Eliminate concentration spikes in SINDy-based surrogate simulations

Eliminate occasional concentration spikes in simulations of the Sparse Identification of Nonlinear Dynamics (SINDy) surrogate ordinary differential equation system trained on one-hour data for the simplified photochemical mechanism with 11 species and 10 reactions, achieving stable trajectories without relying on negative-coefficient buffer terms added to higher-order polynomials.

Background

The paper develops a SINDy-based surrogate model for a simplified atmospheric photochemical mechanism and demonstrates numerical stability and speed improvements over long simulation periods. During testing, some simulations exhibited occasional concentration spikes, which the authors could keep from becoming exploding errors by adding small negative buffer terms to higher-order polynomial components of the discovered equations.

Despite this mitigation, the authors explicitly state they are not yet able to prevent the spikes completely. Addressing this unresolved issue is important for ensuring robust stability of SINDy-based surrogates without ad hoc stabilizing terms, particularly as the approach is scaled to more complex mechanisms.