Julian Simeonov

Edward Holmberg, Elias Ioup, Md Meftahul Ferdaus et al.

This article presents a cross-dataset evaluation of learned native-cell surrogate models for solver-consistent water-surface elevation (WSE) prediction in HEC-RAS 2D. To avoid raster remapping error and information-access confounding, surrogates are evaluated directly on the original nonuniform computational cells under an explicit policy that separates static project inputs, current hydraulic state, project-input forcing, calibration-derived quantities, and future solver-output targets. We introduce the Learned Response-Field Inertia Operator (LRFIO), a no-forcing, increment-based learned surrogate that calibrates an inertial response operator from solved HEC-RAS trajectories and deploys the retained operator through closed-form native-cell rollout. LRFIO evaluates a base-case-first response hierarchy consisting of persistence, global calibrated inertia, and segmented response-field inertia. Segmentation, residual correction, and neuralized inertia are treated as learnable modeling choices, with added complexity retained only when validation evidence justifies its cost. Evaluated across four diverse HEC-RAS 2D benchmarks, LRFIO retains different response structures for different domains, demonstrating adaptive learned complexity. The selector audit shows controlled complexity with a maximum validation regret of 4.30%. During deployment, retained rollout times range from 0.003 s to 0.242 s, and the Beaver Bayou measured-solve comparison gives an estimated 2.75 x 10^4 horizon-normalized speedup over HEC-RAS. These results indicate that the current native-cell increment is a strong solver-conditioned predictive scaffold and that added response-field, neural, or spatial complexity should be retained only when empirically justified.

Enrique Hernández Noguera, Md Meftahul Ferdaus, Elias Ioup et al.

Neural operators for time-dependent PDEs face a structural tension: spectral architectures (FNO and descendants) inherit exponential rollout-error growth from their one-step Lipschitz constant, while hierarchical U-Net operators trade resolution invariance for multi-scale detail. We introduce SpectraNet, an autoregressive neural operator that composes truncated spectral convolutions inside a U-Net hierarchy with a Residual-Target Spectral Block trained under a Semigroup-Consistency Loss. The residual-target parametrization replaces L^T stability blow-up with linear T*delta drift, and the spectral path's parameter count is Theta(L w^2 M^2), independent of grid N. Under a single unified protocol against 16 published neural-operator baselines on Navier-Stokes nu=1e-5 at 64x64, SpectraNet reaches test relative L2 = 0.0822 at 2.04M parameters -- 2.33x fewer than canonical FNO at ~20% lower error -- and wins five of six rows in a cross-PDE comparison against FNO (NS at nu in {1e-4, 1e-3}, PDEBench Shallow-Water 2D and Diffusion-Reaction, with the Active-Matter row going to FNO inside its seed spread). Trained from scratch at native 128^2 under the same protocol, SpectraNet improves to 0.0724 while FNO regresses to 0.3080. Free rollout stays bounded for T=100 where FNO diverges across all 200 test trajectories. On consumer CPU at B=1, SpectraNet runs sub-200ms while the full-attention Transformer that wins raw L2 pays ~60x latency; we do not claim to beat that Transformer on raw L2, only to dominate the lightweight (<=5M parameter, sub-200ms CPU) Pareto frontier. Source code: https://github.com/Enrikkk/spectranet

Edward Holmberg, Pujan Pokhrel, Maximilian Zoch et al.

Physics-based solvers like HEC-RAS provide high-fidelity river forecasts but are too computationally intensive for on-the-fly decision-making during flood events. The central challenge is to accelerate these simulations without sacrificing accuracy. This paper introduces a deep learning surrogate that treats HEC-RAS not as a solver but as a data-generation engine. We propose a hybrid, auto-regressive architecture that combines a Gated Recurrent Unit (GRU) to capture short-term temporal dynamics with a Geometry-Aware Fourier Neural Operator (Geo-FNO) to model long-range spatial dependencies along a river reach. The model learns underlying physics implicitly from a minimal eight-channel feature vector encoding dynamic state, static geometry, and boundary forcings extracted directly from native HEC-RAS files. Trained on 67 reaches of the Mississippi River Basin, the surrogate was evaluated on a year-long, unseen hold-out simulation. Results show the model achieves a strong predictive accuracy, with a median absolute stage error of 0.31 feet. Critically, for a full 67-reach ensemble forecast, our surrogate reduces the required wall-clock time from 139 minutes to 40 minutes, a speedup of nearly 3.5 times over the traditional solver. The success of this data-driven approach demonstrates that robust feature engineering can produce a viable, high-speed replacement for conventional hydraulic models, improving the computational feasibility of large-scale ensemble flood forecasting.

Pujan Pokhrel, Elias Ioup, Md Tamjidul Hoque et al.

In this paper, we present a novel approach for the prediction of rogue waves in oceans using statistical machine learning methods. Since the ocean is composed of many wave systems, the change from a bimodal or multimodal directional distribution to unimodal one is taken as the warning criteria. Likewise, we explore various features that help in predicting rogue waves. The analysis of the results shows that the Spectral features are significant in predicting rogue waves. We find that nonlinear classifiers have better prediction accuracy than the linear ones. Finally, we propose a Random Forest Classifier based algorithm to predict rogue waves in oceanic conditions. The proposed algorithm has an Overall Accuracy of 89.57% to 91.81%, and the Balanced Accuracy varies between 79.41% to 89.03% depending on the forecast time window. Moreover, due to the model-free nature of the evaluation criteria and interdisciplinary characteristics of the approach, similar studies may be motivated in other nonlinear dispersive media, such as nonlinear optics, plasma, and solids, governed by similar equations, which will allow for the early detection of extreme waves