Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where time to solution is important or when evaluation of many similar analysis scenarios is required. One particular area of scientific interest is the setting of inverse problems, where one knows the forward dynamics of a system are described by a partial differential equation and the task is to infer properties of the system given (potentially noisy) observations of these dynamics. We consider the inverse problem of inferring the location of a wave source on a square domain, given a noisy solution to the 2-D acoustic wave equation. Under the assumption of Gaussian noise, a likelihood function for source location can be formulated, which requires one forward simulation of the system per evaluation. Using a standard neural network as a surrogate model makes it computationally feasible to evaluate this likelihood several times, and so Markov Chain Monte Carlo methods can be used to evaluate the posterior distribution of the source location. We demonstrate that this method can accurately infer source-locations from noisy data.

翻译：神经网络已成为一种强大的工具，可作为代理模型为科学问题提供数值解，同时提高计算效率。这种效率对于求解时间至关重要或需要评估大量相似分析场景的数值难题尤为有利。其中一个特别受关注的科学领域是逆问题设定——即已知系统的正向动力学由偏微分方程描述，任务是根据（可能含噪声的）动力学观测推断系统属性。我们考虑的逆问题是在给定二维声波方程含噪解的情况下，推断正方形域内波源的位置。在高斯噪声假设下，可构建波源位置的似然函数，该函数每次评估需要一次正向系统模拟。通过使用标准神经网络作为代理模型，可实现对似然函数的多次计算，进而采用马尔可夫链蒙特卡洛方法评估波源位置的后验分布。我们证明该方法能够从含噪数据中准确推断波源位置。