Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: (a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real-time inversion applications. (b) DL methods exhibit a superior capability for approximating highly complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate selection of the loss function. As we illustrate via theoretical considerations and extensive numerical experiments, these interrelated aspects are critical to recover accurate inversion results. K E Y W O R D S deep learning, deep neural networks, error estimation, geophysical applications, real-time inversion

The aim of this study is to assess the main factors that affect the behaviour of carbon steel and galvanised steel in tropical and non‐tropical marine environments, identifying those factors that directly affect the behaviour. The results from the INNOVA (Chile) and MICAT/PATINA (Venezuela) projects will be used. These projects evaluated metals exposed to different marine environments using procedures outlined in ISO 9223/9226. The results show that temperature has no significant effect on the behaviour of the materials at the study sites in question (Venezuela being 10 °C warmer than Chile), independent of the tropical nature of the exposure environment, while it is precipitation (>600 mm) and chloride and SO2 content in the environment that mainly influence the behaviour of the carbon steel and the galvanised steel. In addition, an artificial neural network was generated to evaluate the corrosion rate of the studied metals, using meteoro‐chemical variables. The neural network for the carbon and galvanised steel was more precise for the exposure sites located in Chile.

onThis article presents the results obtained for the atmospheric corrosion of copper after 3 years of exposure at different sites within the region of Valparaiso, Chile. Frames were installed with samples at seven sites located close to the coast and inland. They were accompanied by devices to measure atmospheric chloride and sulphur dioxide content and weather stations to obtain data on temperature, humidity, amount of rainfall and wind speed. The results show a correlation between corrosion rate and the environmental and meteorological conditions in the area, and with the morphology and electrochemical properties of the corrosion product formed on the copper surface. The sites gave corrosivity categories of C5, C4, C3 and C2. The behaviour of corrosion rate was modelled using power function models and neural networks. The main corrosion products were cuprite, posnjankite, covelite and atacamite. O (M) Covelite, CuS (t) Cuprite, Cu 2 O (M) Covelite, CuS (t) Valparaíso Cuprite, Cu 2 O (M) Covelite, CuS (M) Atacamite, Cu 2 Cl(OH) 3 (M) Brochantite, Cu 4 (SO 4 )(OH) 6 (t) Atacamite, Cu 2 Cl(OH) 3 (M) Covelite, CuS (M) Cuprite, Cu 2 O (t) Thenardite, Na 2 SO 4 (t) M, major; m, minor; t, traces.

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

The present work presents the behavior of carbon steel and galvanized steel against atmospheric corrosion after 3 years of exposure at seven locations around the region of Valparaiso, Chile. Results show a relation between corrosion rates and environmental and meteorological conditions, categorized as CX for the Quintero zone, and C3 and C2 in the remaining six zones. Corrosion rate behaviors and material toughness losses were modeled using power functions and neural networks, found to be a function of environmental exposure time. Losses were greater for carbon steel in coastal and industrial environments, reaching 70 to 80%. This effect was reduced in galvanized steel, not exceeding 15% over the same period of exposure. The relationship between corrosion rate and loss of toughness of both materials was modeled using neural networks. K E Y W O R D S atmospheric corrosion, carbon steel, galvanized steel, industrial environments, marine environments, SEM, toughness, weight loss, XRD