arXiv subjects

Eirik Valseth

Publications and source records attributed to Eirik Valseth.

At least 19 recordsLinked to original sources

arXiv2026

Investigating Forecast Proficiency of Hurricane-Induced Compound Flooding With a Discontinuous Galerkin Shallow Water Equation Solver

Recent severe storms on the U.S. Gulf coast have demonstrated the challenges presented by compound flooding, such as the interactions between rainfall runoff and storm surge. Historically, many studies have neglected these nonlinear interactions, but we propose to use a discontinuous Galerkin shallow water equation solver, which allows for incorporation of rainfall inputs directly onto the finite element mesh. In this work, we analyze the use of parametric rainfall for forecasting scenarios, using Hurricane Beryl (2024) as a case study. Beryl led to extensive flooding due to rainfall and storm surge along the Gulf. We use a collection of the National Oceanic and Atmospheric Administration's short-term advisories along with the best track data to demonstrate the efficacy of the parametric rainfall model for forecasting. Results show that the parametric rainfall input allowed for much more accurate inundation. Areas with heavy rainfall and low surge were affected the most, with many areas peaking over 50 cm above the baseline surge model. Almost none of the available high water marks from Beryl were captured by the standard models, but the compound flooding models capture many of them, the majority of which show relative errors under 10 percent. Results from the advisory forecast simulations were shown to be much closer to the best track hindcast simulation when rainfall forcing was used, even while early forecasts predicted the storm's trajectory much less accurately. The advisory simulations improved even further as Beryl neared the Texas coast, with sampled peak elevations most closely approximating the best track at Advisory 38, a few hours before landfall.

cs.CE↗

arXiv2026

Modeling the Hydrodynamics in the Oslofjord using ADCIRC

This study introduces a new unstructured computational mesh for hydrodynamic simulations of the Oslofjord. The mesh was created with global bathymetry and shoreline data, using OceanMesh2D. It contains 70,410 nodes, with a resolution at the coastline of 50 meters. We use the new mesh to create an ADCIRC model of the fjord. The model is run for four time periods with different characteristics, and validated against the current state of the art and elevation gauges in the fjord. Results show that the model achieves similar results to the model currently used for forecasting in Norway, while requiring much less computation time. Three different combinations of tidal constituents are used to force the model, and analyze the cost and benefits of using additional constituents, finding that they slightly improve results. However, the skill of the tidal forcing boundary condition is limited, because of the small domain of the Oslofjord. In order to further reconcile the results' deviation from the gauge data, especially during extreme weather events, the water surface elevation output from a global ADCIRC model was used to force the model instead of tides.

cs.CE↗

arXiv2026

HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs

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.

cs.CE↗

arXiv2026

Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen

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. We also extend our model to the non-linear Burgers-type equations. 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. We compare our method to linear computational cost explicit dynamics solver using isogeometric analysis. We show that our method can solve non-linear non-stationary problem four times slower than IGA solver can solve the linear problem. It makes it particularly interesting to investigate the non-linear extensions with similar computational cost as the linear formulation.

cs.LG↗

arXiv2026

Wildfires Quasi-Implicit Alternative-Direction Simulations using Isogeometric Finite Element Method

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.

cs.CE↗

arXiv2026

Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models

The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also known as radiation stresses, and their spatial gradients. Accurate storm surge prediction requires coupled circulation and wave models, but the high computational cost of numerical wave models limits their temporal resolution. In this work, we explore a proof-of-concept application of Deep Operator Networks (DeepONets) as a surrogate for the Simulating WAves Nearshore (SWAN) numerical wave model. Unlike grid-dependent surrogate models, DeepONets learn the underlying continuous operator, and thus, can provide highly efficient prediction while enabling discretization-invariant inference. The proposed surrogate model is evaluated using two 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 DeepONet surrogate improves computational efficiency by four orders of magnitude. Furthermore, the model demonstrates consistently high accuracy in predicting the significant wave height and the x- and y- components of the radiation stress gradient, by achieving relative L_2 errors bounded by 1.91%, 10.98%, and 6.88%, respectively, across all unseen test scenarios.

physics.comp-ph↗

arXiv2026

Coupled Continuous-Discontinuous Galerkin Finite Element Solver for Compound Flood Simulations

