arXiv:2502.08881cs.LGstat.ME2025-02被引 1

扩展了非线性参数ODE的高效参数估计方法,提升精度与收敛性。

WENDy for Nonlinear-in-Parameters ODEs

  • 基于弱形式框架,通过局部非凸优化逼近最大似然估计。
  • 在多个基准系统上,精度更高、收敛域更广、速度更快。
  • 支持乘性对数正态噪声,适合复杂动态系统建模与分析。

WENDy 是一种用于常微分方程(ODE)系统参数估计与推断的近期方法,此前仅适用于线性参数的 ODE。本文提出新扩展,可处理更一般的非线性参数 ODE 系统。新算法 WENDy-MLE 通过局部非凸优化逼近最大似然估计,得益于对似然函数及其一阶、二阶导数的解析表达式。该方法在精度、收敛域范围和计算速度上均优于其他弱形式方法及传统的输出误差最小二乘法。此外,框架还扩展至处理乘性对数正态噪声的数据。算法以 Julia 实现,名为 WENDy.jl。通过一系列基准系统的数值实验,全面对比了本方法与其他弱形式方法及输出误差最小二乘法在准确度、精确度、偏差和覆盖率方面的表现。

原文摘要 · Abstract (English)

The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust, computationally efficient, and accurate, but only works for ODEs which are linear-in-parameters. In this work, we derive a novel extension to accommodate systems of a more general class of ODEs that are nonlinear-in-parameters. Our new WENDy-MLE algorithm approximates a maximum likelihood estimator via local non-convex optimization methods. This is made possible by the availability of analytic expressions for the likelihood function and its first and second order derivatives. WENDy-MLE has better accuracy, a substantially larger domain of convergence, and is often faster than other weak form methods and the conventional output error least squares method. Moreover, we extend the framework to accommodate data corrupted by multiplicative log-normal noise. The WENDy.jl algorithm is efficiently implemented in Julia. In order to demonstrate the practical benefits of our approach, we present extensive numerical results comparing our method, other weak form methods, and output error least squares on a suite of benchmark systems of ODEs in terms of accuracy, precision, bias, and coverage.

ODE参数估计弱形式方法非线性模型最大似然

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