Clint Dawson

Alexander Y. Sun, Zhi Li, Wonhyun Lee et al.

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in recent years, however, predicting flood extents at the street and building levels in real-time is still computationally demanding. Here we present a hybrid process-based and data-driven machine learning (ML) approach for flood extent and inundation depth prediction. We used the Fourier neural operator (FNO), a highly efficient ML method, for surrogate modeling. The FNO model is demonstrated over an urban area in Houston (Texas, U.S.) by training using simulated water depths (in 15-min intervals) from six historical storm events and then tested over two holdout events. Results show FNO outperforms the baseline U-Net model. It maintains high predictability at all lead times tested (up to 3 hrs) and performs well when applying to new sites, suggesting strong generalization skill.

Jinpai Zhao, Albert Cerrone, Joannes Westerink et al.

Single-agent systems (SAS) have become the default pattern for LLM-driven scientific workflows, but routing planning, tool use, and synthesis through a single context window comes with a well-known cost: as tool specifications and observational traces accumulate, the effective context available for each decision shrinks, and end-to-end reliability suffers. We present a multi-agent system (MAS) prototype for hydrodynamics in which specialized agents are coordinated through a Layer Execution Graph (LEG). A planner agent constructs query-specific execution topologies from natural-language routing heuristics that capture domain knowledge without hard-coding it as rigid control logic; specialist agents operate under strict tool allowlists and occupy complementary data-class roles. Between layers, consolidator agents fuse parallel outputs into concise briefs, and a reporter agent synthesizes the final response, while the runtime logs provenance for every tool invocation to support auditability. All benchmarks, ablations, and stress tests use Claude Sonnet~4.6 as the backbone model for both specialist and general-purpose agents. Evaluated on 37 queries spanning six complexity categories, the prototype achieves 93.6% factual precision with a 100% pass rate. Accuracy remains above 90% across runs from single-threaded to five independent parallel tracks, and under simulated loss of individual data sources the system degrades gracefully, still returning substantive partial answers. Together, these results suggest that planner-guided, graph-structured multi-agent orchestration can meaningfully alleviate the context-saturation bottlenecks that constrain monolithic single-agent architectures.

Troy Butler, Don Estep, Simon Tavener et al.

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a probability measure on the parameter domain for a given $σ-$algebra. In the case where the number of output quantities is less than the number of parameters, the inverse of the map from parameters to data defines a type of generalized contour map. The approximate contour maps define a geometric structure on events in the $σ-$algebra for the parameter domain. We develop and analyze an inherently non-intrusive method of sampling the parameter domain and events in the given $σ-$algebra to approximate the probability measure. We use results from stochastic geometry for point processes to prove convergence of a random sample based approximation method. We define a numerical $σ-$algebra on which we compute probabilities and derive computable estimates for the error in the probability measure. We present numerical results to illustrate the various sources of error for a model of fluid flow past a cylinder.

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.

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.

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.

Stefanos Giaremis, Noujoud Nader, Clint Dawson et al.

Physics simulation results of natural processes usually do not fully capture the real world. This is caused for instance by limits in what physical processes are simulated and to what accuracy. In this work we propose and analyze the use of an LSTM-based deep learning network machine learning (ML) architecture for capturing and predicting the behavior of the systemic error for storm surge forecast models with respect to real-world water height observations from gauge stations during hurricane events. The overall goal of this work is to predict the systemic error of the physics model and use it to improve the accuracy of the simulation results post factum. We trained our proposed ML model on a dataset of 61 historical storms in the coastal regions of the U.S. and we tested its performance in bias correcting modeled water level data predictions from hurricane Ian (2022). We show that our model can consistently improve the forecasting accuracy for hurricane Ian -- unknown to the ML model -- at all gauge station coordinates used for the initial data. Moreover, by examining the impact of using different subsets of the initial training dataset, containing a number of relatively similar or different hurricanes in terms of hurricane track, we found that we can obtain similar quality of bias correction by only using a subset of six hurricanes. This is an important result that implies the possibility to apply a pre-trained ML model to real-time hurricane forecasting results with the goal of bias correcting and improving the produced simulation accuracy. The presented work is an important first step in creating a bias correction system for real-time storm surge forecasting applicable to the full simulation area. It also presents a highly transferable and operationally applicable methodology for improving the accuracy in a wide range of physics simulation scenarios beyond storm surge forecasting.

Noujoud Nader, Stefanos Giaremis, Clint Dawson et al.

