用神经网络提升细胞模拟精度，直接从数据学习动力机制。
Deep Neural Cellular Potts Models
- 用神经网络构建满足对称性的新型能量函数，替代传统物理公式
- 在真实和合成数据上均超越经典模型，捕捉复杂细胞行为
- 适合生物模拟、发育建模等需要高精度细胞动力学的研究者
细胞庞特斯模型（CPM）是模拟生物细胞集体时空动态的强大计算方法。传统方法依赖物理启发的能量函数来驱动系统演化，但生物学中基本原理尚不明确，这些能量函数仅能近似真实多细胞系统的复杂性。为此，我们提出NeuralCPM，一种可直接从观测数据训练的更表达力强的细胞庞特斯模型。其核心是神经能量函数，一个尊重集体细胞动态普遍对称性的神经网络架构。此外，该方法可通过融合已知生物学机制与神经能量函数，实现领域知识的无缝集成。我们在合成及真实多细胞系统上的评估表明，NeuralCPM 能够建模传统解析能量函数无法解释的细胞动态。
原文摘要 · Abstract (English)
The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation with synthetic and real-world multicellular systems demonstrates that NeuralCPM is able to model cellular dynamics that cannot be accounted for by traditional analytical Hamiltonians.
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