Guofeng Su

Shan Ding, Yongfu Tian, Lang Qin et al.

Driven by rapid advances in artificial intelligence and modern GPU computing capabilities, deep learning methods based on the optimization paradigm have provided new pathways to solve spatiotemporal physical problems, whose mathematical core lies in solving partial differential equations (PDEs). As an emerging class of function-space learning methods, neural operators (NOs) have exhibited great potential in efficient PDE solving. However, existing mainstream neural operator frameworks suffer from critical bottlenecks when modeling time-dependent PDEs over long time horizons, including accuracy degradation, insufficient stability, high training costs, and excessive memory consumption, which severely limit their practical deployment. To address these challenges in long-time prediction with neural operators, we propose a novel spatiotemporally decoupled physics-informed neural operator architecture, termed the physics-informed Stone-Weierstrass neural operator (PI-SWNO). The design is theoretically grounded in the decoupling paradigm combining time-invariant spatial basis functions with time-varying evolution coefficients, as well as the Stone-Weierstrass approximation theorem. By encoding spatial and temporal information via two separate subnetworks, the framework structurally mitigates the accumulation of errors over extended time intervals. Furthermore, we introduce a time-marching batch-wise sampling strategy to resolve the memory bottleneck of full-range modeling over extended time spans, ensuring continuity and convergence of full-time-domain solutions.

Yongfu Tian, Shan Ding, Guofeng Su et al.

Urban flood disaster is one of the most serious natural disasters. Numerous flood simulation models have been proposed and relatively matured. However, two major challenges persist: excessive simplification of the city system and high computational complexity. To break these limitations, this paper develops an Urban Flood Dynamical System Model (UFDSM) based on the concept of the Cellular Automata Urban Flood Model. This model allows flexible customization of cell types and selection of water motion or distribution rules based on actual urban environments to incorporate as much the urban system data as possible. The water motion and distribution rules can be simple, which could reduce the computational complexity, but not arbitrary. So, a sufficient condition is provided so that solutions of dynamical system align with macroscopic physical conditions governing water movement. Then, to preserve the evolutionary properties of the UFDSM, we propose a first-order conservation nonstandard finite difference algorithm. This numerical method ensures positive solutions and conservation of water while maintaining the same fixed-point characteristics as the dynamical system. And, this numerical method is validated by comparing it with an analytical solution.Furthermore, to verify the applicability of our model, we performed an urban flood simulation experiment and compared it to HEC-RAS. There is approximately a 2mm discrepancy in distance dp' and 0.02mm discrepancy in distance d2' , with the relative distance Rp about 7.5% and the relative distance R2 approximately 0.06%. Additionally, the proposed model is easily coupled with other hydrological processes and facilitates data assimilation, thereby offering promising practical applications.

Yongfu Tian, Shan Ding, Guofeng Su et al.

Calibrating the urban underlying surface parameters is crucial for urban flood simulation. We formulate the parameter calibration problem into an optimization problem within the Bayesian framework using the maximum likelihood principle. We adopt the urban flood dynamical system model as the surrogate model and innovatively introduce latent variables inspired by machine learning to represent more uncertainties, which can also be compatible with common physical parameter calibration. For more efficient optimization, we construct the adjoint equation of the surrogate model to obtain gradient information and propose the parameter sharing technique and the localization technique to reduce the computation complexity of the adjoint equation. A simple case verifies the proposed method can converge quickly and is insensitive to the observation time interval. In the case derived from Test 8A, we calibrate Manning's coefficient of urban roads, with a maximum relative error of 13.88% and a minimum of 1.16%.