One of the most promising applications of machine learning (ML) in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of ML-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. We first perform a systematic review of the ML-for-PDE solving literature. Of articles that use ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) compare to a weak baseline. Second, we find evidence that reporting biases, especially outcome reporting bias and publication bias, are widespread. We conclude that ML-for-PDE solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to underreporting of negative results. To a large extent, these issues appear to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms intended to reduce perverse incentives for doing so.

翻译：机器学习（ML）在计算物理学中最具前景的应用之一是加速偏微分方程（PDE）的求解。基于ML的PDE求解器的核心目标是，相比作为基线比较的标准数值方法，能以更快的速度输出足够精确的解。我们首先对ML求解PDE的相关文献进行了系统性综述。在那些使用ML求解流体相关PDE并声称性能优于标准数值方法的文章中，我们确定有79%（60/76）的论文使用了弱基线进行比较。其次，我们发现报告偏倚（特别是结果报告偏倚和发表偏倚）普遍存在的证据。我们的结论是：ML求解PDE的研究存在过度乐观的问题：弱基线导致了过于积极的结果，而报告偏倚则导致负面结果未被充分报告。在很大程度上，这些问题似乎是由与以往可重复性危机相似的因素引起的：研究者的自由度以及对积极结果的偏好。我们呼吁进行自下而上的文化变革以最小化有偏报告，同时实施自上而下的结构性改革，旨在减少导致此类行为的不良激励。