32 citations · 127 across the 22 of their papers we have counts for
6 papers · 1 filter
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…