Do weak baselines and reporting biases extend beyond fluid-related forward PDE problems?

Determine whether the reproducibility issues identified for machine-learning-based solvers of fluid-related forward partial differential equations—specifically weak baselines and reporting biases—also affect research using machine learning for inverse PDE problems, solid mechanics PDEs, quantum mechanics PDEs, and high-dimensional PDEs.

Background

The paper analyzes reproducibility issues in machine-learning approaches to solving fluid-related forward PDEs, identifying weak baseline comparisons and reporting biases as key drivers of overoptimistic claims. The evidence includes a systematic review of 82 papers and multiple replication studies showing that many reported speedups vanish when compared against stronger numerical baselines.

Because the paper’s scope is limited to forward problems in fluid mechanics, it remains uncertain whether the same issues pervade other ML-for-PDE domains. Establishing the presence or absence of similar weaknesses in inverse problems and in other PDE areas (solid mechanics, quantum mechanics, and high-dimensional PDEs) is necessary to assess the broader reliability of ML-based scientific simulation claims.