In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate the quantification of uncertainty in the parameter identification process. A significant challenge in this context is the numerical integration of continuous-time ordinary differential equations (ODEs), crucial for aligning theoretical models with discretely sampled data. This integration introduces additional numerical uncertainty, a factor that is often over looked. To address this issue, the field of probabilistic numerics combines numerical methods, such as numerical integration, with probabilistic modeling to offer a more comprehensive analysis of total uncertainty. By retaining the accuracy of classical deterministic methods, these probabilistic approaches offer a deeper understanding of the uncertainty inherent in the inference process. This paper demonstrates the application of a probabilistic numerical method for solving ODEs in the joint parameter-state identification of nonlinear dynamic systems. The presented approach efficiently identifies latent states and system parameters from noisy measurements. Simultaneously incorporating probabilistic solutions to the ODE in the identification challenge. The methodology's primary advantage lies in its capability to produce posterior distributions over system parameters, thereby representing the inherent uncertainties in both the data and the identification process.

翻译：在工程实践中，从含噪数据中准确建模非线性动态系统既至关重要又颇具挑战。用于贝叶斯辨识此类系统的经典序贯蒙特卡洛方法，可在参数辨识过程中量化不确定性。该领域的一个关键难题在于连续时间常微分方程的数值积分——这对理论模型与离散采样数据的对齐至关重要，但此类积分会引入易被忽视的额外数值不确定性。为解决此问题，概率数值学领域将数值积分等数值方法与概率建模相结合，以提供对总不确定性的更全面分析。在保留经典确定性方法精度的同时，这些概率方法能更深入地揭示推理过程中固有的不确定性。本文展示了一种概率数值方法在非线性动态系统联合参数-状态辨识中求解常微分方程的应用。所提方法能从含噪测量中高效识别潜在状态与系统参数，同时将常微分方程的概率解纳入辨识过程。该方法的核心优势在于能生成系统参数的后验分布，从而表征数据及辨识过程中固有的不确定性。