Identifying Concise, Nonlinear Dynamic Models
Phase portraits of vortex-induced vibration from my dissertation .
A fundamental problem in science is the formulation of a model of a system when no a priori knowledge of the process is available. To this end, symbolic regression methods were developed to search for a model’s structure, as well as its parameters, using a stochastic optimization technique known as genetic programming. However, symbolic regression exhibits a well-known phenomenon known as bloat, in which it produces overly complex solutions. We developed a method known as epigenetic local search  that specifically optimizes model structures for conciseness during optimization via a novel developmental encoding. We applied it to the modeling of wind turbine dynamics , as well as fluid dynamics and other non-linear dynamic systems [3, 4] and showed it could find true underlying physical principles. In comparison to non-linear, auto-regressive models, this approach produced simpler and often more accurate models.
La Cava, W., Helmuth, T., Spector, L., & Danai, K. (2015). Genetic Programming with Epigenetic Local Search. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO) (pp. 1055–1062). ACM Press. link, preprint
La Cava, W., Danai, K., & Spector, L. (2016). Inference of compact nonlinear dynamic models by epigenetic local search. Engineering Applications of Artificial Intelligence, 55, 292–306. link, preprint
La Cava, W., Danai, K., Spector, L., Fleming, P., Wright, A., & Lackner, M. (2016). Automatic identification of wind turbine models using evolutionary multiobjective optimization. Renewable Energy, 87, Part 2, 892–902. link, preprint
La Cava, W. G. (2016). Automatic Development and Adaptation of Concise Nonlinear Models for System Identification. link