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：神经网络作为一种强大的工具，已被广泛用作替代模型，以更高的计算效率为科学问题提供数值解。这种效率对于求解时间敏感或需要评估大量类似分析场景的数值挑战性问题尤为有利。一个备受关注的科学领域是逆问题设定，其中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）动力学观测值推断系统属性。我们考虑一个逆问题：给定二维声波方程的含噪声解，推断方形域内波源的位置。在高斯噪声假设下，可以构建源位置似然函数，每次评估需执行一次正向模拟。通过使用标准神经网络作为替代模型，可多次评估该似然函数，从而利用马尔可夫链蒙特卡洛方法计算波源位置的后验分布。我们证明，该方法能够从含噪声数据中准确推断波源位置。