RASPL Improves Proxy Prediction in Scientific Machine Learning.

In scientific machine learning, it's common to use proxy targets, which are computed from known domain factors, when direct observations are scarce. However, if these same factors are also used as model inputs, a high predictive accuracy might simply indicate that the model is reconstructing the equation used to generate the proxy, rather than genuinely learning robust patterns from potentially degraded or incomplete factor information. This paper introduces a diagnostic framework to identify and analyze this "equation reconstruction" problem. It uses controlled degradation of a key factor (e.g., soil-erodibility in RUSLE-derived soil-loss prediction) to test model robustness. The framework combines various analytical tools, including degraded-formula references, tree-based baselines, and contextual ablations, to thoroughly evaluate model behavior. To address the issue, the researchers propose RASPL (Residual Adaptive Statistical Proxy Learning), a formula-preserving residual framework. RASPL anchors its prediction to the degraded formula estimate and then learns an adaptively gated contextual correction. This approach significantly outperforms direct prediction methods and offers stronger robustness to degradation and tail errors. The findings emphasize that preserving the underlying formula is a central design principle for robust learning from factor-derived proxy targets.