Understanding and modeling dynamic inter-stock dependencies is crucial for effective investment decisions. While graph-based methods have demonstrated potential in capturing stock relationships, existing approaches based on static or discrete-time dynamic graphs fail to address the continuous evolution of market dynamics. In this work, we propose CFC-GMixer, a novel continuous-time graph framework that synergizes multi-scale temporal features with graph-based continuous-time modeling. Our architecture consists of two main components: (1) a Time Mixer module that extracts multi-scale temporal features to capture market dynamics at different time horizons, enabling effective graph relationship modeling, (2) a unified CFC-GCN module that leverages these hierarchical features to simultaneously model adaptive inter-stock relationships and their continuous temporal evolution through Graph Convolutional Networks (GCN) and Closed-Form Continuous-Time Networks (CFC). Experiments on three real-world datasets demonstrate that CFC-GMixer outperforms state-of-the-art methods in both accuracy and precision.

Stock recommendation plays a critical role in financial investment decision-making. In real-world markets, stocks exhibit complex interdependencies through correlated price movements. Existing approaches derive stock relationships either from fundamental information (e.g., industry categories) or price temporal patterns. However, these methods face limitations: domain expertise-based approaches fail to capture implicit correlations, while short-term relationship modeling suffers from inadequate temporal feature representation. To address these challenges, we propose ALSGCN, an Attention-based Long- and Short-term Graph Convolutional Network for stock recommendation. ALSGCN captures dynamic stock relationships through two key components: (1) a market-aware mechanism that models long-term dependencies by incorporating the influence of large-cap stocks, and (2) an attention-based temporal feature extraction module that adaptively weights information across time steps. These complementary relationship representations are integrated through a multichannel graph attention module for effective feature learning. Extensive experiments on two real-world datasets demonstrate that ALSGCN consistently outperforms state-of-the-art baselines across most evaluation metrics. Code is available at https://github.com/hongnianwang/ALSGCN.

In this article, to explore the efficiency and precision of the 3-D finite volume method (FVM) for the logging while drilling (LWD) ultradeep resistivity measurements, we compared four different schemes: field-based total-field FVM, coupled potentials total-field FVM, field-based secondary-field FVM, and coupled potentials secondary-field FVM. The fast and accurate discretization of scattered current density in the secondary-field method is another issue we focus on. On the one hand, we improve the discretization accuracy of the scattered current density near the source by extracting the direct waves in the background electric field. On the other hand, based on the dyadic Green’s functions (DGFs) of vector potentials, the number of Sommerfeld integrals in the background electric field is reduced as much as possible through the background field library and interpolation. The numerical results show that the accuracy and stability of the secondary-field method are better than those of the total-field method and the efficiency of the background electric field is greatly improved through the library and interpolation. Based on the premises of the LWD ultradeep resistivity measurements and the direct solver, the accuracy of the field-based and coupled potentials methods is almost the same, however, the field-based method is much more efficient. Overall, we believe that the field-based secondary-field FVM and the direct solver constitute a more efficient modeling scheme with high precision for LWD ultradeep resistivity measurements.

With the development of computation methods and the requirement of data processing, it is often required to execute electromagnetic (EM) simulations in a lot of different complex formation models simultaneously. For this purpose, in this article, we advance a contraction high-order Born approximation (CHBA) of scattered EM fields from arbitrary perturbation in conductivity based on the 3-D finite volume method (FVM) of coupled potentials. We manage to apply the CHBA to efficiently and precisely simulate the logging while drilling (LWD) ultra-deep resistivity measurement in multiple perturbation models based on arbitrarily given anisotropic reference models. First, from the energy conservation of the EM fields, we derive the rigorous contraction operator about the modified scattered EM fields through the variable transformations. After that, the modified scattered EM fields are expanded into an unconditionally convergent series. All terms of the series can be obtained by solving the Helmholtz equation with recursively right-hand terms. Then, we apply the relative residuals of the modified scattered EM fields to determine the truncation order of the series and acquire the reliable CHBA solution. The Helmholtz equation is discretized by the 3-D FVM and solved by the parallel direct sparse solver (PARDISO). We thus obtain the EM fields of multiple sources in the multiple perturbation models simultaneously. Finally, the numerical results validate the algorithm and compare the EM responses in multiple perturbation models.

