/2022
Monte Carlo Gradient in Optimization Constrained by Radiative Transport Equation
Can Monte Carlo (MC) solvers be directly used in gradient-based methods ...
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07/23/2022
Adjoint DSMC for Nonlinear Spatially-Homogeneous Boltzmann Equation With a General Collision Model
We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC)...
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05/28/2022
A Quadrature Perspective on Frequency Bias in Neural Network Training with Nonuniform Data
Small generalization errors of over-parameterized neural networks (NNs) ...
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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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02/13/2022
Efficient Natural Gradient Descent Methods for Large-Scale Optimization Problems
We propose an efficient numerical method for computing natural gradient ...
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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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09/13/2021
Implicit Regularization Effects of the Sobolev Norms in Image Processing
In this paper, we propose to use the general L^2-based Sobolev norms (i....
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09/02/2020
Adjoint DSMC for nonlinear Boltzmann equation constrained optimization
Applications for kinetic equations such as optimal design and inverse pr...
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08/26/2020
Anderson Acceleration for Seismic Inversion
The state-of-art seismic imaging techniques treat inversion tasks such a...
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04/07/2020
Stability of Gibbs Posteriors from the Wasserstein Loss for Bayesian Full Waveform Inversion
Recently, the Wasserstein loss function has been proven to be effective ...
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02/10/2020
Anderson Acceleration Using the H^-s Norm
Anderson acceleration (AA) is a technique for accelerating the convergen...
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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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11/15/2019