标题： 基于粒子滤波的系统方法用于在具有源项的对流扩散方程中估计时变参数 显示英文标题

标题： A Systematic Particle Filter for Estimating Time-Varying Parameters in Advection-Diffusion Equations with Source Terms

摘要： 许多使用偏微分方程（PDEs）建模的现实世界系统涉及必须从有限、噪声的系统观测中估计的未知参数。 通常假设这些未观测参数为常数，但其中一些可能随时间变化。 本研究提出了一种两阶段的离线-在线数值过程，用于系统地估计和量化时变参数（TVPs）在时依赖PDEs中的不确定性，特别关注源项中包含TVP的对流扩散模型。 在一维测试问题集上的数值结果表明，所提出的估计过程在跟踪不同形式的未知TVP的同时，能够从离散空间位置和时间处的解的部分、噪声观测中同时估计影响TVP演化模型的方差参数。 显示英文摘要

摘要： Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved parameters may vary with time. This work proposes a two-phase, offline-online numerical procedure for systematically estimating and quantifying uncertainty in time-varying parameters (TVPs) in time-dependent PDEs, specifically focusing on advection-diffusion models with TVPs involved in the source terms. Numerical results on a set of one-dimensional test problems demonstrate the effectiveness of the proposed estimation procedure in tracking unknown TVPs of different forms, while simultaneously estimating variance parameters affecting the TVP evolution model, from partial, noisy observations of the solution at discrete spatial locations and times.