用微尺度数据发现生物系统宏观方程，验证了偏微分方程在多尺度建模中的潜力。
Evaluating PDE discovery methods for multiscale modeling of biological signals
- 结合粒子模拟与PDE发现框架，从微观数据推导中尺度动态规律。
- 五种方法均能准确恢复钙扩散项，预测浓度变化趋势吻合度高。
- 适合从事生物多尺度建模、机制发现的科研人员参考。
生物系统具有非线性特征，存在未观测变量，其动力学物理原理部分未知，行为表征极具挑战。尤其其活动涉及相互依赖的多时空尺度，需建立跨尺度关联机制。为解决尺度间桥梁问题，本文采用偏微分方程（PDE）发现方法，从微观数据中推断中尺度动态特性。我们构建融合粒子模拟与PDE发现的框架，在受控条件下开展初步实验，评估五种前沿PDE发现方法在星形胶质细胞钙扩散粒子模拟中的表现。评估指标包括所发现方程的形式及钙浓度预测的时间演化。结果表明，多个方法能准确恢复扩散项，证实了PDE发现从微观数据捕捉生物系统宏观动态的可行性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。