用新模型提升海洋模拟速度,预测一年数据仅需数秒。
Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models
- 用学习的线性时间算子构建动态稳定的新代理模型
- 预测误差仅几厘米,一年预报准确率高达99.5%
- 比传统方法快300到1400倍,适合气候模拟和集合预报
尽管基于奇异值分解(POD)的代理模型在水动力学中广泛应用,但其在真实海岸海洋建模中的应用仍有限。本文提出一种灵活的柯尔莫哥洛夫自编码器(Koopman autoencoder)框架,融合气象强迫与边界条件,并系统比较其与基于POD的代理模型性能。该模型在隐空间中采用学习得到的线性时间算子,通过特征值正则化增强时间稳定性,结合时间展开技术实现长期稳定准确预测。在三个涵盖不同动力学状态的测试案例上评估,时间分辨率达30分钟,预测周期长达一年。所有案例中,带时间展开的降维代理模型均保持高精度,相对均方根误差为0.0068–0.14,决定系数达0.61–0.995,其中流速预测误差最大,水面高度最小。在其中两个案例中,柯尔莫哥洛夫自编码器优于基于POD的代理模型。与实测数据相比,代理模型对水面高度的预测误差增加-0.64%至12%,对应误差仅几厘米,对多数实际应用可接受;推理速度提升300–1400倍,支持集合预报与长期气候模拟等高效工作流。
原文摘要 · Abstract (English)
While proper orthogonal decomposition (POD)-based surrogates are widely explored for hydrodynamic applications, the use of Koopman autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary conditions, and systematically compares its performance against POD-based surrogates. The Koopman autoencoder employs a learned linear temporal operator in latent space, enabling eigenvalue regularization to promote temporal stability. This strategy is evaluated alongside temporal unrolling techniques for achieving stable and accurate long-term predictions. The models are assessed on three test cases spanning distinct dynamical regimes, with prediction horizons up to one year at 30-minute temporal resolution. Across all cases, the reduced order surrogates with temporal unrolling achieve high accuracy with relative root-mean-squared-errors of 0.0068-0.14 and $R^2$-values of 0.61-0.995, where prediction errors are largest for current velocities, and smallest for water surface elevations. In two of the three cases, the Koopman Autoencoder have higher accuracy than the POD-based surrogates. Comparing to in-situ observations, the surrogate yields -0.64% to 12% increase in water surface elevation prediction error when compared to prediction errors of the physics-based model. These error levels, corresponding to a few centimeters, are acceptable for many practical applications, while inference speed-ups of 300-1400x enables workflows such as ensemble forecasting and long climate simulations for coastal-ocean modelling.
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