The field of symbolic regression and dynamical systems is experiencing significant growth, with innovative methods being developed to improve the accuracy and efficiency of these systems. One of the key areas of focus is the development of new techniques for symbolic regression, including the use of dimension reduction and iterative procedures to identify valid substitutions and improve the performance of state-of-the-art algorithms. Additionally, researchers are exploring the application of symbolic regression to complex dynamical systems, such as Hamiltonian systems, and developing new methods for learning the governing equations of these systems directly from observational data.

Noteworthy papers in this area include: Looking for Signs: Reasoning About FOBNNs Using SAT, which presents a sound and efficient reduction of the first-order FOBNN transition relation to a propositional logic formula, enabling the use of modern SAT solvers to reason on the full transition graph. Discovering Symmetries of ODEs by Symbolic Regression, which adapts search-based symbolic regression to the task of finding generators of Lie point symmetries, allowing for the discovery of symmetries that existing computer algebra systems cannot find. H-FEX: A Symbolic Learning Method for Hamiltonian Systems, which proposes a novel symbolic learning method that introduces interaction nodes to capture intricate interaction terms effectively, demonstrating the ability to recover Hamiltonian functions of complex systems that accurately capture system dynamics and preserve energy over long time horizons.