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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…
Real-time inverse solutions via neural matrix operators
Julie Pham, Thomas O'Leary-Roseberry, Omar Ghattas +1
Rapid data assimilation is required for real-time prediction and control in digital twins. For many physical systems, the data assimilation task requires the solution of a physics-…
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…