A Finite Element based Deep Learning solver for parametric PDEs

We introduce a dynamic Deep Learning (DL) architecture based on the Finite Element Method (FEM) to solve linear parametric Partial Differential Equations(PDEs). The connections between neurons in the architecture mimic the Finite Element connectivity graph when applying mesh refinements. We select and discuss several losses employing preconditioners and different norms to enhance convergence. For simplicity, we implement the resulting Deep-FEM in one spatial domain (1D), although its extension to 2D and 3D problems is straightforward. Extensive numerical experiments show in general good approximations for both symmetric positive definite (SPD) and indefinite problems in parametric and non-parametric problems. However, in some cases, lack of convexity prevents us from obtaining high-accuracy solutions.This work has received funding from: the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS); the European Regional Development Fund (ERDF) through the Interreg V-A Spain-France-Andorra program POCTEFA 2014-2020 Project PIXIL (EFA362/19); the Spanish Ministry of Science and Innovation projects with references PID2019-108111RB-I00 (FEDER/AEI) and PDC2021-121093-I00, the "BCAM Severo Ochoa" accreditation of excellence (SEV-2017-0718); and the Basque Government through the BERC 2018-2021 program, the three Elkartek projects 3KIA (KK-2020/00049), EXPERTIA (KK-2021/00048), and SIGZE (KK-2021/00095), and the Consolidated Research Group MATHMODE (IT1294-19) given by the Department of Education

Modeling extra-deep electromagnetic logs using a deep neural network

Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We have developed a methodology to construct a deep neural network (DNN) model trained to reproduce a full set of extra-deep EM logs consisting of 22 measurements per logging position. The model is trained in a 1D layered environment consisting of up to seven layers with different resistivity values. A commercial simulator provided by a tool vendor is used to generate a training data set. The data set size is limited because the simulator provided by the vendor is optimized for sequential execution. Therefore, we design a training data set that embraces the geologic rules and geosteering specifics supported by the forward model. We use this data set to produce an EM simulator based on a DNN without access to the proprietary information about the EM tool configuration or the original simulator source code. Despite using a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multilayer synthetic case and a section of a published historical operation from the Goliat field. The observed average evaluation time of 0.15 ms per logging position makes it also suitable for future use as part of evaluation-hungry statistical and/or Monte Carlo inversion algorithms within geosteering workflows.POCTEFA 2014-2020 PIXIL (EFA362/19) MTM2016-76329-

A Simulation Method for the Computation of the E

We propose a set of numerical methods for the computation of the frequency-dependent eff ective primary wave velocity of heterogeneous rocks. We assume the rocks' internal microstructure is given by micro-computed tomography images. In the low/medium frequency regime, we propose to solve the acoustic equation in the frequency domain by a Finite Element Method (FEM). We employ a Perfectly Matched Layer to truncate the computational domain and we show the need to repeat the domain a su cient number of times to obtain accurate results. To make this problem computationally tractable, we equip the FEM with non-fitting meshes and we precompute multiple blocks of the sti ffness matrix. In the high-frequency range, we solve the eikonal equation with a Fast Marching Method. Numerical results con rm the validity of the proposed methods and illustrate the e ffect of density, porosity, and the size and distribution of the pores on the e ective compressional wave velocity

Deep learning enhanced principal component analysis for structural health monitoring

This paper proposes a Deep Learning Enhanced Principal Component Analysis (PCA) approach for outlier detection to assess the structural condition of bridges. We employ partially explainable autoencoder architecture to replicate and enhance the data compression and reconstruction ability of PCA. The particularity of the method lies in the addition of residual connections to account for nonlinearities. We apply the proposed method to monitoring data obtained from two bridges under real operation conditions and compare the results before and after adding the residual connections. Results show that the addition of residual connections enhances the outlier detection ability of the network, allowing to detect lighter damages

Bridge damage identification under varying environmental and operational conditions combining Deep Learning and numerical simulations

This work proposes a novel supervised learning approach to identify damage in operating bridge structures. We propose a method to introduce the effect of environmental and operational conditions into the synthetic damage scenarios employed for training a Deep Neural Network, which is applicable to large-scale complex structures. We apply a clustering technique based on Gaussian Mixtures to effectively select Q representative measurements from a long-term monitoring dataset. We employ these measurements as the target response to solve various Finite Element Model Updating problems before generating different damage scenarios. The synthetic and experimental measurements feed two Deep Neural Networks that assess the structural health condition in terms of damage severity and location. We demonstrate the applicability of the proposed method with a real full-scale case study: the Infante Dom Henrique bridge in Porto. A comparative study reveals that neglecting different environmental and operational conditions during training detracts the damage identification task. By contrast, our method provides successful results during a synthetic validation

Square root strategy: a novel method to linearize an optical communication system with electronic equalizers

We demonstrate a non-linear function after the photodetector that linearizes dispersion-limited IM-DD systems, enhancing the performance of linear electronic equalization. Results showed a clear improvement in terms of chromatic dispersion tolerance

Square root strategy: a novel method to linearize an optical communication system with electronic equalizers

We demonstrate a non-linear function after the photodetector that linearizes dispersion-limited IM-DD systems, enhancing the performance of linear electronic equalization. Results showed a clear improvement in terms of chromatic dispersion tolerance