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

Area of Science:

• Computational Biology
• Mathematical Biology
• Bioinformatics

Background:

• Mathematical models are crucial for understanding biological pattern formation.
• Current model and parameter selection relies heavily on empirical methods, limiting efficiency and accuracy.

Purpose of the Study:

• To develop a data-driven approach for validating mathematical models of biological pattern formation.
• To automate the selection of appropriate mathematical models and estimation of their parameters.

Main Methods:

• Utilized Contrastive Language-Image Pre-training (CLIP) for zero-shot feature extraction to map pattern images to a latent space for model selection.
• Developed a novel technique for rapid approximate Bayesian inference using Natural Gradient Boosting (NGBoost) for parameter estimation.
• The approach requires minimal constraints, such as time-series data or initial conditions.

Main Results:

• Demonstrated high accuracy and correspondence to analytical features when tested with Turing patterns.
• The developed strategy enables efficient validation of mathematical models based on spatial patterns.
• The method is applicable to various types of mathematical models.

Conclusions:

• The proposed data-driven strategy offers an efficient and accurate method for validating mathematical models in biological pattern formation.
• Automated model selection and parameter estimation using CLIP and NGBoost advance the field of computational biology.