mlsanityData to 14 Oct 2026

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

arXiv 2505.22573 ↗First posted 28 May 2025cs.LGcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 44 of its 65 references that are in the map. First posted on arXiv 28 May 2025.

Builds on

44 of 65 references.

References · 44

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32 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Simulation-Based Inference: A Practical Guidecited by 32
  2. 2026When Does AI for PDEs Yield Scientific Evidence?cited by 1
  3. 2026PhysDEM: Physics-Defined Energy-Matching Diffusion for Spatiotemporal Field Generation under Scarce Measurementscited by 0
  4. 2026SBNO : Schr"odinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Informationcited by 0

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  5. 2025Physically consistent and uncertainty-aware learning of spatiotemporal dynamics
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  7. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data
  8. 2025Generalized Spherical Neural Operators: Green's Function Formulation