Enabling global interpolation, derivative estimation and model identification from sparse multi-experiment time series data via neural ODEs
Enabling global interpolation, derivative estimation and model identification from sparse multi-experiment time series data via neural ODEs
复制标题
DOI：
10.1016/j.engappai.2023.107611
复制
发表时间：
2024-04
期刊：
影响因子：
--
通讯作者：
William Bradley;Ron Volkovinsky;Fani Boukouvala
中科院分区：
文献类型：
--
作者：
William Bradley;Ron Volkovinsky;Fani Boukouvala
根据状态测量估计系统状态的变化率是几个系统分析和建模工作流程中的关键步骤。当数据受到噪声或随机性干扰时，已有许多用于推断时间序列导数的插补模型，但从稀疏时间序列数据集估计导数的通用方法很少。当前方法的一个显著缺点是，它们不能全局拟合由不相同的初始条件(即，多个实验或轨迹)产生的数据，这些方法主要是局部的。在这篇贡献中，神经性ODE(节点)被证明可以缩小这一差距。通过一系列基准测试，我们表明，由于节点的微分公式，这些数据平滑器可以推断稀疏数据的系统动力学，即使代数方法不太可能或基本上不可能进行准确的内插。通过提供的导数估计和模型识别的案例研究，我们讨论了我们所建议的工作流的优点和局限性，并确定了节点导致统计显著改善的情况。综上所述，所提出的方法在从多个实验中分层的稀疏数据中推断导数时具有优势，并为进一步的模型开发和分析方法(例如，参数估计、模型识别、灵敏度分析)奠定了基础。
Estimation of the rate of change of a system's states from state measurements is a key step in several system analysis and model-building workflows. While numerous interpolating models exist for inferring derivatives of time series when data is disturbed by noise or stochasticity, general-purpose methods for estimating derivatives from sparse time series datasets are largely lacking. A notable weakness of current methods, which are largely local, is their inability to globally fit data arising from non-identical initial conditions (i.e., multiple experiments or trajectories). In this contribution, Neural ODEs (NODEs) are demonstrated to close this gap. Through a series of benchmarks, we show that because of the differential formulation of NODEs, these data smoothers can infer system dynamics of sparse data, even when accurate interpolation by algebraic methods is unlikely or fundamentally impossible. Through the presented case studies for derivative estimation and model identification, we discuss the advantages and limitations of our proposed workflow and identify cases where NODEs lead to statistically significant improvements. In summary, the proposed method is shown to be advantageous when inferring derivatives from sparse data stratified across multiple experiments and serves as a foundation for further model development and analysis methods (e.g., parameter estimation, model identification, sensitivity analysis).