On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

TL;DR

This paper proposes a taxonomy of PDE evaluation metrics and discusses their advantages and limitations. It aims to promote standardized and reliable practices in PDE discovery. The paper provides recommendations for ML experts and users of PDE discovery methods.

Why It Matters

The evaluation of discovered PDEs is crucial for scientific advancement and real-world applications. Standardized practices can prevent overly interpreted conclusions and ensure the validity of new physical theories. Reliable PDE discovery methods can lead to breakthroughs in various fields, including physics and engineering.

Key Findings

• taxonomy of PDE evaluation metrics
• importance of considering multiple properties
• need for standardized practices