用傅里叶神经算子实现函数参数的高效贝叶斯推断
FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators
- 基于傅里叶神经算子与流匹配目标，构建函数空间上的推断模型
- 所需模拟次数仅为现有方法的1/10，且支持任意离散化评估
- 适用于气候、冰川等时空过程建模，适合科研人员处理复杂函数参数
基于模拟的推断（SBI）是科学模拟器中进行贝叶斯推断的成熟方法，但当前主要适用于低维参数模型。然而，在气候与地球科学等涉及时空过程的领域中，函数值参数的推断尤为困难。本文提出FNOPE方法，采用傅里叶神经算子（FNO）架构结合流匹配目标，实现高效的后验估计。实验表明，FNOPE在仅需极少量模拟的情况下，即可完成函数参数的高精度推断，其模拟预算仅为现有最优方法的十分之一。此外，该方法支持在任意网格离散下进行后验评估，并可同时估计向量参数。我们在多个基准任务及冰川学中的复杂空间推断任务上验证了其有效性，显著拓展了SBI在新科学领域的应用边界。
原文摘要 · Abstract (English)
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.
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