arXiv subjects

Shukai Cai

Publications and source records attributed to Shukai Cai.

3 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↗

arXiv2026

Learning the Exact Flux: Neural Riemann Solvers with Hard Constraints

Godunov-type methods, which obtain numerical fluxes through local Riemann problems at cell interfaces, are among the most fundamental and widely used numerical methods in computational fluid dynamics. Exact Riemann solvers faithfully solve the underlying equations, but can be computationally expensive due to the iterative root-finding procedures they often require. Consequently, most practical computations rely on classical approximate Riemann solvers, such as Rusanov and Roe, which trade accuracy for computational speed. Neural networks have recently shown promise as an alternative for approximating exact Riemann solvers, but most existing approaches are data-driven or impose weak constraints. This may result in problems with maintaining balanced states, symmetry breaking, and conservation errors when integrated into a Godunov-type scheme. To address these issues, we propose a hard-constrained neural Riemann solver (HCNRS) and enforce five constraints: positivity, consistency, mirror symmetry, Galilean invariance, and scaling invariance. Numerical experiments are carried out for the shallow water and ideal-gas Euler equations on standard benchmark problems. In the absence of hard constraints, violations of the well-balanced property, mass conservation, and symmetry are observed. Notably, in the Euler implosion problem, the exact Riemann solver with MUSCL-Hancock captures the jet structure well, whereas the Rusanov flux is too diffusive and smears it out. HCNRS accurately reproduces the solution obtained by the exact Riemann solver. In contrast, an unconstrained neural formulation lacks mirror symmetry, which makes the solution depend on the choice of flux normal direction. As a result, the jet is either shifted or lost, along with diagonal symmetry.

physics.comp-ph↗

arXiv2026

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↗