Article
Geochemistry & Geophysics
Feiyan Wang, Zhengyong Ren, Lihong Zhao
Summary: The study presents a goal-oriented adaptive finite-element algorithm for accurately modeling marine controlled-source electromagnetic responses. By approximating the solutions to both the primal and dual problems, it can flexibly handle complex geological settings and survey geometries. The method demonstrates robustness in dealing with both moderate and strong electrical anisotropy.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Geochemistry & Geophysics
Xiaodong Yang, Mingxin Yue, Daiming Hu, Yong Li, Xiaoping Wu
Summary: A goal-oriented iteration algorithm with adaptive error estimation has been proposed for 3-D modeling of time-domain marine controlled-source electromagnetic (CSEM) method. The algorithm effectively suppresses computational error and balances accuracy and efficiency by updating time step and mesh size staggeredly. Results show that the time derivative of the magnetic field is sensitive to high-resistivity reservoirs, suggesting the collection of both electric and magnetic field data over the target area to reveal submarine sediment structures and oil and gas reservoirs.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2022)
Article
Engineering, Multidisciplinary
Felipe V. Caro, Vincent Darrigrand, Julen Alvarez-Aramberri, Elisabete Alberdi, David Pardo
Summary: This work extends an automatic energy-norm hp-adaptive strategy to non-elliptic problems and goal-oriented adaptivity. It proposes an error indicator for quasi-optimal hp-unrefinements based on a multi-level hierarchical data structure and alternating h- and p-refinements. The strategy eliminates the basis functions with the lowest contributions to the solution, improving efficiency and accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Geochemistry & Geophysics
Paula Rulff, Laura M. Buntin, Thomas Kalscheuer
Summary: A 3-D forward modelling code was developed for controlled source electromagnetic problems, balancing solution accuracy and problem size through goal-oriented mesh refinement. Improvements were made in error estimation for complex models, including weighting adjoint source terms, optimizing for conductivity contrasts, and formulating element-wise estimators relative to electromagnetic field amplitudes.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2021)
Article
Computer Science, Interdisciplinary Applications
Pengliang Yang
Summary: This paper presents the first application of a frequency domain CSEM inversion approach using fictitious wave domain timestepping modelling. It proves the potential of marine controlled-source electromagnetic (CSEM) method in accurately detecting hydrocarbon bearing formations.
COMPUTERS & GEOSCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
X. Ju, R. Mahnken, L. Liang, Y. Xu
Summary: In this work, a two-level optimization framework based on goal-oriented error estimation is proposed for parameter identification in a class of linear micromorphic elasticity problems. By utilizing sensitivity analysis and Lagrange method, parameters optimization and error estimation are achieved, confirming the effectiveness of the adaptive procedure.
COMPUTERS & STRUCTURES
(2021)
Article
Geochemistry & Geophysics
Dieter Werthmuller, Wim A. Mulder, Evert C. Slob
Summary: 3-D controlled-source electromagnetic data is typically computed directly in the domain of interest and transformed through a Fourier transform to another domain. The speed of modeling is influenced by factors such as solver efficiency, method robustness, and grid optimization techniques. Careful selection of evaluation points and grid dependencies can lead to significant reductions in computation times.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2021)
Article
Mathematics, Applied
Shukai Du, Samuel N. Stechmann
Summary: This study proposes an adaptive-mesh inversion method for solving the inverse problem of radiative transfer. By simultaneously addressing the optimization problems of inversion and mesh adaptivity and utilizing a goal-oriented error estimator, the mesh-refinement process is guided efficiently to solve the inverse problem.
Article
Geochemistry & Geophysics
Dieter Werthmuller, Raphael Rochlitz, Octavio Castillo-Reyes, Lindsey Heagy
Summary: The study compared the use of open-source codes for large-scale 3-D controlled-source electromagnetic surveys, demonstrating that these codes can compute comparable CSEM responses for challenging models. It also highlighted various issues that need to be addressed and emphasized the importance of appropriately discretizing the model. The research provided accurate responses for different models and mesh types, showcasing the significance of the chosen discretization method.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2021)
Article
Geosciences, Multidisciplinary
Jiankai Li, Ying Liu, Yuguo Li, Bo Han, Ji Cai
Summary: This paper introduces a goal-oriented adaptive edge-based finite element algorithm for modeling marine controlled-source electromagnetic responses in 3-D dipping anisotropic conductive media. The algorithm avoids source singularity by adopting the secondary field formulation for quasi-static Maxwell's equations. It is implemented on unstructured tetrahedral grids and can simulate complex model geometries.