The article advances a 3-D adaptive regularization nonlinear inversion of the logging while drilling (LWD) ultradeep multicomponent resistivity (LWD-UDMCR) by the Gauss-Newton (GN) method. We manage to reconstruct the pixel-based horizontal and vertical conductivities simultaneously in a goal domain outside an arbitrary dipping borehole. The piecewise constant functions are used to describe the spatial distribution of the block-based and the pixel-based conductivity. The background formation is assumed as the horizontally layered transversely isotropic (TI) media, and the background electromagnetic (EM) fields are determined analytically by the transmission line method (TLM). We then use the 3-D finite volume method (FVM) of secondary field coupled potentials and parallel direct sparse solver (PARDISO) to simulate the tool responses and Fréchet derivatives simultaneously. Through the projection operator and OpenMP parallel technique, we further enhance the computational efficiency of the pixel-based explicit Fréchet derivatives and set up a complete normalization linearized response. After that, the large normal equation from the quadratic objective function is solved by the preconditioned conjugate gradient (PCG) to determine the gradient of the objective function. By properly controlling the maximum component of the gradient per iteration step, we acquire an adaptive regularization factor so that the stabilization of the inversion solution is assured as well as the realization of the best fit of the input data with the modeling logs. Finally, numerical tests validate the algorithm and antinoise ability.

The article proposes an efficient global optimization of adaptive boundary detection from the logging while drilling (LWD) azimuthal electromagnetic (EM) measurements. The goal is to realize real-time geo-steering in 1-D layered transversely isotropic (TI) formation with an arbitrarily deviated borehole. The method includes apparent resistivity (APR) extraction and 0-D inversion, 1-D adaptive regularized iterative inversion, and global optimization. The APR extraction and 0-D inversion are used to quickly determine the initial horizontal and vertical resistivities of the bed where the tool is located. Subsequently, the 1-D regularized inversion is performed to achieve a local minimum solution near an arbitrarily given initial model. For solving the non-unique problem and acquiring the globally optimal solution, several different initial values are selected according to the possible range per model parameter to construct a serial of initial models. The OpenMP parallel technique is applied for simultaneous inversions at all initial models. Multiple inversion solutions may be obtained due to the non-uniqueness. The one with the minimal residual function in all inversion results will become the globally optimal solution. Furthermore, the tool response and its exact explicit Fréchet derivative with respect to each model parameter are analytically calculated, while an adaptive regularization factor ensures a gradual reduction of the objective function. The correction of field data is required to reduce the mandrel effect. The inversion results of synthetic and field data demonstrated that the proposed inversion algorithm efficiently provides the reliable bed boundaries and resistivities around the wellbore.

Machine learning has demonstrated success in clinical risk prediction modeling with complex electronic health record (EHR) data. However, the evolving nature of clinical practices can dynamically change the underlying data distribution over time, leading to model performance drift. Adopting an outdated model is potentially risky and may result in unintentional losses. In this paper, we propose a novel Hybrid Adaptive Boosting approach (HA-Boost) for transfer learning. HA-Boost is characterized by the domain similarity-based and class imbalance-based adaptation mechanisms, which simultaneously address two critical limitations of the classical TrAdaBoost algorithm. We validated HA-Boost in predicting hospital-acquired acute kidney injury using real-world longitudinal EHRs data. The experiment results demonstrate that HA-Boost stably outperforms the competing baselines in terms of both Area Under Receiver Operating Characteristic and Area Under Precision-Recall Curve across a 7-year time span. This study has confirmed the effectiveness of transfer learning as a superior model updating approach in a dynamic environment.

A new approximation algorithm is developed to compute the electromagnetic (EM) tensor Green’s function in the biaxial anisotropic media based on the Fourier series expansion. First, a rectangular region is chosen as the computation region, in which the EM field can be expressed as a 2-D Fourier series. The Fourier coefficients can be regarded as the EM field in discrete wavenumber domain. We further obtain the EM solution in the spatial domain in the form of Fourier series. Then, we use the finite terms of the Fourier series to approximate the EM field for enhancement of computation efficiency. Because the new method avoids the numerical integration in the infinite wavenumber domain, it is more convenient to implement than other methods based on integral transform. Finally, the spatial distribution of the tensor Green’s function for a transversely isotropic medium is presented to verify the proposed approach. The agreements between the results obtained by the present method and the analytic solution demonstrate the validity and the robustness of our algorithm.

