Title: VISE:Variational Integration with Symbolic Expressions
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Structure Preserving, ordinary differential equations, symbolic expression

Abstract: We introduce VISE, a novel family of numerical integration method that combines symbolic regression with structure-preserving variational 
integrators to efficiently solve Lagrangian and Hamiltonian ordinary differential equations. Unlike general symbolic regression methods, which seek a single static closed-form expression that may diverge outside the training data or fail to form a valid expression, VISE operates as a hybrid numerical integrator that combines the interpretability of symbolic expressions with the structure-preservation of variational methods. The symbolic expressions serve as adaptive approximation functions with fixed forms whose parameters 
are dynamically updated through discrete Euler-Lagrange equations at each time step. VISE maintains interpretability and inherits the symplectic structure of Hamiltonian systems. Compared to conventional numerical integrators, VISE allows for larger time steps and fewer degrees of freedom, making it potentially suitable for high-dimensional, time-dependent problems where traditional solvers are computationally prohibitive. By leveraging the strengths of both symbolic regression and variational integrators, VISE offers a promising approach for efficiently and accurately solving complex time-dependent systems.