JOURNAL OF APPLIED GEOPHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiaozhe Ju, Rolf Mahnken, Yangjian Xu, Lihua Liang
Summary: In this paper, a goal-oriented finite element method is developed for a class of micromorphic hyperelasticity problems, incorporating size effects by enriched kinematics. By introducing generalized solutions, an abstract weak formulation suitable for error estimation is established and discretized using finite element techniques. Exact error representations for user-defined quantities of interest are obtained based on duality techniques. The resulting discretizations of both primal and dual problems are shown to be consistent, ensuring optimal convergence order. Numerical aspects and an efficient error estimator are discussed, along with their application in a greedy adaptive mesh refinement algorithm.
COMPUTATIONAL MECHANICS
(2022)
Article
Geochemistry & Geophysics
M. Weiss, T. Kalscheuer, Z. Ren
Summary: This paper presents a parallel spectral element approach for forward modelling of realistic 3-D land-based controlled-source electromagnetic problems. The method combines the flexibility of the finite element method in using unstructured grids with the accuracy of the spectral method. Complex-shaped structures and topography can be accommodated by using unstructured hexahedral meshes. The method allows for arbitrary distributions of conductivity, magnetic permeability and dielectric permittivity. Numerical examples and convergence studies demonstrate the advantages and trade-offs of the method in terms of computational resources and accuracy.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Geochemistry & Geophysics
Ming Zhang, Colin G. Farquharson, Tingting Lin
Summary: This paper proposes a procedure of forward modeling 3-D frequency-domain wire-source electromagnetic data using the meshless generalized finite-difference (MGFD) method. The advantages of this method over mainstream forward-modeling methods are that mesh generation is not needed and it has high computational efficiency and a concise modeling process.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Geochemistry & Geophysics
J. Porte, F. Bretaudeau, J. F. Girard
Summary: Frequency-dependent complex resistivity (CR) is used to study the properties of Earth materials and the interaction between pore spaces and fluids. We developed a modeling and inversion code to consider the electromagnetic (EM) induction in the data and successfully recovered the CR and its frequency variation from CSEM data.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Ludovic Chamoin, Frederic Legoll
Summary: A goal-oriented strategy is introduced for multiscale computations using the MsFEM, incorporating the concept of Constitutive Relation Error and the solution of adjoint problems to control errors. A local and non-intrusive enrichment technique is proposed to enhance error bounds in order to reach a trade-off between certified reliability and computational cost in the MsFEM context. Performance of the method is tested on various numerical cases, showing highly accurate error estimation and efficient adaptive procedures.
COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Angel Javier Omella, Julen Alvarez-Aramberri, Magdalena Strugaru, Vincent Darrigrand, David Pardo, Hector Gonzalez, Carlos Santos
Summary: In this study, we presented a set of numerical methods for calculating the frequency-dependent effective primary wave velocity of heterogeneous rocks. The proposed methods have been validated through numerical results, which also demonstrate the impact of density, porosity, and the size and distribution of pores on the effective compressional wave velocity.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Angel Javier Omella, Ricardo Celorrio, David Pardo
Summary: This work focuses on characterizing narrow vertical cracks of finite size using optically excited lock-in thermography, proposing a sensitivity analysis to quantify the influence of model parameters on surface temperature, and utilizing numerical methods and weighted least squares to determine and reconstruct parameters. Theoretical uncertainty of reconstructed parameters and surface temperature sensitivities are explored, along with a numerical experiment to validate the findings.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Judit Munoz-Matute, David Pardo, Leszek Demkowicz
Summary: The DPG method is widely used for discretization of PDEs, and in this work, we extended it to time-dependent hyperbolic PDEs by reducing the second order system in time to first order and calculating the optimal testing analytically. The resulting method was validated for linear wave equations in 1D/2D + time, providing expressions for solutions in element interiors and allowing for design of error estimators for adaptivity.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Mostafa Shahriari, David Pardo, Jon A. Rivera, Carlos Torres-Verdin, Artzai Picon, Javier Del Ser, Sebastian Ossandon, Victor M. Calo
Summary: Deep learning is a numerical method for approximating functions, widely used in computational mechanics, particularly in the field of oil and gas exploration. Despite its ability to quickly solve inverse problems, DL methods require expert design decisions to achieve reliable results.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Judit Munoz-Matute, David Pardo, Leszek Demkowicz
Summary: The study utilizes the DPG method in the time variable for linear parabolic problems, calculating optimal test functions and showing equivalence to exponential integrators for trace variables. The method allows for computation of approximate solutions within time element interiors and enables the construction of a posteriori error estimations for adaptivity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Sergio Rojas, David Pardo, Pouria Behnoudfar, Victor M. Calo
Summary: This study presents a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization, which provides stable solutions on each mesh instance and minimizes errors by automatic mesh refinement.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Geochemistry & Geophysics
Kyubo Noh, David Pardo, Carlos Torres-Verdin
Summary: This study demonstrates the applicability of real-time 2.5-D DL inversion in well geosteering for imaging the subsurface electrical conductivity distribution. By developing a DL inversion workflow and utilizing fault detection and inversion modules, we are able to detect and quantify arbitrary dipping fault planes. Furthermore, using multidimensional inversion and deep-sensing measurements improves the inversion performance.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2022)
Article
Engineering, Multidisciplinary
Ana Fernandez-Navamuel, Filipe Magalhaes, Diego Zamora-Sanchez, Angel J. Omella, David Garcia-Sanchez, David Pardo
Summary: This paper proposes a Deep Learning Enhanced Principal Component Analysis (PCA) approach for outlier detection to assess the structural condition of bridges. By adding residual connections, the outlier detection ability of the network is enhanced, allowing for the detection of lighter damages.
STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Carlos Uriarte, David Pardo, Angel Javier Omella
Summary: We propose a dynamic Deep Learning architecture based on the Finite Element Method to solve linear parametric Partial Differential Equations. The architecture emulates the connectivity graph of the Finite Element method during mesh refinements. Different losses employing preconditioners and norms are discussed to improve convergence. The Deep-FEM is implemented in 1D but can be extended to 2D and 3D problems. Numerical experiments demonstrate good approximations for both symmetric positive definite and indefinite problems in parametric and non-parametric cases, with the exception of non-convex cases.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Civil
Ana Fernandez-Navamuel, Diego Zamora-Sanchez, Angel J. Omella, David Pardo, David Garcia-Sanchez, Filipe Magalhaes
Summary: This study proposes a supervised Deep Learning approach for damage identification in bridge structures. The methodology incorporates Finite Element simulations to enrich the training phase of a Deep Neural Network. The ultimate goal is to estimate the location and severity of damage from measurements of the dynamic response of the structure. The method successfully predicts the damage condition for real damage scenarios even in presence of measurement uncertainty.
ENGINEERING STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
Jamie M. Taylor, David Pardo, Ignacio Muga
Summary: When using Neural Networks to solve PDEs, the choice of the loss function is crucial. This work proposes the use of a Discrete Sine/Cosine Transform to accurately compute the H-1 norm, leading to the development of the Deep Fourier-based Residual (DFR) method. The DFR method efficiently approximates solutions to PDEs, particularly in cases where H2 regularity is lacking.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Carlos Uriarte, David Pardo, Ignacio Muga, Judit Munoz-Matute
Summary: Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. In the context of neural networks, this method becomes numerically unstable when approaching the trial solution. To overcome this, the authors propose the Deep Double Ritz Method (D2RM), which combines two neural networks for approximating trial functions and optimal test functions through a nested double Ritz minimization strategy. Numerical results demonstrate the robustness of the proposed method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Mechanical
Ana Fernandez-Navamuel, David Pardo, Filipe Magalhaes, Diego Zamora-Sanchez, Angel J. Omella, David Garcia-Sanchez
Summary: This work proposes a novel supervised learning approach to identify damage in operating bridge structures. The proposed method introduces environmental and operational conditions into synthetic damage scenarios used for training a Deep Neural Network. The method is applicable to large-scale complex structures. A comparative study reveals the importance of considering different conditions during training for accurate damage identification.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Geochemistry & Geophysics
Mohammad Mahdi Abedi, David Pardo
Summary: This study uses self-supervised deep learning to fill gaps in seismic data, proposing a new method of rearranging data and using a specific architecture and training strategy to reconstruct seismic events more accurately.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2022)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Felipe Vinicio Caro, Vincent Darrigrand, Julen Alvarez-Aramberri, Elisabete Alberdi Celaya, David Pardo
Summary: Our Goal-Oriented Adaptive (GOA) strategy is based on global and uniform h- or p-refinements followed by basis function removal based on estimated importance. Our Finite Element implementation uses a multi-level hierarchical data structure and represents the error in the QoI using a different bilinear symmetric positive definite form.
COMPUTATIONAL SCIENCE, ICCS 2022, PT II
(2022)
