用神经网络建模生化反应动力学,兼顾可解释性与数据适应性。
Learning dynamical systems with biochemically informed neural ordinary differential equations

- 用神经网络表示生化过程,通过线性层映射到状态变化率
- 在多个生物模型中准确恢复轨迹和过程结构
- 适合已知部分机理但过程形式未知的生物系统建模
生化反应的常微分方程模型通常基于反应物之间的相互作用构建,其动力学来源于一系列交互过程。核心挑战在于每个过程的函数形式往往事先未知,且难以从数据中推断。本文提出生化先验神经常微分方程(BINODEs),一种保留机制模型中化学计量结构的神经-ODE框架,其中各过程由神经网络表示。神经网络过程的输出通过类似于化学计量矩阵的线性层映射为状态导数。该架构可直接嵌入生物先验信息,如过程特定输入、符号约束和单调性假设。我们分析了神经网络过程对多种标准生化速率定律的逼近性质,并证明该框架在Monod、Lotka-Volterra、药代动力学及超昼夜内分泌模型中均能准确恢复轨迹与过程级结构。结果表明,BINODEs为部分已知的生化或生物动力系统建模提供了一种兼具机制可解释性与数据驱动灵活性的有效折衷方案。
原文摘要 · Abstract (English)
Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka--Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.
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