Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations
This addresses the challenge of interpretable modeling for experimental data in scientific domains like physics and chemistry, though it appears incremental by building on existing methods.
The paper tackles the problem of modeling empirical data without closed-form expressions, such as stress-strain curves, by proposing Shape Arithmetic Expressions (SHAREs), which combine flexible shape functions from Generalized Additive Models with complex feature interactions, resulting in a framework that balances flexibility and interpretability.
Symbolic regression has excelled in uncovering equations from physics, chemistry, biology, and related disciplines. However, its effectiveness becomes less certain when applied to experimental data lacking inherent closed-form expressions. Empirically derived relationships, such as entire stress-strain curves, may defy concise closed-form representation, compelling us to explore more adaptive modeling approaches that balance flexibility with interpretability. In our pursuit, we turn to Generalized Additive Models (GAMs), a widely used class of models known for their versatility across various domains. Although GAMs can capture non-linear relationships between variables and targets, they cannot capture intricate feature interactions. In this work, we investigate both of these challenges and propose a novel class of models, Shape Arithmetic Expressions (SHAREs), that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. SHAREs also provide a unifying framework for both of these approaches. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints based on the model's size.