32 citations · 114 across the 16 of their papers we have counts for
18 papers
Convergence of a Randomized Newton Method in Nonconvex Optimization
Edward Huynh, Björn Engquist
We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to addi…
Diffusion-guided optimization for full waveform inversion
Yiran Shen, Yangkang Chen, Björn Engquist
We present a diffusion-guided full waveform inversion (FWI) study in which pretrained diffusion generative models are used as learned regularizers inside a PDE-constrained seismic…
Sampling Using Hybrid Stochastic Dynamics
Björn Engquist, Kui Ren, Yunan Yang
This work proposes a framework for sampling from the Gibbs distribution of a given potential using hybrid stochastic dynamics. In this framework, two distinct sampling dynamics are…
Sampling with Adaptive Variance for Multimodal Distributions
Björn Engquist, Kui Ren, Yunan Yang
We propose and analyze a class of adaptive sampling algorithms for multimodal distributions on a bounded domain, which share a structural resemblance to the classic overdamped Lang…
Adaptive State-Dependent Diffusion for Derivative-Free Optimization
Björn Engquist, Kui Ren, Yunan Yang
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probabil…
Neural Inverse Operators for Solving PDE Inverse Problems
Roberto Molinaro, Yunan Yang, Björn Engquist +1
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need…
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization
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. A key component in the algorithm is th…
A Generalized Weighted Optimization Method for Computational Learning and Inversion
Björn Engquist, Kui Ren, Yunan Yang
The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression mode…
Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping
Bjorn Engquist, Yunan Yang
Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE-constrained optimization is used to determine unknown parameters in a wave…
The quadratic Wasserstein metric for inverse data matching
Bjorn Engquist, Kui Ren, Yunan Yang
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein () distance as the measure of data discrepancy in computational solutions…
Seismic Inversion and the Data Normalization for Optimal Transport
Björn Engquist, Yunan Yang
Full waveform inversion (FWI) has recently become a favorite technique for the inverse problem of finding properties in the earth from measurements of vibrations of seismic waves o…
Seismic Imaging and Optimal Transport
Björn Engquist, Yunan Yang
Seismology has been an active science for a long time. It changed character about 50 years ago when the earth's vibrations could be measured on the surface more accurately and more…
Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion
Yunan Yang, Björn Engquist, Junzhe Sun +1
Conventional full-waveform inversion (FWI) using the least-squares norm () as a misfit function is known to suffer from cycle skipping. This increases the risk of computing a…
Optimal Transport for Seismic Full Waveform Inversion
Bjorn Engquist, Brittany D. Froese, Yunan Yang
Full waveform inversion is a successful procedure for determining properties of the earth from surface measurements in seismology. This inverse problem is solved by a PDE constrain…
Homogenization Model for Aberrant Crypt Foci
Isabel N. Figueiredo, Carlos Leal, Giuseppe Romanazzi +1
Several explanations can be found in the literature about the origin of colorectal cancer. There is however some agreement on the fact that the carcinogenic process is a result of…
Fast Sweeping Methods for Hyperbolic Systems of Conservation Laws at Steady State II
Bjorn Engquist, Brittany D. Froese, Yen-Hsi Richard Tsai
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We f…
Application of the Wasserstein metric to seismic signals
Bjorn Engquist, Brittany D. Froese
Seismic signals are typically compared using travel time difference or difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismo…
Fast Sweeping Methods for Hyperbolic Systems of Conservation Laws at Steady State
Bjorn Engquist, Brittany D. Froese, Yen-Hsi Richard Tsai
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new a…