Sparse, interpretable, and parsimonious reduced-order modeling of hydrodynamic forces in undulating swimmers

Modeling the complex fluid–structure interactions in fish-like propulsion is a significant challenge, and high-fidelity simulations are computationally prohibitive for design optimization or real-time control. To address this, we introduce sparse identification of nonlinear dynamics (SINDy) for fish-like motion (SINDy-Fish), a sparse, human-interpretable, and parsimonious reduced-order modeling framework for predicting hydrodynamic forces on undulating swimmers. Leveraging sparse regression, specifically, the mixed-integer optimization sparse regression on high-fidelity computational fluid dynamics data, SINDy-Fish discovers the underlying governing equations from data. We apply this framework to an anguilliform (eel-like) swimmer at a Reynolds number of 5000 and across biologically relevant, thrust-producing Strouhal numbers (St = 0.3–0.5). Model parsimony and accuracy are systematically balanced using the Akaike Information Criterion. The results show exceptional predictive accuracy, with R2 scores exceeding 0.94 for lift and 0.995 for drag on unseen test data. The identified model for lift is a self-excited, self-limiting nonlinear oscillator with cubic nonlinearity, which successfully recovers a stable limit cycle, while drag is modeled by a concise algebraic expression of the lift dynamics. By generating explicit, computationally efficient equations, SINDy-Fish provides a powerful and scalable tool for the design, optimization, and real-time control of energy-efficient bioinspired underwater robots.