Shared Symbolic Backbones Enable Physically Consistent Multi-Output Regression

Traditional symbolic regression applies one output at a time, which breaks down when state variables are coupled through shared physical parameters. Manuel Rodriguez introduces a neuro-evolutionary method that searches for a "shared symbolic backbone"—a set of latent symbolic units discovered once and reused by multiple outputs via sparse additive or multiplicative read-outs. The discrete model structure evolves through mutation and crossover, while continuous parameters are tuned by gradient descent and inherited by offspring. This approach targets process systems where cross-output consistency matters more than raw prediction error.

Tested on benchmarks with known ground truth and a hydrothermal liquefaction yield case, the method reveals that coupling does not universally lower prediction error. Its core value lies in enforcing and diagnosing consistency when a physically shared factor is embedded in a latent expression and weakly identifiable from data—for example, Langmuir-Hinshelwood denominators where independent PySR fails to close the consistency gap. Conversely, for well-identifiable systems like the Van de Vusse benchmark, independent regression matches or outperforms the coupled model. Rather than a general-purpose predictor, this framework is a structured shared-mechanism extractor, most valuable when the target structure is sparse, shared, weakly identifiable, or constrained by closure.