Attention U-Net as a surrogate model for groundwater prediction

Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical methodologies, such as Finite Difference (FD) and Finite Element (FE) Methods, use iterative solvers which are associated with high computational cost. This study proposes a physics-based convolutional encoder-decoder neural network as a surrogate model to quickly calculate the response of the groundwater system. Holding strong promise in cross-domain mappings, encoder-decoder networks are applicable for learning complex input-output mappings of physical systems. This manuscript presents an Attention U-Net model that attempts to capture the fundamental input-output relations of the groundwater system and generates solutions of hydraulic head in the whole domain given a set of physical parameters and boundary conditions. The model accurately predicts the steady state response of a highly heterogeneous groundwater system given the locations and piezometric head of up to 3 wells as input. The network learns to pay attention only in the relevant parts of the domain and the generated hydraulic head field corresponds to the target samples in great detail. Even relative to coarse finite difference approximations the proposed model is shown to be significantly faster than a comparative state-of-the-art numerical solver, thus providing a base for further development of the presented networks as surrogate models for groundwater prediction

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software

A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6

Modern Machine Learning Tools for Monitoring and Control of Industrial Processes: A Survey

Over the last ten years, we have seen a significant increase in industrial data, tremendous improvement in computational power, and major theoretical advances in machine learning. This opens up an opportunity to use modern machine learning tools on large-scale nonlinear monitoring and control problems. This article provides a survey of recent results with applications in the process industry.Comment: IFAC World Congress 202

Network design decisions in supply chain planning

Structuring global supply chain networks is a complex decision-making process. The typical inputs to such a process consist of a set of customer zones to serve, a set of products to be manufactured and distributed, demand projections for the different customer zones, and information about future conditions, costs (e.g. for production and transportation) and resources (e.g. capacities, available raw materials). Given the above inputs, companies have to decide where to locate new service facilities (e.g. plants, warehouses), how to allocate procurement and production activities to the variousmanufacturing facilities, and how to manage the transportation of products through the supply chain network in order to satisfy customer demands. We propose a mathematical modelling framework capturing many practical aspects of network design problems simultaneously. For problems of reasonable size we report on computational experience with standard mathematical programming software. The discussion is extended with other decisions required by many real-life applications in strategic supply chain planning. In particular, the multi-period nature of some decisions is addressed by a more comprehensivemodel, which is solved by a specially tailored heuristic approach. The numerical results suggest that the solution procedure can identify high quality solutions within reasonable computational time