Hamidreza Eivazi

Study Region: Goslar and Göttingen, Lower Saxony, Germany. Study Focus: In July 2017, the cities of Goslar and Göttingen experienced severe flood events characterized by short warning time of only 20 minutes, resulting in extensive regional flooding and significant damage. This highlights the critical need for a more reliable and timely flood forecasting system. This paper presents a comprehensive study on the impact of radar-based precipitation data on forecasting river water levels in Goslar. Additionally, the study examines how precipitation influences water level forecasts in Göttingen. The analysis integrates radar-derived spatiotemporal precipitation patterns with hydrological sensor data obtained from ground stations to evaluate the effectiveness of this approach in improving flood prediction capabilities. New Hydrological Insights for the Region: A key innovation in this paper is the use of residual-based modeling to address the non-linearity between precipitation images and water levels, leading to a Spatiotemporal Radar-based Precipitation Model with residuals (STRPMr). Unlike traditional hydrological models, our approach does not rely on upstream data, making it independent of additional hydrological inputs. This independence enhances its adaptability and allows for broader applicability in other regions with RADOLAN precipitation. The deep learning architecture integrates (2+1)D convolutional neural networks for spatial and temporal feature extraction with LSTM for timeseries forecasting. The results demonstrate the potential of the STRPMr for capturing extreme events and more accurate flood forecasting.

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, for example, the finite element method, is costly due to the demand of solving initial boundary‐value problems at multiple scales. On the other hand, multiscale finite element computations are commended for their ability to integrate micro‐structural properties into macroscopic computational analyses using homogenization techniques. Recently, neural operator‐based surrogate models have shown trustworthy performance for solving a wide range of partial differential equations. In this work, we propose a hybrid method in which we utilize deep operator networks for surrogate modeling of the microscale physics. This allows us to embed the constitutive relations of the microscale into the model architecture and to predict microscale strains and stresses based on the prescribed macroscale strain inputs. Furthermore, numerical homogenization is carried out to obtain the macroscale quantities of interest. We apply the proposed approach to quasi‐static problems of solid mechanics. The results demonstrate that our constitutive relations‐aware DeepONet can yield accurate solutions even when being confronted with a restricted dataset during model development.

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs for solving the Reynolds-averaged Navier–Stokes equations for incompressible turbulent flows without any specific model or assumption for turbulence and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier–Stokes equations for laminar flows by solving the Falkner–Skan boundary layer. We then apply PINNs for the simulation of four turbulent-flow cases, i.e., zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over a NACA4412 airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.