Opals.jl：Julia语言中用于数据同化的全面可组合框架
Opal.jl: a comprehensive, composable framework for data assimilation in Julia
AI总结：
该研究推出Julia包Opals.jl，为数据同化提供统一可组合框架，集成多工具与生态系统，经多基准验证其有效性。
AI中文摘要：
数据同化（DA）与逆建模是将基于物理的模型和观测结果相结合的不可或缺工具，但实现这些方法的软件往往碎片化：序贯（卡尔曼、粒子）滤波器和变分（3D/4D-Var）估计器通常作为独立代码库开发，各自绑定特定类别的正向模型——例如用于常微分方程（ODE）的简单时间推进方案，或用于偏微分方程（PDE）的完整有限元（FE）离散化。本研究介绍Opals.jl，这是一个Julia包，它通过为广泛的DA方法和正向模型后端提供统一环境，克服了这种碎片化，所有这些都可通过单一高级接口访问。从少量基础方法出发，可通过将其与高级功能组合构建复杂推理工具，例如协方差定位/膨胀、在线噪声协方差估计、偏差感知校正以及基于克里金的降阶代理校准。该包原生集成于用于ODE控制系统的SciML生态系统，以及用于PDE全阶和降阶离散化的Gridap/GridapROMs。值得注意的是，其API设计允许降阶代理替换全阶求解器而无需更改代码，甚至在驱动程序层面也无需更改。我们在Lorenz-63基准、带有偏差观测的Van der Pol振子问题、从稀疏速度和压力测量中推断未知雷诺数的方腔湍流Navier-Stokes流动，以及使用降阶代理替代更标准全阶模型的热方程这四个场景中演示了该库。
英文摘要：
Data assimilation (DA) and inverse modelling are indispensable tools for combining physics-based models with observations, yet the software that implements them is often fragmented: sequential (Kalman and particle) filters and variational (3D/4D-Var) estimators are typically developed as separate codebases, each tied to a specific class of forward model - for example, simple time-marching schemes for ordinary differential equations (ODEs), or full finite element (FE) discretisations of partial differential equations (PDEs). In this work, we present Opal.jl, a Julia package that overcomes this fragmentation by providing a unified environment for a wide range of DA methods and forward model backends, all accessible behind a single high-level interface. Starting from a handful of basic methods, complex inference tools can be built by composing them with advanced capabilities, such as covariance localisation/inflation, online noise covariance estimation, bias-aware correction, and kriging-based calibration of reduced-order surrogates. The package integrates natively with the SciML ecosystem for ODE-governed systems, and with Gridap/GridapROMs for both full-order and reduced-order discretisations of PDEs. Notably, the API is designed to allow a reduced-order surrogate to replace a full-order solver with no change to the code, even at the driver level. We demonstrate the library on a Lorenz-63 benchmark, on a Van der Pol oscillator problem with biased observations, on a turbulent Navier-Stokes flow past a square cavity, where the unknown Reynolds number is inferred from sparse velocity and pressure measurements, and finally on a heat equation using a reduced-order surrogate instead of a more standard full-order model.
