Eirik Valseth

Benjamin Pachev, Prateek Arora, Carlos del-Castillo-Negrete et al.

Storm surge is a major natural hazard in coastal regions, responsible both for significant property damage and loss of life. Accurate, efficient models of storm surge are needed both to assess long-term risk and to guide emergency management decisions. While high-fidelity regional- and global-ocean circulation models such as the ADvanced CIRCulation (ADCIRC) model can accurately predict storm surge, they are very computationally expensive. Here we develop a novel surrogate model for peak storm surge prediction based on a multi-stage approach. In the first stage, points are classified as inundated or not. In the second, the level of inundation is predicted . Additionally, we propose a new formulation of the surrogate problem in which storm surge is predicted independently for each point. This allows for predictions to be made directly for locations not present in the training data, and significantly reduces the number of model parameters. We demonstrate our modeling framework on two study areas: the Texas coast and the northern portion of the Alaskan coast. For Texas, the model is trained with a database of 446 synthetic hurricanes. The model is able to accurately match ADCIRC predictions on a test set of synthetic storms. We further present a test of the model on Hurricanes Ike (2008) and Harvey (2017). For Alaska, the model is trained on a dataset of 109 historical surge events. We test the surrogate model on actual surge events including the recent Typhoon Merbok (2022) that take place after the events in the training data. For both datasets, the surrogate model achieves similar performance to ADCIRC on real events when compared to observational data. In both cases, the surrogate models are many orders of magnitude faster than ADCIRC.

Zhi-Song Liu, Markus Büttner, Matthew Scarborough et al.

Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes, specifically, to predict flooding resulting from tsunamis and storm surges. We propose a Downscaling Neural Network for Coastal Simulation (DNNCS) for spatiotemporal enhancement to learn the high-resolution numerical solution. Given images of coastal simulations produced on low-resolution computational meshes using low polynomial order discontinuous Galerkin discretizations and a coarse temporal resolution, the proposed DNNCS learns to produce high-resolution free surface elevation and velocity visualizations in both time and space. To model the dynamic changes over time and space, we propose grid-aware spatiotemporal attention to project the temporal features to the spatial domain for non-local feature matching. The coordinate information is also utilized via positional encoding. For the final reconstruction, we use the spatiotemporal bilinear operation to interpolate the missing frames and then expand the feature maps to the frequency domain for residual mapping. Besides data-driven losses, the proposed physics-informed loss guarantees gradient consistency and momentum changes, leading to a 24% reduction in root-mean-square error compared to the model trained with only data-driven losses. To train the proposed model, we propose a coastal simulation dataset and use it for model optimization and evaluation. Our method shows superior downscaling quality and fast computation compared to the state-of-the-art methods.

Shukai Cai, Sourav Dutta, Mark Loveland et al.

Wave setup plays a significant role in transferring wave-induced energy to currents and causing an increase in water elevation. This excess momentum flux, known as radiation stress, motivates the coupling of circulation models with wave models to improve the accuracy of storm surge prediction, however, traditional numerical wave models are complex and computationally expensive. As a result, in practical coupled simulations, wave models are often executed at much coarser temporal resolution than circulation models. In this work, we explore the use of Deep Operator Networks (DeepONets) as a surrogate for the Simulating WAves Nearshore (SWAN) numerical wave model. The proposed surrogate model was tested on three distinct 1-D and 2-D steady-state numerical examples with variable boundary wave conditions and wind fields. When applied to a realistic numerical example of steady state wave simulation in Duck, NC, the model achieved consistently high accuracy in predicting the components of the radiation stress gradient and the significant wave height across representative scenarios.

Benjamin Pachev, Prateek Arora, Jinpai Zhao et al.

Storm surge is a significant threat to coastal communities across the globe, responsible for loss of life and enormous property damage. Consequently, significant efforts have been expended to develop high-fidelity physics-based models for storm surge prediction. However, such models are often extremely computationally expensive and require supercomputing resources. In recent years, there has been a growing trend towards data-driven surrogate models, which approximate the capabilities of high-fidelity models at a tiny fraction of the computational cost. Most datasets of high-fidelity storm surge model output are limited to narrow geographical regions, with the majority focused on the continental United States and China. This trend is reflected in the scope of existing storm surge surrogate models. In this work, we present a novel dataset for training storm surge surrogate models with global applicability. The dataset consists of high-resolution peak surge output from the ADvanced CIRCulation (ADCIRC) model for over 15,000 landfalling synthetic storms distributed across the world. To the author's knowledge, it is the largest dataset of its kind ever assembled, and is unique in its global scope. We additionally present a machine learning model for peak storm surge based on computer vision architecture. The model is trained on our new global dataset and can accurately predict maximum storm surge in disparate geographical regions - including those for which few or no surrogate models exist. Both the dataset and accompanying model are publicly available, with the aim to support the development of additional storm surge models with global reach.

