Evaluating PDE discovery methods for multiscale modeling of biological signals

TL;DR

This paper evaluates PDE discovery methods for modeling multiscale biological signals, demonstrating their ability to recover diffusion dynamics from particle-based simulations of calcium in astrocytes.

Contribution

It introduces a framework combining particle simulations with PDE discovery and assesses multiple methods on biological data, highlighting their effectiveness in capturing key dynamics.

Findings

Several PDE discovery methods accurately recover diffusion terms.

Methods effectively predict calcium concentration variations.

PDE discovery shows promise for multiscale biological modeling.

Abstract

Biological systems are non-linear, include unobserved variables and the physical principles that govern their dynamics are partly unknown. This makes the characterization of their behavior very challenging. Notably, their activity occurs on multiple interdependent spatial and temporal scales that require linking mechanisms across scales. To address the challenge of bridging gaps between scales, we leverage partial differential equations (PDE) discovery. PDE discovery suggests meso-scale dynamics characteristics from micro-scale data. In this article, we present our framework combining particle-based simulations and PDE discovery and conduct preliminary experiments to assess equation discovery in controlled settings. We evaluate five state-of-the-art PDE discovery methods on particle-based simulations of calcium diffusion in astrocytes. The performances of the methods are evaluated on both the form of the discovered equation and the forecasted temporal variations of calcium concentration. Our results show that several methods accurately recover the diffusion term, highlighting the potential of PDE discovery for capturing macroscopic dynamics in biological systems from microscopic data.