Application of genetic programming for model-free identification of nonlinear multi-physics systems

This study provides a general methodology based on genetic programming (GP) to identify nonlinear multi-physics systems. The proposed GP-based method aims to discover governing equations for the systems, characterized by a set of ordinary differential equations (ODEs), solely from the measured data. The GP-based methodology employs expression trees, having mathematical components in their nodes, to randomly construct candidate models (i.e., ODEs) for the systems and fits them into the measured data set by applying evolutionary processes (e.g., crossover and mutation) over consecutive generations. To enhance the convergence of the identification process, the model fitness is evaluated by computing model outputs that are numerical solutions of the ODEs (i.e., candidate models) under the measured input, and comparing them to the measured output. The proposed generalization of the GP-based method leads to an additional computational burden which is resolved with parallel processing on high-performance computing systems. We demonstrate the applicability of the methodology to two distinct models originating from different physical systems: a Bouc–Wen model from mechanics and an environmental soil-moisture model from ecohydrology. For the Bouc–Wen model, governing equations that are close to the reference model were discovered. The GP-identified models yielded output errors less than 8%, regardless of errors embedded in training data, up to 5%. For the soil-moisture model, relatively simple models are identified with output errors similar to, or less than, 10%. It is shown that the method under discussion is useful in providing some physical insight into the equations that govern complex, nonlinear, multi-physics systems.