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

TL;DR

FNOPE introduces a Fourier Neural Operator-based method for efficient Bayesian inference on function-valued parameters in scientific simulations, significantly reducing computational costs and supporting flexible domain discretizations.

Contribution

It presents a novel SBI approach using FNOs with flow matching, enabling inference of function-valued parameters with lower simulation budgets and greater flexibility.

Findings

Performs inference with fewer simulations than existing methods

Supports arbitrary domain discretizations for posterior evaluation

Successfully applied to complex spatial inference in glaciology

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.