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One of the most promising applications of machine learning in computational physics is the accelerated solution of partial differential equations (PDEs). The main goal of a machine learning-based partial differential equation solver is to produce solutions that are accurate enough faster than standard numerical methods to serve as a baseline comparison. Waxaan marka hore sameyneynaa dib u eegis nidaamsan oo ku saabsan suugaanta barashada mashiinka ee ku saabsan xalinta isleegyada kala duwan ee kaladuwan. Of all the papers reporting the use of ML to solve fluid partial differential equations and claiming superiority over standard numerical methods, we identified 79% (60/76) compared to weak baselines. Midda labaad, waxaan helnay caddeyn ku saabsan warbixin baahsan ee eexda, gaar ahaan gaar ahaan natiijada warbixinta iyo daabacaadda eexda. We conclude that machine learning research on solving partial differential equations is overly optimistic: weak input data can lead to overly positive results, and reporting bias can lead to underreporting of negative results. In large part, these problems appear to be caused by factors similar to past reproducibility crises: investigator discretion and positive outcome bias. Waxaan ugu yeernaa isbedelka dhaqanka ee hoose si loo yareeyo warbixinta ee xuska iyo dib-u-habaynta dhisme-kor-dhismeedka si loo yareeyo dhiirrigelinta qalloocan si sidaas loo sameeyo.
The code needed to reproduce the results in Table 2 can be found on GitHub: https://github.com/nickmcgreivy/WeakBaselinesMLPDE/ (ref. 125) and on Code Ocean: https://codeocean.com/capsule/9605539/ Geed / v1 (isku xirka 126) iyo https://codecean.com/capule/0799002/tree/v1 (isku xirka 127).
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