FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators
This work addresses the limitation of SBI in high-dimensional, function-valued inference for scientific domains like glaciology, representing an incremental advancement by adapting existing neural operator architectures to this bottleneck.
The paper tackles the problem of performing simulation-based inference (SBI) on function-valued parameters, which is challenging in fields like climate science, by introducing FNOPE, a method using Fourier Neural Operators with flow matching. The result shows that FNOPE can infer function-valued parameters at a fraction of the simulation budget of state-of-the-art methods, enabling posterior evaluation at arbitrary discretizations and handling vector-valued parameters.
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.