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bayesian inference 1bayesian neural networks 1elliptic partial differential equations 1energy projection 1hamiltonian pdes 1long-time simulation 1neural operators 1operator splitting 1posterior contraction 1soliton dynamics 1

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math.NA2026

Operator-Split Bayesian Learning for Elliptic PDEs with Unequal Interior and Boundary Data

Emmanuel E. Oguadimma

The paper introduces an operator-split Bayesian learning framework that uses independent Bayesian neural‑network priors for interior source and boundary data to solve second‑order…