在高数据污染下同时进行模型发现和状态估计
Simultaneous model discovery and state estimation under high data corruption
AI总结：
本文提出了一种基于稀疏回归的模型发现和状态估计方法，通过统计似然函数和优化算法在高噪声环境下实现高效建模。
摘要：
本文提出了一种稀疏回归策略，用于从不完整和噪声数据中发现常微分方程。通过统计动机的似然函数对方程参数和状态变量进行推断。通过迭代删除项并使用统计信息准则比较模型来强制稀疏性。使用Levenberg-Marquardt方法的二阶变体进行大规模优化，其中梯度和Hessian通过自动微分计算。所提出的方法在几个具有不同噪声和不完整数据水平的系统上进行了说明和测试。与最先进的系统识别算法进行比较，展示了所提出方法的竞争力。
英文摘要：
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated likelihood function. Sparsity is enforced by a selection algorithm which iteratively removes terms and compares models using statistical information criteria. Large scale optimization is performed using a second-order variant of the Levenberg-Marquardt method, where the gradient and Hessian are computed via automatic differentiation. The proposed method is illustrated and tested on several systems with varying levels of noisy and incomplete data. Comparisons are made to a state-of-the-art algorithm for system identification, demonstrating competitiveness of the proposed approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
