Prior-Informed Symbolic Regression for Multiview Scientific Discovery
TL;DR
This work presents a multiview symbolic regression method that decomposes predictions into a shared core equation and view-specific residual corrections, and demonstrates that effective multiview symbolic regression depends more on appropriate initialization of the search space than on sophisticated search operators.
Abstract
Scientific modeling often requires discovering mathematical relationships that generalize across multiple related datasets while capturing context-specific deviations. We present a multiview symbolic regression method that decomposes predictions into a shared core equation and view-specific residual corrections. Through systematic ablation studies, we identify domain-informed initialization as the critical success factor: seeding the evolutionary population with common scientific building blocks (polynomials, trigonometric functions, and rational expressions) improves performance by two orders of magnitude compared to random initialization. The multiview decomposition is optimized via NSGA-II with three objectives: prediction accuracy, core complexity, and residual complexity. Additional mechanisms, including elite protection and motif-based enhancement provide consistent but marginal gains. We evaluate our approach on synthetic benchmarks with known ground-truth decompositions and on oceanographic data modeling microbial metabolism across depth layers. On the ocean dataset, our method achieves 99% lower mean squared error than standard multiview symbolic regression, gradient boosting, and neural baselines across 50 prediction targets, while producing interpretable equations that reveal temperature and oxygen as dominant environmental drivers. Our results demonstrate that effective multiview symbolic regression depends more on appropriate initialization of the search space than on sophisticated search operators.