Storm surge forecasting remains a critical challenge in mitigating the impacts of tropical cyclones on coastal regions, particularly given recent trends of rapid intensification and increasing nearshore storm activity. Traditional high fidelity numerical models such as ADCIRC, while robust, are often hindered by inevitable uncertainties arising from various sources. To address these challenges, this study introduces StormNet, a spatio-temporal graph neural network (GNN) designed for bias correction of storm surge forecasts. StormNet integrates graph convolutional (GCN) and graph attention (GAT) mechanisms with long short-term memory (LSTM) components to capture complex spatial and temporal dependencies among water-level gauge stations. The model was trained using historical hurricane data from the U.S. Gulf Coast and evaluated on Hurricane Idalia (2023). Results demonstrate that StormNet can effectively reduce the root mean square error (RMSE) in water-level predictions by more than 70\% for 48-hour forecasts and above 50\% for 72-hour forecasts, as well as outperform a sequential LSTM baseline, particularly for longer prediction horizons. The model also exhibits low training time, enhancing its applicability in real-time operational forecasting systems. Overall, StormNet provides a computationally efficient and physically meaningful framework for improving storm surge prediction accuracy and reliability during extreme weather events.

C G Krishnanunni, Tan Bui-Thanh, Clint Dawson

This work presents a novel algorithm for progressively adapting neural network architecture along the depth. In particular, we attempt to address the following questions in a mathematically principled way: i) Where to add a new capacity (layer) during the training process? ii) How to initialize the new capacity? At the heart of our approach are two key ingredients: i) the introduction of a ``shape functional" to be minimized, which depends on neural network topology, and ii) the introduction of a topological derivative of the shape functional with respect to the neural network topology. Using an optimal control viewpoint, we show that the network topological derivative exists under certain conditions, and its closed-form expression is derived. In particular, we explore, for the first time, the connection between the topological derivative from a topology optimization framework with the Hamiltonian from optimal control theory. Further, we show that the optimality condition for the shape functional leads to an eigenvalue problem for deep neural architecture adaptation. Our approach thus determines the most sensitive location along the depth where a new layer needs to be inserted during the training phase and the associated parametric initialization for the newly added layer. We also demonstrate that our layer insertion strategy can be derived from an optimal transport viewpoint as a solution to maximizing a topological derivative in $p$-Wasserstein space, where $p>= 1$. Numerical investigations with fully connected network, convolutional neural network, and vision transformer on various regression and classification problems demonstrate that our proposed approach can outperform an ad-hoc baseline network and other architecture adaptation strategies. Further, we also demonstrate other applications of topological derivative in fields such as transfer learning.

Hai V. Nguyen, Tan Bui-Thanh, Clint Dawson

Efficient real-time solvers for forward and inverse problems are essential in engineering and science applications. Machine learning surrogate models have emerged as promising alternatives to traditional methods, offering substantially reduced computational time. Nevertheless, these models typically demand extensive training datasets to achieve robust generalization across diverse scenarios. While physics-based approaches can partially mitigate this data dependency and ensure physics-interpretable solutions, addressing scarce data regimes remains a challenge. Both purely data-driven and physics-based machine learning approaches demonstrate severe overfitting issues when trained with insufficient data. We propose a novel Tikhonov autoencoder model-constrained framework, called TAE, capable of learning both forward and inverse surrogate models using a single arbitrary observation sample. We develop comprehensive theoretical foundations including forward and inverse inference error bounds for the proposed approach for linear cases. For comparative analysis, we derive equivalent formulations for pure data-driven and model-constrained approach counterparts. At the heart of our approach is a data randomization strategy, which functions as a generative mechanism for exploring the training data space, enabling effective training of both forward and inverse surrogate models from a single observation, while regularizing the learning process. We validate our approach through extensive numerical experiments on two challenging inverse problems: 2D heat conductivity inversion and initial condition reconstruction for time-dependent 2D Navier-Stokes equations. Results demonstrate that TAE achieves accuracy comparable to traditional Tikhonov solvers and numerical forward solvers for both inverse and forward problems, respectively, while delivering orders of magnitude computational speedups.

Peter Rivera-Casillas, Sourav Dutta, Shukai Cai et al.

Coastal regions are particularly vulnerable to the impacts of rising sea levels and extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs dimensionality reduction to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. Although MITONet is applicable to a wide range of problems, we showcase its capabilities by forecasting regional tide-driven dynamics described by the two-dimensional shallow-water equations, while incorporating initial conditions, boundary conditions, and a varying domain parameter. We demonstrate MITONet's performance in a real-world application, highlighting its ability to make accurate predictions by extrapolating both in time and parametric space.

