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

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.

@article{moss2025_2505.22573,
  title={ FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators },
  author={ Guy Moss and Leah Sophie Muhle and Reinhard Drews and Jakob H. Macke and Cornelius Schröder },
  journal={arXiv preprint arXiv:2505.22573},
  year={ 2025 }
}