Data-driven discovery and parameter estimation of mathematical models in biological pattern formation

Mathematical modeling has been utilized to explain biological pattern formation, but the selections of models and parameters have been made empirically. In the present study, we propose a data-driven approach to validate the applicability of mathematical models. Specifically, we developed methods to automatically select the appropriate mathematical models based on the patterns of interest and to estimate the model parameters. For model selection, we employed Contrastive Language-Image Pre-training (CLIP) for zero-shot feature extraction, mapping the given pattern images to latent space and specifying the appropriate model. For parameter estimation, we developed a novel technique that rapidly performs approximate Bayesian inference based on Natural Gradient Boosting (NGBoost). This method allows for parameter estimation under minimal constraints; i.e., it does not require time-series data or initial conditions and is applicable to various types of mathematical models. We tested the method with Turing patterns and demonstrated its high accuracy and correspondence to analytical features. Our strategy enables efficient validation of mathematical models using spatial patterns.