Accelerating tropical cyclone wave height estimation via machine learning and deep latent surrogates

• Delivers fast and accurate Wind-to-Wave estimation by replacing the commercial MIKE21 model with a deep latent surrogate that runs on a workstation-level CPU, reducing computational cost and time by several orders of magnitude while achieving high accuracy ( R 2 = 0.97 , MSE = 0.13 m 2 ). • Benchmarks recent surrogate methods in ML and DL, including point-based, spatio-temporal, and our proposed deep latent model, along with their respective optimisation techniques evaluated on extreme H s . • Introduces a range of pre-processing approaches to address the common issue in ML of underestimating the maximum value of H s during tropical cyclones. Tropical cyclones (TCs) are a major driver of coastal damage and require reliable risk assessment–particularly for extreme coastal waves. Classical partial differential equation (PDE)- based wave models such as SWAN, WAVEWATCH III and MIKE21 have long been used for such estimations, but remain computationally expensive, with practitioners increasingly requiring faster, lightweight tools. This study presents machine learning (ML) and deep learning (DL) surrogates that emulate commercial-grade wind-to-wave models. Our modelling framework aims to estimate Significant Wave Height ( H s ) during TCs, and we target its common underestimation in ML models. The data pre-processing pipeline explicitly targets the under-estimation of the maximum values of H s . It combines oversampling of rare extremes, loss functions weighted toward high-impact cases, and dimensionality reduction via principal component analysis (PCA) to rebalance inputs in a latent space. We evaluate both point-trained tree ensembles for nearshore estimation (Random Forest, XGBoost), and architectures that model space-time structure–convolutional neural networks (CNNs), temporal convolutional networks (TCNs), and long short-term memory (LSTM) networks–in order to capture the complex space-time dependencies in wave dynamics that simpler models fail to represent. We find that a PCA-TCN-LSTM surrogate results in the best peak H s estimation. Across models, runtime drops from around 40 hours on CPU clusters to seconds on a personal computer while maintaining high accuracy for H s (MSE = 0.13 m 2 , R 2 = 0.97 ). These surrogates provide practical tools for scientists, engineers, and first responders to conduct low-cost, real-time coastal-hazard assessment and strengthen climate resilience.