ML models suffer from overoptimism when applied to partial differential equations in computational physics

​A key application of machine learning in computational physics is accelerating the solution of partial differential equations (PDEs). Machine-learning-based PDE solvers aim to produce accurate solutions more quickly than standard numerical methods, used as the baseline for comparison.

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BuzzRobot guest, Nick McGreivy from Princeton University, reviewed the ML-for-PDE-solving literature and found that 79% (60/76) of articles claiming ML outperforms standard methods use weak baselines. He also noted widespread reporting biases, including outcome and publication biases.

Conclusion: ML-for-PDE-solving research is overoptimistic due to weak baselines and under-reported negative results.

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