Data-driven modeling for dynamic systems has gained widespread attention in recent years. Its inverse formulation, parameter estimation, aims to infer the inherent model parameters from observations. However, parameter degeneracy, where different combinations of parameters yield the same observable output, poses a critical barrier to accurately and uniquely identifying model parameters. In the context of WECC composite load model (CLM) in power systems, utility practitioners have observed that CLM parameters carefully selected for one fault event may not perform satisfactorily in another fault. Here, we innovate a joint conditional diffusion model-based inverse problem solver (JCDI), that incorporates a joint conditioning architecture with simultaneous inputs of multi-event observations to improve parameter generalizability. Simulation studies on the WECC CLM show that the proposed JCDI effectively reduces uncertainties of degenerate parameters, thus the parameter estimation error is decreased by 42.1% compared to a single-event learning scheme. This enables the model to achieve high accuracy in predicting power trajectories under different fault events, including electronic load tripping and motor stalling, outperforming standard deep reinforcement learning and supervised learning approaches. We anticipate this work will contribute to mitigating parameter degeneracy in system dynamics, providing a general parameter estimation framework across various scientific domains.

翻译：近年来，动态系统的数据驱动建模受到广泛关注。其逆问题形式——参数估计——旨在从观测数据中推断模型固有参数。然而，参数退化现象（即不同参数组合产生相同观测输出）对准确且唯一地识别模型参数构成了关键障碍。在电力系统WECC复合负荷模型（CLM）的背景下，行业实践者发现，针对某一故障事件精心选择的CLM参数在另一故障中可能表现不佳。本文创新性地提出了一种基于联合条件扩散模型的逆问题求解器（JCDI），该求解器采用联合条件架构，同时输入多事件观测数据以提升参数泛化能力。在WECC CLM上的仿真研究表明，所提出的JCDI能有效降低退化参数的不确定性，与单事件学习方案相比，参数估计误差降低了42.1%。这使得模型能够高精度预测不同故障事件（包括电子负载跳闸和电机堵转）下的功率轨迹，其性能优于标准的深度强化学习和监督学习方法。我们预期这项工作将有助于缓解系统动力学中的参数退化问题，为跨科学领域提供一个通用的参数估计框架。