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

Guy Moss, Leah Sophie Muhle, Reinhard Drews, Jakob H. Macke, Cornelius Schröder

Keywords: simulation-based inference, Fourier Neural Operators, flow matching, applications

TL;DR: We propose a method for performing simulation-based inference (SBI) of function-valued parameters, and apply it to spatial inference problems in the geosciences.

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.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 12176