Jinpai Zhao, Nishant Panda, Yen Ting Lin et al.

We introduce HyCOP, a modular framework that learns parametric PDE solution operators by composing simple modules (advection, diffusion, learned closures, boundary handling) in a query-conditioned way. Rather than learning a monolithic map, HyCOP learns a policy over short programs - which module to apply and for how long - conditioned on regime features and state statistics. Modules may be numerical sub-solvers or learned components, enabling hybrid surrogates evaluated at arbitrary query times without autoregressive rollout. Across diverse PDE benchmarks, HyCOP produces interpretable programs, delivers order-of-magnitude OOD improvements over monolithic neural operators, and supports modular transfer through dictionary updates (e.g., boundary swaps, residual enrichment). Our theory characterizes expressivity and gives an error decomposition that separates composition error from module error and doubles as a process-level diagnostic.

Leszek Siwik, Maciej Sikora, Natalia Leszczyńska et al.

In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate a robust variational framework for the time-dependent advection-diffusion problem and establish the boundedness and inf-sup stability of the corresponding discrete weak formulation. Based on this mathematical foundation, we construct a robust loss function that is directly related to the true approximation error, defined as the difference between the neural network approximation and the (unknown) exact solution. Additionally, a collocation-based strategy is introduced to speed up neural network training. As a case study, we investigate pollution propagation caused by snowmobile traffic in Longyearbyen, Spitsbergen, supported by detailed in-field measurements collected using dedicated sensors. The proposed framework is applied to analyze the effects of thermal inversion on pollutant accumulation. Our results demonstrate that thermal inversion traps dense and humid air masses near the ground, significantly enhancing particulate matter (PM) concentration and worsening local air quality.

Juliusz Wasieleski, Tomasz Służalec, Maciej Woźniak et al.

We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equations, we develop quasi-implicit time integration schemes using direction splitting of the differential operators. We use the Peaceman-Rachford and Strang splitting methods, including the Crank-Nicolson method. Based on these discretizations, we derive variational formulations and explore the Kronecker product structure of the matrices. In the wildfire model, there are some non-linear terms that we treat explicitly. We perform a detailed analysis of how treating these terms affects the stability of the time integration scheme. Namely, we show that a quasi-implicit time integration scheme achieves 10 times higher simulation accuracy. We present two wildfire simulations. The first is a simulation of the 2024 wildfire disaster in the Valparaíso region of Chile. The second one is a simulation of the 2019 wildfire disaster in Las Palmas de Gran Canaria, Spain. We discuss the numerical results and compare them against satellite images and measurement records. We also present a numerical experiment for comparison with the state-of-the-art wildfire simulation model FARSITE. Our sequential code has a linear computational cost of ${\cal O}(N)$. We also present the parallel scalability of the WILDFIRE-IGA-ADS code to illustrate the possibility of running the code on a local workstation.

Jinpai Zhao, Albert Cerrone, Eirik Valseth et al.

Storm surge forecasting plays a crucial role in coastal disaster preparedness, yet existing machine learning approaches often suffer from limited spatial resolution, reliance on coastal station data, and poor generalization. Moreover, many prior models operate directly on unstructured spatial data, making them incompatible with modern deep learning architectures. In this work, we introduce a novel approach that projects unstructured water elevation fields onto structured Red Green Blue (RGB)-encoded image representations, enabling the application of Convolutional Long Short Term Memory (ConvLSTM) networks for end-to-end spatiotemporal surge forecasting. Our model further integrates ground-truth wind fields as dynamic conditioning signals and topo-bathymetry as a static input, capturing physically meaningful drivers of surge evolution. Evaluated on a large-scale dataset of synthetic storms in the Gulf of Mexico, our method demonstrates robust 48-hour forecasting performance across multiple regions along the Texas coast and exhibits strong spatial extensibility to other coastal areas. By combining structured representation, physically grounded forcings, and scalable deep learning, this study advances the frontier of storm surge forecasting in usability, adaptability, and interpretability.