Most work in equation discovery is concerned with assisting the empirical approach to modeling physical systems. Following this approach, the observed system is modeled on a trial-and-error basis to fit observed data. None of the available domain knowledge about the observed system (or a very limited portion thereof) is used in the modeling process. The empirical approach is contrasts with the theoretical approach to modeling, in which the basic physical processes involved in the observed system are first identified. A human expert then uses domain knowledge about the identified processes to write down a proper structure of the model equations.
Recently, we developed a modeling framework based on equation discovery methods that deal with the problem of integrating the theoretical and empirical approaches to modeling of dynamic systems by integrating different types of theoretical knowledge in the discovery process. Two different types of domain-specific modeling knowledge are considered herein. The first concerns basic processes that govern the behavior of systems in the observed domain. The second concerns existing models that are already established in the domain.
The newly developed modeling framework is successfully applied to different tasks of modeling real-world systems from artificial and real measurement data in the domains of population dynamics (modeling algae and phytoplankton growth in Lagoon of Venice and Danish Lake Glumsoe), neurophysiology (reconstructing Fitzhugh-Nagumo model of neurosignals transmission), classical mechanics, hydrodynamics (modeling water level change in the Danish Ringkobing fjord), and Earth science (revising the CASA model of fluxes of all major biogenic "greenhouse" gases and reactive tropospheric gases).
You can find a more comprehensive description of the modeling framework in my PhD Thesis titled "Using domain knowledge for automated modeling of dynamic systems with equation discovery" or in the jornal-lenght article.
Created: November, 1998
Updated: March, 2004