Search Results for author: Yunan Yang

Found 8 papers, 0 papers with code

Generative modeling of time-dependent densities via optimal transport and projection pursuit

no code implementations19 Apr 2023 Jonah Botvinick-Greenhouse, Yunan Yang, Romit Maulik

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

no code implementations8 Feb 2023 Björn Engquist, Kui Ren, Yunan Yang

This paper develops and analyzes a stochastic derivative-free optimization strategy.

Neural Inverse Operators for Solving PDE Inverse Problems

no code implementations26 Jan 2023 Roberto Molinaro, Yunan Yang, Björn Engquist, Siddhartha Mishra

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions.

Operator learning

Tuning Frequency Bias in Neural Network Training with Nonuniform Data

no code implementations28 May 2022 Annan Yu, Yunan Yang, Alex Townsend

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

no code implementations12 Apr 2022 Björn Engquist, Kui Ren, Yunan Yang

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

no code implementations13 Feb 2022 Levon Nurbekyan, Wanzhou Lei, Yunan Yang

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

no code implementations ICLR 2022 Björn Engquist, Kui Ren, Yunan Yang

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

no code implementations15 Nov 2019 Bjorn Engquist, Kui Ren, Yunan Yang

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.

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