I present a method of statically implementing the Sparse Identification of Nonlinear Dynamics (SINDy) framework and the underlying sequential threshold least squares (STLSQ) optimization algorithm to determine best-fit multi-color photometric bandpass transformations between SDSS and LSST. In phase 1, the method is validated against synthetic photometry derived from 1,820 SDSS Stripe 82 clean F and G stellar spectra. -degree SINDy models trained on this sample independently anchor to the corresponding SDSS bandpass magnitudes and exhibit lower residual root-mean-square errors (RMSE) than standard 1D polynomial fits. Although preliminary models seem to outperform the 1D polynomial fits and can transform four bands ( ) with eBOSS derived data, they were evaluated solely on training data and remain susceptible to overfitting, with minor false non-linearities from spectral padding noted as a constraint in the redder bandpasses ( ). In Phase 2, the framework is applied by cross-matching 1,229 stars in the Stripe 82 region ( & ). SDSS photometry from DR19 is matched to synthetic LSST photometry from "The Monster" reference catalog utilizing an 80/20 train/test split. The -, -, and -degree model performances are evaluated against the 20% holdout set. While higher-order SINDy models exhibit signs of overfitting, the overall best-fit SINDy models for each band achieve a 15.7% lower RMSE on average for the test residuals compared to the best-fit 1D polynomials. This improvement is primarily driven by the -order multi-color
- and -band fits, which reduce RMSE by 41.2% and 46.1%, respectively, while the remaining four bands differ by only a few millimagnitudes. Future work will focus on fitting SINDy models to isolated stellar spectral types and color ranges rather than an unconstrained stellar population. Additionally, implementing a sophisticated grid search method to determine the optimal SINDy hyperparameters (sparsity threshold and normalization ) will be necessary to maximize predictive performance while mitigating the risk of overfitting.