[论文解读] Turning mechanistic models into forecasters by using machine learning

Amit K. Chakraborty, Hao Wang+1 more|arXiv (Cornell University)|Feb 4, 2026

Model Reduction and Neural Networks被引用 0

一句话总结

原文直接回答摘要：作者开发了一个数据驱动框架，通过稀疏回归发现随时间变化的参数来扩展力学ODE模型，并利用ML对这些参数进行预测，以提升学习和预测性能；在四个数据集上得到验证，并在基线CNN-LSTM和GBM上具有更好表现。

ABSTRACT

The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from time-series data using a library of functions constructed from the measured variables. However, these methods typically assume time-invariant coefficients, which limits their ability to capture evolving system dynamics. To overcome this limitation, we allow some of the parameters to vary over time, learn their temporal evolution directly from data, and infer a system of equations that incorporates both constant and time-varying parameters. We then transform this framework into a forecasting model by predicting the time-varying parameters and substituting these predictions into the learned equations. The model is validated using datasets for Susceptible-Infected-Recovered, Consumer--Resource, greenhouse gas concentration, and Cyanobacteria cell count. By dynamically adapting to temporal shifts, our proposed model achieved a mean absolute error below 3\% for learning a time series and below 6\% for forecasting up to a month ahead. We additionally compare forecasting performance against CNN-LSTM and Gradient Boosting Machine (GBM), and show that our model outperforms these methods across most datasets. Our findings demonstrate that integrating time-varying parameters into data-driven discovery of differential equations improves both modeling accuracy and forecasting performance.

研究动机与目标

• 感知在固定参数力学模型之外学习演化动态系统的必要性。
• 引入基于两阶段SINDy的方法来识别哪些参数应随时间变化。
• 将时变参数与预测相结合，通过ML对其进行预测。
• 通过将预测的时变参数代入学习到的ODE，展示预测能力。

提出的方法

• 从状态变量和输入变量构建候选函数库，全部次数最大为 d。
• 以两阶段方式应用稀疏非线性动力学辨识（SINDy）来识别常数系数和时变系数。
• 在滑动窗口内，选择前 N 个活跃项，其系数被视为时变，其余项保持不变。
• 利用由外部协变量（如天气变量）驱动的机器学习模型预测时变系数。
• 用预测参数更新ODE右端项以生成预测。
• 在各数据集上将预测性能与CNN-LSTM和GBM基线进行比较。

实验结果

研究问题

• RQ1 与常数系数SINDy相比，时变参数能否提高模型拟合和预测准确性？
• RQ2 如何高效地识别哪些参数应随时间变化？
• RQ3 能否从协变量中准确预测时变参数，以及这对状态预测有何影响？
• RQ4 所提框架是否能在模拟与真实动力系统（SIR、CR、GHG、蓝藻）之间泛化？

主要发现

• 学习时间序列时的平均绝对误差低于3%，预测至多一个月时误差低于6%。
• 框架通过允许选定参数变化来适应时序变化，同时保持其他参数不变。
• 在大多数数据集上，该方法优于基线CNN-LSTM和GBM。
• 时变参数整合在SIR、CR、GHG浓度、蓝藻计数等系统中显著提升建模精度与预测性能。