Computer simulations are used to model of complex physical systems. Often, these models represent the solutions (or at least approximations) to partial differential equations that are obtained through costly numerical integration. This paper presents a survey of two important statistical/machine learning approaches that have shaped the field of scientific modeling. Firstly we survey the developments on Bayesian calibration of computer models since the seminal work by Kennedy and O’Hagan. In their paper, the authors proposed an elegant way to use the Gaussian processes to extend calibration beyond parameter and observation uncertainty and include model-form and data size uncertainty. Secondly, we also survey physics-informed neural networks, a topic that has been receiving growing attention due to the potential reduction in computational cost and modeling flexibility. In addition, in order to help the interested reader to familiarize with these topics and venture into custom implementations, we present a summary of applications and software tools. Finally, we close the paper with suggestion for future research directions and a thought provoking call for action.

计算机模拟用于对复杂的物理系统进行建模。通常，这些模型表示通过昂贵的数值积分获得的偏微分方程的解（或至少是近似值）。本文介绍了塑造科学建模领域的两种重要的统计/机器学习方法。首先，我们考察了肯尼迪和奥哈根开创性工作以来计算机模型的贝叶斯校准的发展。在他们的论文中，作者提出了一种优雅的方法，可以使用高斯过程将校准扩展到参数和观测不确定性之外，并包括模型形式和数据大小不确定性。其次，我们还调查了物理学上的神经网络，由于计算成本和建模灵活性的潜在降低，该主题已引起越来越多的关注。另外，为了帮助感兴趣的读者熟悉这些主题并尝试定制的实现，我们提供了应用程序和软件工具的摘要。最后，我们在结尾处提出了对未来研究方向的建议，并提出了引发行动的思考。