The hydro-mechanical behavior of clay-sulfate rocks, especially their swelling properties, poses significant challenges in geotechnical engineering. This study presents a hybrid constrained machine learning (ML) model developed using the categorical boosting algorithm (CatBoost) tuned with a Bayesian optimization algorithm to predict and analyze the swelling behavior of these complex geological materials. Initially, a coupled hydro-mechanical model based on the Richards' equation coupled to a deformation process with linear kinematics implemented within the finite element framework OpenGeoSys was used to simulate the observed ground heave in Staufen, Germany, caused by water inflow into the clay-sulfate bearing Triassic Grabfeld Formation. A systematic parametric analysis using Gaussian distributions of key parameters, including Young's modulus, Poisson's ratio, maximum swelling pressure, permeability, and air entry pressure, was performed to construct a synthetic database. The ML model takes time, spatial coordinates, and these parameter values as inputs, while water saturation, porosity, and vertical displacement are outputs. In addition, penalty terms were incorporated into the CatBoost objective function to enforce physically meaningful predictions. Results show that the hybrid approach effectively captures the nonlinear and dynamic interactions that govern hydro-mechanical processes. The study demonstrates the ability of the model to predict the swelling behavior of clay-sulfate rocks, providing a robust tool for risk assessment and management in affected regions. The results highlight the potential of ML-driven models to address complex geotechnical challenges.

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a compact neural network to adjust the smoothness indicators within the WENO scheme. This modification enhances the accuracy of the numerical results, particularly near abrupt shocks. Unlike previous deep learning-based methods, no additional post-processing steps are necessary for maintaining consistency. We demonstrate the superiority of our new approach using several examples from the literature for the two-dimensional Euler equations of gas dynamics. Through intensive study of these test problems, which involve various shocks and rarefaction waves, the new technique is shown to outperform traditional fifth-order WENO schemes, especially in cases where the numerical solutions exhibit excessive diffusion or overshoot around shocks.

By incorporating the residual of the differential equation into the loss function of a neural network-based surrogate model, PINNs can seamlessly combine measured data with physical constraints given by differential equations. PINNs can also be viewed as a surrogate model for solving differential equations by incorporating additional data or as a data-driven correction (or even discovery) of the underlying physical system. By the end of the year 2022, we had experienced several waves of the COVID-19 pandemic with different variants of the virus prevailing at different time intervals. Various levels of interventions and protective measures were implemented to counteract the uncontrolled spreading of the disease. We focus exemplarily on the time until the fourth wave (i.e., the omicron wave) of the COVID-19 pandemic in Germany that had its peak in February and March 2022. The B.1.617.2 (delta) variant of SARS-CoV-2, which is characterized by a higher contagiosity than the previous B.1.1.7 (alpha), B.1.351

In this work we propose a stochastic primal-dual preconditioned three-operator splitting algorithm for solving a class of convex three-composite optimization problems. Our proposed scheme is a direct three-operator splitting extension of the SPDHG algorithm [Chambolle et al. 2018]. We provide theoretical convergence analysis showing ergodic O(1/K) convergence rate, and demonstrate the effectiveness of our approach in imaging inverse problems.