A general framework for extrapolation-aware prediction reliability in forward and inverse analyses of Gaussian...

Area of Science:

• Machine Learning
• Data Science
• Chemical Engineering

Background:

• Gaussian mixture regression (GMR) and direct inverse analysis (DIA) are vital for molecular, material, and process design.
• Their reliability diminishes when extrapolating beyond training data limits.

Purpose of the Study:

• To introduce a novel Index of Extrapolation (IoE) for assessing extrapolation potential and prediction trustworthiness in GMR models.
• To enhance the reliability and interpretability of machine learning models in data-driven design.

Main Methods:

• The IoE is defined as the negative logarithm of the probability density function.
• It stably distinguishes between interpolation-like and extrapolation-like regions within GMR models.
• Validation involved numerical simulations and applications to diverse datasets (solubility, superconductivity, batch processes).

Main Results:

• The IoE effectively differentiates interpolation and extrapolation regions.
• High IoE regions correlate with decreased prediction reliability and increased error dispersion.
• Successful application across organic solubility, inorganic superconductivity, and batch process datasets.

Conclusions:

• The proposed IoE offers a practical and generalizable framework for evaluating model applicability domains.
• It enhances the trustworthiness of machine learning models, crucial for scientific discovery.
• This supports more efficient data-driven design of novel molecules, materials, and processes.