Author

Ralf Herbrich

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#artificial intelligence Preprint Sep 2026

Efficient Message Passing for Partial Differential Equation Priors

Prior information for real-world physical quantities is most elegantly expressed via partial differential equations (PDEs). In this paper, we propose a novel way to solve PDEs using probabilistic inference on a factor graph. In general, factor graphs provide a natural way to encode prior knowledge into a model as expli...

Анна Петровна Казачкова, Leonhard Hennicke, Rainer Schlösser et al. · 0 citations

#artificial intelligence Preprint Sep 2026

Direct Message Approximation (DMA): A Consistency-Based Framework for Tractable Approximate Inference on Factor Graphs

Direct Message Approximation (DMA), which approximates factor-to-variable messages directly rather than the marginal, is introduced and a master theorem (proper messages, any graph) bounding marginal KL from message KL is proved, with three structural corollaries.

Ralf Herbrich, Rainer Schlösser, Jan Lemcke et al. · 1 citation