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.

Naveen Sudharsan, Manmeet Singh, Harsh Kamath et al.

The UT GraphCast Hindcast Dataset from 1979 to 2024 is a comprehensive global weather forecast archive generated using the Google DeepMind GraphCast Operational model. Developed by researchers at The University of Texas at Austin under the WCRP umbrella, this dataset provides daily 15 day deterministic forecasts at 00UTC on an approximately 25 km global grid for a 45 year period. GraphCast is a physics informed graph neural network that was trained on ECMWF ERA5 reanalysis. It predicts more than a dozen key atmospheric and surface variables on 37 vertical levels, delivering a full medium range forecast in under one minute on modern hardware.

Gurpreet Singh, Soumyajit Gupta, Clint Dawson

Hyperspectral unmixing involves separating a pixel as a weighted combination of its constituent endmembers and corresponding fractional abundances, with the current state of the art results achieved by neural models on benchmark datasets. However, these networks are severely over-parameterized and consequently, the invariant endmember spectra extracted as decoder weights have a high variance over multiple runs. These approaches perform substantial post-processing while requiring an exact specification of the number of endmembers and specialized initialization of weights from other algorithms like VCA. We show for the first time that a two-layer autoencoder (SCA), with $2FK$ parameters ($F$ features, $K$ endmembers), achieves error metrics that are scales apart ($10^{-5})$ from previously reported values $(10^{-2})$. SCA converges to this low error solution starting from a random initialization of weights. We also show that SCA, based upon a bi-orthogonal representation, performs a self-correction when the number of endmembers are over-specified. Numerical experiments on Samson, Jasper, and Urban datasets demonstrate that SCA outperforms previously reported error metrics for all the cases while being robust to noise and outliers.

Gurpreet Singh, Soumyajit Gupta, Matthew Lease et al.

Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex functions along with considerations of user preferences in balancing trade-offs. Pareto solutions represent optimal frontiers for jointly optimizing multiple competing objectives. A major obstacle for frequently used linear-scalarization strategies is that the resulting optimization problem might not always converge to a global optimum. Furthermore, such methods only return one solution point per run. A Pareto solution set is a subset of all such global optima over multiple runs for different trade-off choices. Therefore, a Pareto front can only be guaranteed with multiple runs of the linear-scalarization problem, where all runs converge to their respective global optima. Consequently, extracting a Pareto front for practical problems is computationally intractable with substantial computational overheads, limited scalability, and reduced accuracy. We propose a robust, low cost, two-stage, hybrid neural Pareto optimization approach that is accurate and scales (compute space and time) with data dimensions, as well as number of functions and constraints. The first stage (neural network) efficiently extracts a weak Pareto front, using Fritz-John conditions as the discriminator, with no assumptions of convexity on the objectives or constraints. The second stage (efficient Pareto filter) extracts the strong Pareto optimal subset given the weak front from stage 1. Fritz-John conditions provide us with theoretical bounds on approximation error between the true and network extracted weak Pareto front. Numerical experiments demonstrates the accuracy and efficiency on a canonical set of benchmark problems and a fairness optimization task from prior works.

Gurpreet Singh, Soumyajit Gupta, Matthew Lease et al.

In a Big Data setting computing the dominant SVD factors is restrictive due to the main memory requirements. Recently introduced streaming Randomized SVD schemes work under the restrictive assumption that the singular value spectrum of the data has exponential decay. This is seldom true for any practical data. Although these methods are claimed to be applicable to scientific computations due to associated tail-energy error bounds, the approximation errors in the singular vectors and values are high when the aforementioned assumption does not hold. Furthermore from a practical perspective, oversampling can still be memory intensive or worse can exceed the feature dimension of the data. To address these issues, we present Range-Net as an alternative to randomized SVD that satisfies the tail-energy lower bound given by Eckart-Young-Mirsky (EYM) theorem. Range-Net is a deterministic two-stage neural optimization approach with random initialization, where the main memory requirement depends explicitly on the feature dimension and desired rank, independent of the sample dimension. The data samples are read in a streaming setting with the network minimization problem converging to the desired rank-r approximation. Range-Net is fully interpretable where all the network outputs and weights have a specific meaning. We provide theoretical guarantees that Range-Net extracted SVD factors satisfy EYM tail-energy lower bound at machine precision. Our numerical experiments on real data at various scales confirms this bound. A comparison against the state of the art streaming Randomized SVD shows that Range-Net accuracy is better by six orders of magnitude while being memory efficient.