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Research questionHow can informative Bayesian priors be constructed and sampled for PDE inverse problems with infinite-dimensional parameters?PDE inverse problems require inferring function-valued parameters from incomplete information, while prior assumptions must remain mathematically well-defined in infinite dimensions. Posterior sampling becomes difficult when those priors must capture informative structure rather than remain simple reference measures.
Machine Learning
Research Paper
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse ProblemThe source considers infinite-dimensional Bayesian inference for PDE inverse problems, using continuous normalizing flows defined through neural ordinary differential equations in Hilbert space. It establishes well-posedness, gives training procedures for two data settings and two posterior-sampling algorithms, and reports applications to smooth inverse, inverse scattering, and inverse heat-conduction problems with numerical support.research paper · Sep 3, 2026
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