AI 中文总结
该研究提出iNODE框架，将实用可识别性融入神经微分方程设计，经基准测试表明其可选择紧凑架构、降低参数不确定性并提升动态建模的外推与恢复能力。
AI 中文摘要
神经常微分方程（NODE）及混合NODE模型可为复杂动态系统提供灵活的连续时间表征，但其表达能力可能超出可用数据的信息含量。因此，这些模型在重现观测轨迹的同时，可能存在参数弱可识别性、神经组件约束不足以及外推不可靠的问题。本文提出可识别性感知神经常微分方程（iNODE）框架，将实用可识别性融入神经微分方程的设计中。iNODE模型将神经组件作为显式解析函数嵌入控制方程，支持直接敏感性分析、基于Fisher信息的置信区间计算以及可识别性感知的架构选择。候选架构在数据支持约束下生成，经联合校准后根据预测精度、简约性和参数可识别性进行排序。我们采用四个受控真实基准（涵盖全数据驱动与混合形式、潜在时变参数、部分可观测性以及稀疏或含噪测量），将完整iNODE工作流与当前常用的传统NODE及混合NODE工作流进行对比评估。在相同训练数据和评估场景下，iNODE工作流选择了更紧凑的架构，降低了参数不确定性，并提升了外推能力和潜在动力学恢复效果。这些结果确立了实用可识别性作为简约可靠神经微分方程的模型设计原则。
英文摘要
Neural ordinary differential equations (NODE) and hybrid NODE models provide flexible continuous-time representations of complex dynamic systems, but their expressive capacity can exceed the information content of the available data. Consequently, these models may reproduce observed trajectories while retaining weakly identifiable parameters, poorly constrained neural components, and unreliable extrapolation. Here we introduce identifiability-aware neural ordinary differential equations (iNODE), a framework that incorporates practical identifiability into neural differential equation design. iNODE models embed neural components as explicit analytic functions within the governing equations, enabling direct sensitivity analysis, Fisher-information-based confidence intervals, and identifiability-aware architecture selection. Candidate architectures are generated under data-support constraints, jointly calibrated, and ranked according to predictive accuracy, parsimony, and parameter identifiability. We evaluate the complete iNODE workflow against conventional NODE and hybrid NODE workflows representative of current practice using four controlled ground-truth benchmarks spanning fully data-driven and hybrid formulations, latent time-varying parameters, partial observability, and sparse or noisy measurements. Using the same training data and evaluation scenarios, the iNODE workflow selected more compact architectures, reduced parameter uncertainty, and improved extrapolation and recovery from latent-dynamics. These results establish practical identifiability as a model-design principle for parsimonious and reliable neural differential equations.