Several recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be correctly modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a locally conservative coupled DG-CG discretization of the shallow water equations and integrate it into the Advanced Circulation Model (ADCIRC). We also modify the continuity equation to include spatially and temporally variable rainfall into the model using parametric rainfall models. We demonstrate the capabilities of the scheme though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach.

physics.comp-ph↗

arXiv2026

Global Location-Invariant Peak Storm Surge Prediction

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.

cs.CE↗

arXiv2026

Downscaling Neural Network for Coastal Simulations

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.

eess.IV↗

arXiv2025

GPU-acceleration of the Discontinuous Galerkin Shallow Water Equations Model (DG-SWEM) with OpenACC

This paper presents a porting of {DG-SWEM}, a first-order discontinuous Galerkin solver for storm surge based on the Advanced Circulation Model (ADCIRC), to NVIDIA GPUs. Time-explicit discontinuous Galerkin methods contain a large number of degrees of freedom but have been shown to exhibit a large amount of data parallelism due to the loose coupling between elements, and thus are naturally mapped to the GPU architecture. A previous framework in porting DG-SWEM to GPUs required converting subroutines from Fortran to C++ to be used with CUDA C++. By using OpenACC and Unified Memory, we simplify the porting process and maintain a single codebase for both CPU and GPU versions. We test the code using a large Hurricane Harvey scenario on NVIDIA's Grace Hopper chip, and compare the GPU code's performance on multiple H200 nodes to the CPU version on the same amount of Grace CPU nodes.

physics.comp-ph↗

arXiv2025

Storm Surge in Color: RGB-Encoded Physics-Aware Deep Learning for Storm Surge Forecasting

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.

cs.CE↗

arXiv2025

Potential Effects of Loading Terminal Locations on Surface Trajectories of Oil Spill Transport

We present an investigation comparing the potential impacts of offshore and onshore crude oil loading sites on surface trajectories of spilled oil particles in the regions near the Port of Corpus Christi, Texas. Oil transport is established in a two step procedure. First, the circulation and flow characteristics of seawater throughout the coastal ocean are established for various flow conditions, including current and proposed channel depth, seasonality changes, and extreme weather events. Then, spilled oil is modeled as distinct particles released at either the proposed onshore or offshore loading locations. The particle trajectories are tracked and used to assess the spread into diverse coastal ecosystems with extensive plant, sea, and land life. The models indicate that the extent of spread of these simulated oil spills to ecologically significant regions is greater when initiated at the onshore loading site than at the offshore site.

physics.comp-ph↗

arXiv2024

Stabilization of isogeometric finite element method with optimal test functions computed from $L_2$ norm residual minimization

We compare several stabilization methods in the context of isogeometric analysis and B-spline basis functions, using an advection-dominated advection\revision{-}diffusion as a model problem. We derive (1) the least-squares finite element method formulation using the framework of Petrov-Galerkin method with optimal test functions in the $L_2$ norm, which guarantee automatic preservation of the \emph{inf-sup} condition of the continuous formulation. We also combine it with the standard Galerkin method to recover (2) the Galerkin/least-squares formulation, and derive coercivity constant bounds valid for B-spline basis functions. The resulting stabilization method are compared with the least-squares and (3) the Streamline-Upwind Petrov-Galerkin (SUPG)method using again the Eriksson-Johnson model problem. The results indicate that least-squares (equivalent to Petrov-Galerkin with $L_2$-optimal test functions) outperforms the other stabilization methods for small Péclet numbers, while strongly advection-dominated problems are better handled with SUPG or Galerkin/least-squares.

math.NA↗

arXiv2024

Graph grammars and Physics Informed Neural Networks for simulating of pollution propagation on Spitzbergen

In this paper, we present two computational methods for performing simulations of pollution propagation described by advection-diffusion equations. The first method employs graph grammars to describe the generation process of the computational mesh used in simulations with the meshless solver of the three-dimensional finite element method. The graph transformation rules express the three-dimensional Rivara longest-edge refinement algorithm. This solver is used for an exemplary application: performing three-dimensional simulations of pollution generation by the coal-burning power plant and its propagation in the city of Longyearbyen, the capital of Spitsbergen. The second computational code is based on the Physics Informed Neural Networks method. It is used to calculate the dissipation of the pollution along the valley in which the city of Longyearbyen is located. We discuss the instantiation and execution of the PINN method using Google Colab implementation. We discuss the benefits and limitations of the PINN implementation.

