发表机构
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge（剑桥大学纯数学与统计数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非线性逆问题中观测噪声相依的情形，给出后验一致性的充分条件，并应用于纳维-斯托克斯方程与空间非均匀反应-扩散方程，提出含时间累积的达西输运算子新稳定性估计。
AI 中文摘要
设 $\theta \to \mathcal G(\theta)$ 为从参数到建模动力系统的某类非线性偏微分方程解的映射。我们在观测 $\mathcal G(\theta)$ 且噪声相依（用于建模测量传感器潜在的时间相关性）的条件下，给出了证明 $\theta$ 后验一致性的条件。我们提供了两个例子：一是具有未知粘度和初始条件的纳维-斯托克斯方程，二是扩散系数在空间上变化（非均匀）的反应-扩散型方程，后者需要对具有时间累积的达西输运算子建立新的稳定性估计。
英文摘要
Let $θ\to \mathcal G(θ)$ be a map from a parameter to the solution of some non-linear partial differential equation modelling a dynamical system. We provide conditions to show posterior consistency for $θ$ under observations of $\mathcal G(θ)$ with dependent noise, modelling potential time-correlations of the sensors used to make the measurements. We provide two examples, namely the Navier-Stokes equations with unknown viscosity and initial condition, as well as a Reaction-Diffusion type equation with diffusivity coefficient that is varying (heterogeneous) in space, which requires novel stability estimates for a Darcy transport operator with accumulation in time.
