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Found 8 papers, 0 papers with code
Generative modeling of time-dependent densities via optimal transport and projection pursuit
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to high dimensional problems.
Adaptive State-Dependent Diffusion for Derivative-Free Optimization
This paper develops and analyzes a stochastic derivative-free optimization strategy.
Neural Inverse Operators for Solving PDE Inverse Problems
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions.
Tuning Frequency Bias in Neural Network Training with Nonuniform Data
Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency residuals.
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems.
Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems
We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems.
A Generalized Weighted Optimization Method for Computational Learning and Inversion
The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes.
The quadratic Wasserstein metric for inverse data matching
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems.
