Evaluating PDE discovery methods for multiscale modeling of biological signals
This work addresses the problem of multiscale modeling in biological signals for researchers, but it is incremental as it focuses on preliminary experiments in controlled settings.
The paper tackled the challenge of bridging gaps between scales in biological systems by evaluating PDE discovery methods on particle-based simulations of calcium diffusion in astrocytes, finding that several methods accurately recovered the diffusion term.
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.