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FNOPE Simulation-based inference on function spaces with Fourier Neural Operators

G Moss, LS Muhle, R Drews, JH Macke… - arXiv preprint arXiv …, 2025 - arxiv.org
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… We present FNOPE, a simulation-based inference method using Fourier Neural Operators to efficiently infer function-valued parameters. On a variety of task, we showed …

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@article{2505.22573v1,
Author        = {Guy Moss and Leah Sophie Muhle and Reinhard Drews and Jakob H. Macke and Cornelius Schröder},
Title         = {FNOPE: Simulation-based inference on function spaces with Fourier Neural
  Operators},
Eprint        = {2505.22573v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {cs.LG},
Abstract      = {Simulation-based inference (SBI) is an established approach for performing
Bayesian inference on scientific simulators. SBI so far works best on
low-dimensional parametric models. However, it is difficult to infer
function-valued parameters, which frequently occur in disciplines that model
spatiotemporal processes such as the climate and earth sciences. Here, we
introduce an approach for efficient posterior estimation, using a Fourier
Neural Operator (FNO) architecture with a flow matching objective. We show that
our approach, FNOPE, can perform inference of function-valued parameters at a
fraction of the simulation budget of state of the art methods. In addition,
FNOPE supports posterior evaluation at arbitrary discretizations of the domain,
as well as simultaneous estimation of vector-valued parameters. We demonstrate
the effectiveness of our approach on several benchmark tasks and a challenging
spatial inference task from glaciology. FNOPE extends the applicability of SBI
methods to new scientific domains by enabling the inference of function-valued
parameters.},
Year          = {2025},
Month         = {May},
Url           = {http://arxiv.org/abs/2505.22573v1},
File          = {2505.22573v1.pdf}
}

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