Neuro-Evolutionary Method for Coupled Multi-Output Symbolic Regression

A novel neuro-evolutionary approach to symbolic regression overcomes the constraints of conventional methods, which typically focus on a single output. In process systems, state variables are interconnected through common physical parameters, leading to precise but often unclear individual equations when regression is performed independently. The new technique identifies a common symbolic framework—a collection of latent symbolic units that can be discovered once and applied across multiple outputs using sparse additive or multiplicative read-outs. The structure of the discrete model evolves through mutation and crossover, while continuous parameters are optimized via gradient descent and passed down to offspring. This method was tested against benchmarks with established ground truth and a hydrothermal liquefaction yield scenario. Findings suggest that while coupling does not universally enhance performance, this strategy facilitates the creation of physically consistent multi-output models.