9 papers
Structure-Preserving Dimension Reduction and Surrogates for Partially Linear Bayesian Inverse Problems
Ziheng Zhang, Dingcheng Luo, Thomas O'Leary-Roseberry +2
Many Bayesian inverse problems are characterized by two parameter vectors with distinct roles. A medium property, operator coefficient, or geometry block enters the forward model n…
Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
Boyuan Yao, Dingcheng Luo, Lianghao Cao +3
We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFN…
Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen +1
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solutio…
LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport
Lianghao Cao, Joshua Chen, Michael Brennan +3
We present LazyDINO, a transport map variational inference method for fast, scalable, and efficiently amortized solutions of high-dimensional nonlinear Bayesian inverse problems wi…
Gaussian mixture Taylor approximations of risk measures constrained by PDEs with Gaussian random field inputs
Dingcheng Luo, Joshua Chen, Peng Chen +1
This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient,…
Inference of Heterogeneous Material Properties via Infinite-Dimensional Integrated DIC
Joseph Kirchhoff, Dingcheng Luo, Thomas O'Leary-Roseberry +1
We present a scalable and efficient framework for the inference of spatially-varying parameters of continuum materials from image observations of their deformations. Our goal is th…
Tempered Multifidelity Importance Sampling for Gravitational Wave Parameter Estimation
Bassel Saleh, Aaron Zimmerman, Peng Chen +1
Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies…
Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems
Lianghao Cao, Thomas O'Leary-Roseberry, Omar Ghattas
We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional Bayesian inverse problems (BIPs). While geometric…
Tensor train construction from tensor actions, with application to compression of large high order derivative tensors
Nick Alger, Peng Chen, Omar Ghattas
We present a method for converting tensors into tensor train format based on actions of the tensor as a vector-valued multilinear function. Existing methods for constructing tensor…