Inferring the Structure of Ordinary Differential Equations
This work addresses the need for interpretable models in understanding physical phenomena, though it is incremental as it builds on existing symbolic regression methods.
The authors tackled the problem of inferring the structure of ordinary differential equations (ODEs) from observational data to improve interpretability over black-box systems, and their extended AIFeynman approach performed best on a benchmark of dynamical systems but struggled with more complex cases like Cart-Pole.
Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and are less amenable for further expert investigation. Alternatively, the dynamics can be analysed via symbolic regression. In this paper, we extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems based on observations from the resulting trajectories. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available. Although the proposed approach performs best on this benchmark, we observed difficulties of all the compared symbolic regression approaches on more complex systems, such as Cart-Pole.