math.NA↗

arXiv2024

Efficacy of reduced order source terms for a coupled wave-circulation model in the Gulf of Mexico

During hurricanes, coupled wave-circulation models are critical tools for public safety. The standard approach is to use a high fidelity circulation model coupled with a wave model which uses the most advanced source terms. As a result, the models can be highly computationally expensive and so this study investigates the potential consequences of using highly simplified (reduced order) source terms within the wave model component of the coupled wave-circulation model. The trade-off between run time and accuracy with respect to observations is quantified for a set of two storms that impacted the Gulf of Mexico, Hurricane Ike and Hurricane Ida. Water surface elevations as well as wave statistics (significant wave height, peak period, and mean wave direction) are compared to observations. The usage of the reduced order source terms yielded significant savings in computational cost. Additionally, relatively low amounts of additional error with respect to observations during the simulations with reduced order source terms. However, large changes in global model outputs of the wave statistics were observed based on the choice of source terms particularly near the track of each hurricane.

physics.flu-dyn↗

arXiv2024

Simulating the aftermath of Northern European Enclosure Dam (NEED) break and flooding of European coast

The Northern European Enclosure Dam (NEED) is a hypothetical project to prevent flooding in European countries following the rising ocean level due to melting arctic glaciers. This project involves the construction of two large dams between Scotland and Norway, as well as England and France. The anticipated cost of this project is 250 to 500 billion euros. In this paper, we present the simulation of the aftermath of flooding on the European coastline caused by a catastrophic break of this hypothetical dam. From our simulation results, we can observe that there is a traveling wave after the accident, with a velocity of around 10 kilometers per hour, raising the sea level permanently inside the dammed region. This observation implies a need to construct additional dams or barriers protecting the northern coastline of the Netherlands and the interior of the Baltic Sea. Our simulations have been obtained using the following building blocks. First, a graph transformation model was applied to generate an adaptive mesh approximating the topography of the Earth. We employ the composition graph grammar model for breaking triangular elements in the mesh without the generation of hanging nodes. Second, the wave equation is formulated in a spherical latitude-longitude system of coordinates and solved by a high-order time integration scheme using the generalized $α$ method.

cs.CE↗

arXiv2023

A Discontinuous Galerkin Finite Element Model for Compound Flood Simulations

Recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff with accompanying flooding. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a local discontinuous Galerkin method for modified shallow water equations. In this modification, nonzero sources to the continuity equation are included to incorporate rainfall into the model using parametric rainfall models from literature as well as hindcast data. The discontinuous Galerkin spatial discretization is accompanied with a strong stability preserving explicit Runge Kutta time integrator. Hence, temporal stability is ensured through the CFL condition and we exploit the embarrassingly parallel nature of the developed method using MPI parallelization. We demonstrate the capabilities of the developed method though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach.

cs.CE↗

arXiv2023

WAVEx: Stabilized Finite Elements for Spectral Wind Wave Models Using FEniCSx

The prediction of the wind wave spectrum of the ocean using numerical models are an important tool for researchers, engineers, and communities living in coastal areas. The governing equation of the wind wave models, the Wave Action Balance Equation, presents unique challenges for implementing reliable numerical models because it is highly advective, highly nonlinear and high dimensional. Historically, most operational models have utilized finite difference methods, others have used finite volume methods but relatively few attempts at using finite element methods. In this work, we seek to fill this gap by investigating several different finite element discretizations of the Wave Action Balance Equation. The methods, which include streamline upwind Petrov-Galerkin (SUPG), least squares, and discontinuous Galerkin, are implemented and convergence properties are examined for some simplified 2-D test cases. Then, a new spectral wind wave model, WAVEx, is formulated and implemented for the full problem setting. WAVEx uses continuous finite elements along with SUPG stabilization in geographic/spectral space that allows for fully unstructured triangular meshes in both geographic and spectral space. For propagation in time, a second order fully implicit finite difference method is used. When source terms are active, a second order operator splitting scheme is used to linearize the problem. In the splitting scheme, propagation is solved using the implicit method and the nonlinear source terms are treated explicitly. Several test cases, including analytic tests and laboratory experiments, are demonstrated and results are compared to analytic solutions, observations, as well as output from another model that is used operationally.

physics.flu-dyn↗