Learning Equations from Biological Data with Limited Time Samples.

Area of Science:

• Computational Biology
• Systems Biology
• Mathematical Modeling

Background:

• Equation learning methods show potential for biological data modeling.
• Previous studies explored equation learning with rich datasets.
• Performance with common biological data challenges (noise, sparsity) is underexplored.

Purpose of the Study:

• To develop and evaluate an equation learning methodology for inferring dynamical systems models from noisy spatiotemporal biological data.
• To investigate the methodology's robustness against sparse sampling, high noise levels, and data heterogeneity.
• To assess the ability to infer underlying equations and predict system dynamics from limited data.

Main Methods:

• A comprehensive equation learning methodology including data denoising, equation learning, model selection, and post-processing.
• Systematic evaluation of the methodology using simulated biological data with controlled challenges.
• Analysis of model inference accuracy and predictive performance under varying data conditions.

Main Results:

• The methodology accurately infers underlying equations from noisy and sparsely sampled spatiotemporal data.
• Successful prediction of unobserved system dynamics is achieved with a small number of time samples.
• Robust performance is demonstrated across tested challenges including noise and data heterogeneity.

Conclusions:

• Equation learning is a viable tool for model discovery and selection in diverse areas of biology.
• An informative dataset is crucial for successful application of equation learning methods.
• The presented methodology offers a robust approach for data-driven modeling, with applications in areas like glioblastoma multiforme tumor invasion prediction.