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：在工程领域，从噪声污染数据中准确建模非线性动态系统既关键又复杂。经典的顺序蒙特卡罗(SMC)方法用于这些系统的贝叶斯辨识，有助于量化参数辨识过程中的不确定性。此背景下的一大挑战是连续时间常微分方程(ODEs)的数值积分，这对于将理论模型与离散采样数据对齐至关重要。这种积分引入了额外的数值不确定性，而这一因素往往被忽视。为解决此问题，概率数值学将数值方法（如数值积分）与概率建模相结合，以提供对总不确定性的更全面分析。在保持经典确定性方法精度的同时，这些概率方法能更深入地理解推理过程中固有的不确定性。本文展示了将概率数值方法用于求解非线性动态系统联合参数-状态辨识中的ODEs。所提方法能从噪声测量中高效辨识潜在状态和系统参数，同时将ODEs的概率解融入辨识挑战中。该方法的主要优势在于其能够生成系统参数的后验分布，从而表征数据和辨识过程中固有的不确定性。