While 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 Koopman autoencoder with temporal unrolling yields the best overall accuracy compared to the POD-based surrogates, achieving relative root-mean-squared-errors of 0.01-0.13 and $R^2$-values of 0.65-0.996. Prediction errors are largest for current velocities, and smallest for water surface elevations. Comparing to in-situ observations, the surrogate yields -0.65% to 12% change 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.

翻译：虽然基于本征正交分解的代理模型在水动力应用中已得到广泛探索，但Koopman自编码器在实际海岸-海洋建模中的应用仍相对有限。本文提出了一种融合气象强迫与边界条件的柔性Koopman自编码器架构，并系统性地比较了其与基于本征正交分解的代理模型的性能。该Koopman自编码器在潜空间中采用可学习的线性时间算子，通过特征值正则化提升时间稳定性。该策略与时间展开技术相结合，以实现稳定且准确的长期预测。模型在涵盖不同动力学机制的三组测试案例中进行评估，预测时间跨度最长可达一年，时间分辨率为30分钟。在所有案例中，采用时间展开的Koopman自编码器相比基于本征正交分解的代理模型展现出最佳的综合精度，其相对均方根误差为0.01-0.13，$R^2$值为0.65-0.996。预测误差在流速分量上最大，在水面高程上最小。与现场观测数据对比，该代理模型相比基于物理的原始模型，其水面高程预测误差变化范围为-0.65%至12%。这些误差水平（对应数厘米量级）对多数实际应用是可接受的，同时300-1400倍的推理加速比为海岸-海洋建模中的集合预报与长期气候模拟等工作流程提供了可行性。