用神经场重参数化4DVAR,提升天气预报初始条件精度与稳定性。
On the Effect of Neural Field Reparameterization for 4DVAR
- 用神经网络连续表示时空状态,优化参数空间提升稳定性。
- 在2D柯尔莫哥洛夫流和3D泰勒-格林涡旋上精度优于传统4DVAR。
- 无需真实训练数据,适合实时气象业务应用。
四维变分数据同化(4DVAR)是数值天气预报的核心,但计算成本高且对初值敏感,因其目标函数非凸。本文提出基于神经场的4DVAR重构方法,将时空状态建模为由神经网络参数化的连续函数。优化参数空间可利用神经场的谱偏差,起到隐式正则化作用,稳定状态估计并抑制虚假高频振荡,无需显式背景误差协方差信息。通过参数化完整时空轨迹,该框架支持时间并行优化,并可通过物理信息损失直接融入物理约束。在混沌基准测试(包括2D柯尔莫哥洛夫流和3D泰勒-格林涡旋)中,神经再参数化生成的初始条件比经典4DVAR更准确。结合可分离神经架构(SPINNs),实现显著加速。不同于多数机器学习方法,本框架无需真实训练数据,为业务化数据同化提供稳健可扩展的替代方案。
原文摘要 · Abstract (English)
Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, yet it remains computationally intensive and sensitive to initialization due to the non-convexity of its objective function. We propose a neural field-based reformulation of 4DVAR in which the spatiotemporal state is represented as a continuous function parameterized by a neural network. We demonstrate that optimizing in parameter space leverages the spectral bias of neural fields, acting as an implicit regularizer that stabilizes state estimation and suppresses spurious high-frequency oscillations without requiring explicit background error covariance information. Furthermore, by parameterizing the full spatiotemporal trajectory, our framework enables parallel-in-time optimization and incorporates physical constraints directly through physics-informed losses. Evaluations on chaotic benchmarks, including 2D Kolmogorov flow and 3D Taylor-Green vortices, show that neural reparameterization produces more accurate initial conditions than classical 4DVAR. When combined with separable neural architectures (SPINNs), the method achieves substantial speedups. Unlike many machine learning approaches, this framework requires no ground-truth training data, offering a robust and scalable alternative for operational data assimilation.
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