Physics-informed structural diagnostics of model-data agreement beyond scalar metrics.

Area of Science:

• Machine Learning
• Physics
• Data Science

Background:

• Current validation metrics for physics-informed machine learning (PIML) often fail to detect violations of underlying physical laws.
• Scalar accuracy metrics are insensitive to structural incompatibilities between models and data.
• There is a need for validation methods that can differentiate systematic physical errors from random data dispersion.

Purpose of the Study:

• To introduce a novel physics-informed validation framework, the Agreement-Entropy Map (AEM).
• To provide a method for diagnosing model-data agreement by distinguishing structural incompatibility from conditional stochastic dispersion.
• To offer a general and interpretable validation principle for PIML, especially with limited or imperfect data.

Main Methods:

• Developed the Agreement-Entropy Map (AEM) framework for PIML validation.
• Utilized a physically motivated linearization of governing relations.
• Combined regression geometry with an information-theoretic dispersion measure (Gaussian plug-in entropy of residuals).
• Applied the framework to thermodynamic systems as a testbed.

Main Results:

• AEM successfully identified structural bias, variance-driven artifacts, and ensemble effects missed by conventional metrics.
• The framework demonstrated its ability to distinguish between structural incompatibility and stochastic dispersion.
• Validation was performed on matched comparison domains, applicable to both experiment-experiment and model-experiment comparisons.

Conclusions:

• The Agreement-Entropy Map (AEM) provides a more sensitive and interpretable validation approach for PIML.
• AEM enhances the reliability of PIML models by revealing subtle physical inconsistencies.
• This framework is particularly valuable for PIML applications with limited, heterogeneous, or damaged data.