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.

翻译：虽然基于本征正交分解（POD）的替代模型在水动力学应用中已被广泛探索，但Koopman自编码器在真实海岸-海洋建模中的应用仍相对有限。本文提出一种引入气象强迫项和边界条件的灵活Koopman自编码器公式，并将其性能与基于POD的替代模型进行系统比较。该Koopman自编码器在潜空间中采用学习得到的线性时间算子，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共同被评估，以实现稳定且准确的长期预测。模型在三种涵盖不同动力学机制的测试案例上进行评估，预测时长达一年且时间分辨率为30分钟。在所有案例中，采用时间展开的降阶替代模型实现了高精度：相对均方根误差为0.0068-0.14，决定系数R²值为0.61-0.995，其中流速的预测误差最大，水面高程的误差最小。在三个案例中的两个案例里，Koopman自编码器的精度高于基于POD的替代模型。与实地观测相比，该替代模型的水面高程预测误差相较于基于物理模型的预测误差增加了-0.64%至12%。这些误差水平（对应数厘米）对许多实际应用而言是可接受的，同时其推理速度提升300-1400倍，从而支持诸如集合预报和海岸-海洋建模的长期气候模拟等工作流程。