Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares

TL;DR

This study compares physics-informed neural networks and regularized least-squares methods for modeling calcium signaling in cell cultures, highlighting current limitations and potential improvements in system identification techniques.

Contribution

It introduces a methodology for analyzing calcium delivery in cells and compares PINN and CRLSM approaches, revealing current performance gaps and future research directions.

Findings

CRLSM provides good parameter estimates and data fit.

PINNs currently underperform compared to CRLSM in this context.

Further hyperparameter tuning may enhance PINN performance.

Abstract

Data-driven discovery of dynamics in biological systems allows for better observation and characterization of processes, such as calcium signaling in cell culture. Recent advancements in techniques allow the exploration of previously unattainable insights of dynamical systems, such as the Sparse Identification of Non-Linear Dynamics (SINDy), overcoming the limitations of more classic methodologies. The latter requires some prior knowledge of an effective library of candidate terms, which is not realistic for a real case study. Using inspiration from fields like traffic density estimation and control theory, we propose a methodology for characterization and performance analysis of calcium delivery in a family of cells. In this work, we compare the performance of the Constrained Regularized Least-Squares Method (CRLSM) and Physics-Informed Neural Networks (PINN) for system identification and parameter discovery for governing ordinary differential equations (ODEs). The CRLSM achieves a fairly good parameter estimate and a good data fit when using the learned parameters in the Consensus problem. On the other hand, despite the initial hypothesis, PINNs fail to match the CRLSM performance and, under the current configuration, do not provide fair parameter estimation. However, we have only studied a limited number of PINN architectures, and it is expected that additional hyperparameter tuning, as well as uncertainty quantification, could significantly improve the performance in future works.