32 citations · 127 across the 22 of their papers we have counts for
22 papers
Differential-Equation Constrained Optimization With Stochasticity
Qin Li, Li Wang, Yunan Yang
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the mo…
HV Geometry for Signal Comparison
Ruiyu Han, Dejan Slepčev, Yunan Yang
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thu…
Generative modeling of time-dependent densities via optimal transport and projection pursuit
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 req…
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…
Learning dynamics on invariant measures using PDE-constrained optimization
Jonah Botvinick-Greenhouse, Robert Martin, Yunan Yang
We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the…
Monte Carlo Gradient in Optimization Constrained by Radiative Transport Equation
Qin Li, Li Wang, Yunan Yang
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically p…
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…
Implicit Regularization Effects of the Sobolev Norms in Image Processing
Bowen Zhu, Jingwei Hu, Yifei Lou +1
In this paper, we propose to use the general -based Sobolev norms, i.e., norms where , to measure the data discrepancy due to noise in image processing…
Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures
Yunan Yang, Levon Nurbekyan, Elisa Negrini +2
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for e…
Adjoint DSMC for nonlinear Boltzmann equation constrained optimization
Russel Caflisch, Denis Silantyev, Yunan Yang
Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the…
Anderson Acceleration for Seismic Inversion
Yunan Yang
The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based opti…
Stability of Gibbs Posteriors from the Wasserstein Loss for Bayesian Full Waveform Inversion
Matthew M. Dunlop, Yunan Yang
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this lo…
Anderson Acceleration Based on the Sobolev Norm for Contractive and Noncontractive Fixed-Point Operators
Yunan Yang, Alex Townsend, Daniel Appelö
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in i…
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…
Analysis and Application of Optimal Transport For Challenging Seismic Inverse Problems
Yunan Yang
In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-wavef…
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…