AI 中文总结
HyperODE是一种无需重新训练即可在近似质量守恒的compartmental模型类别中运行的零样本替代模型，可快速完成动力系统模拟与逆推理，性能与专用替代模型相当，还可扩展至破坏质量守恒及受外部驱动的ODE。
AI 中文摘要
理解和控制复杂动力系统通常需要在广阔的参数空间中执行数千次数值模拟，这十分耗时。机器学习替代模型可通过预测不同初始条件和参数值下的状态轨迹显著加速模拟，但这类替代模型专门针对某一个模拟模型，若修改基础微分方程，例如添加生理状态或改变流行病学接触网络，已训练好的模型就会失效，需从头开始进行计算成本高昂的重新训练。我们提出HyperODE，这是一种无需重新训练即可在整个近似质量守恒的 compartmental 模型类别中运行的替代模型。通过将常微分方程（ODE）的结构映射为有向超图，HyperODE将系统交互的函数形式与神经网络架构解耦。HyperODE接收以带有分位数定义的任意参数分布的ODE形式呈现的compartmental模型，将其转换为超图，并以分位数形式输出原始ODE中所有状态的轨迹分布。我们随后利用该替代模型构建编码器，该编码器接收含噪轨迹并输出原始ODE参数的分布，从而一次性完成模型校准。在训练中从未见过的系列模型和系统规模上，HyperODE在单次前向传播中生成校准后的分位数带，其加权区间得分和覆盖率与针对每种结构的专用替代模型相当；对于逆推理，HyperODE使用单个共享编码器在几毫秒内即可从含噪状态轨迹生成校准结果，性能可与现有方法媲美。HyperODE还将零样本能力扩展至破坏质量守恒的ODE及受外部驱动的ODE。
英文摘要
Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming. Machine learning surrogates significantly accelerate simulation by predicting state trajectories across different initializations and parameter values. However, surrogate models are specialized to one simulation model. Modifying the underlying differential equations - e.g., adding a physiological state or altering an epidemiological contact network - renders trained models obsolete and forces computationally expensive retraining from scratch. We introduce HyperODE, a surrogate capable of operating across an entire class of approximately mass-conserving compartmental models without retraining. By mapping the structure of ordinary differential equations (ODEs) into directed hypergraphs, HyperODE decouples the functional form of system interactions from the neural network architecture. HyperODE takes a compartmental model in the form of an ODE with an arbitrary parameter distribution defined through quantiles and transforms it into a hypergraph. It outputs the distribution of the trajectories for all the states in the original ODE in the form of quantiles. We then use this surrogate to build an encoder that takes a noisy trajectory and outputs a distribution over the parameters of the original ODE, thus calibrating the model in a single pass. On families and system sizes never seen in training, HyperODE produces calibrated quantile bands in a single forward pass, with weighted-interval score and coverage on par with specialized surrogates for each structure. For inverse inference, HyperODE produces calibration from noisy state trajectories in a few milliseconds with a single shared encoder, competitive with existing methods. HyperODE extends zero-shot to ODEs that break mass conservation and to external forcing.
Comments13 pages, 14 figures
