arXiv subjects

Mark Loveland

Publications and source records attributed to Mark Loveland.

6 recordsLinked to original sources

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↗

arXiv2025

A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics

Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. Yet high-fidelity numerical models are often too computationally expensive for real-time use, and lower-cost approaches, such as traditional model order reduction algorithms or conventional neural networks, typically struggle to generalize to out-of-distribution conditions. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs latent-space operator learning to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. We showcase MITONet's predictive capabilities by forecasting regional tide-driven dynamics in the Shinnecock Inlet in New York and riverine flow in a section of the Red River in Louisiana, both described by the two-dimensional shallow-water equations (2D SWE), while incorporating initial conditions, time-varying boundary conditions, and domain parameters such as the bottom friction coefficient. Despite the distinct flow regimes, the complex geometries and meshes, and the wide range of bottom friction coefficients studied, MITONet displays consistently high predictive skill, with anomaly correlation coefficients above 0.9, a maximum normalized root mean square error of 0.011, and computational speedups between 100x-1,250x, even for 175 days of autoregressive rollout forecast from random initial conditions and with unseen parameter values.

cs.CE↗

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↗

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↗

arXiv2022

Extending FEniCS to Work in Higher Dimensions Using Tensor Product Finite Elements

We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is structured as a Cartesian product of two lower dimensional subdomains. In this study we consider Dirichlet problems for scalar linear partial differential equations, though the methodology can be extended to non-linear problems. The utilization of tensor product finite elements allows us to construct a global system of linear algebraic equations that only relies on the finite element infrastructure of the lower dimensional subdomains contained in FEniCS. We demonstrate the effectiveness of our methodology in four distinctive test cases. The first test case is a Poisson equation posed in a four dimensional domain which is a Cartesian product of two unit squares solved using the classical Galerkin finite element method. The second test case is the wave equation in space-time, where the computational domain is a Cartesian product of a two dimensional space grid and a one dimensional time interval. In this second case we also employ the Galerkin method. The third test case is an advection dominated advection-diffusion equation where the global domain is a Cartesian product of two one dimensional intervals in which the streamline upwind Petrov-Galerkin method is applied to ensure discrete stability. The final test case uses the Galerkin approach to solve a Poisson problem on a Cartesian product of two intervals with a spatially varying, non-separable diffusivity term. In all cases, a p=1 basis is used and optimal L^2 convergence rates of order h^{p+1} of the errors are achieved with respect to h refinement

math.NA↗

arXiv2021

Classification of COVID-19 X-ray Images Using a Combination of Deep and Handcrafted Features

Coronavirus Disease 2019 (COVID-19) demonstrated the need for accurate and fast diagnosis methods for emergent viral diseases. Soon after the emergence of COVID-19, medical practitioners used X-ray and computed tomography (CT) images of patients' lungs to detect COVID-19. Machine learning methods are capable of improving the identification accuracy of COVID-19 in X-ray and CT images, delivering near real-time results, while alleviating the burden on medical practitioners. In this work, we demonstrate the efficacy of a support vector machine (SVM) classifier, trained with a combination of deep convolutional and handcrafted features extracted from X-ray chest scans. We use this combination of features to discriminate between healthy, common pneumonia, and COVID-19 patients. The performance of the combined feature approach is compared with a standard convolutional neural network (CNN) and the SVM trained with handcrafted features. We find that combining the features in our novel framework improves the performance of the classification task compared to the independent application of convolutional and handcrafted features. Specifically, we achieve an accuracy of 0.988 in the classification task with our combined approach compared to 0.963 and 0.983 accuracy for the handcrafted features with SVM and CNN respectively.

eess.IV↗