We presented a semi-analytic solution for the sensitivity of the response tensor of the multi-component induction logging (MCIL) tool in a homogeneous biaxial anisotropic (BA) medium. By using the perturbation principle and the spectral representation of electromagnetic (EM) fields, the sensitivity was formulated as a seven-fold integral whose integrand involves two sets of spectral electric fields. Fortunately, such a complicated integral can be reduced to a three-fold integral, which consists of two parts: one is a definite integral over the spatial variablezthat can be analytically integrated; the remaining is a two-fold integral over the spectral variable k that is computed by numerical quadrature. We verified our formulation by comparing it with the exact solution and the finite-difference (FD) approximation.

Human mobility forecasting in a city is of utmost importance to transportation and public safety, but with the process of urbanization and the generation of big data, intensive computing and determination of mobility pattern have become challenging. This study focuses on how to improve the accuracy and efficiency of predicting citywide human mobility via a simpler solution. A spatio-temporal mobility event prediction framework based on a single fully-convolutional residual network (STAR) is proposed. STAR is a highly simple, general and effective method for learning a single tensor representing the mobility event. Residual learning is utilized for training the deep network to derive the detailed result for scenarios of citywide prediction. Extensive benchmark evaluation results on real-world data demonstrate that STAR outperforms state-of-the-art approaches in single-and multi-step prediction while utilizing fewer parameters and achieving higher efficiency.

First, we directly introduce the cosine transform to compute the time-domain electromagnetic (EM) response excited by cause step turnoff. Then, we advance a novel semianalytic algorithm based on integration, summation, and cube spline interpolation (ISCSI) method to efficiently accomplish the cosine transform. The ISCSI method divides the integral into a sum of partial integrals, which can be solved by cube spline interpolation combined with Newton-Leibniz formula. On the basis, we apply a known convolution method to further compute the time-domain response by arbitrarily waveform in airborne transient EM measurement. Finally, numerical tests valid the ISCSI method is easier to implement and more efficient than the traditional digital filter method because the ISCSI method only requires less frequency sampling amount to accomplish the cosine transform.

In this paper, we set up an efficient Fréchet derivative algorithm of inversion of multicomponent induction logging (MCIL) data in horizontal layered transversely isotropic (TI) formations based on transmission line method (TLM) in order to simultaneously reconstruct the model vector including both horizontal and vertical conductivities, horizontal interfaces, borehole dipping angle, and tool azimuth in deviated well from the MCIL data. First, MCIL responses in the TI model are efficiently determined by both the spectrum EM fields obtained by TLM and the semianalytical computation of Sommerfeld integrals based on the cubic spline interpolation. Then, the Born approximations are executed to derive the MCIL Fréchet derivatives as the sixfold integrals of the products of two spectrum EM fields in infinite domains. By using the integral characters of the 2-D Dirac function, the sixfold integrals of Fréchet derivatives are further simplified into twofold integrals: One is the Sommerfeld integral in the radial spectrum domain, and the other is the definite integral in the vertical spatial domain. They are efficiently computed by the semianalytical approach similar to the MCIL simulation. Therefore, we obtain the linear equations between changes in the MCIL responses and small perturbations in the model vector. After that, we iteratively modify all of the model parameters to realize the best fit between the input data and the synthetic data of the inverted model by the normalization of the Fréchet derivative and singular value decomposition technique. Finally, we apply numerical results to investigate the characteristics of the Fréchet derivatives and to validate the inversion method and its antinoise ability.

An efficient and reliable numerical mode matching (NMM) method is developed to simulate the responses of multicomponent induction logging (MCIL) in the horizontally layered inhomogeneous transversally isotropic (TI) formations with the borehole and the invasion zone. The computation of MCIL responses is entirely transformed into three axially symmetrical problems on the Fourier harmonic components of the electromagnetic (EM) fields. The two extra singular differential operators about the horizontal EM components are introduced to describe the influence of the accumulation charge at the cylindrical interfaces on the EM fields excited by the horizontal magnetic dipoles. The first and second kinds of homogeneous boundary conditions of the different harmonic components of horizontal electrical fields near the borehole axis are derived to ensure that the EM problems become well posed in the cylindrical coordinate system. Then, the NMM is applied to solve the three axisymmetric problems with the extra singular differential operators. The numerical results demonstrate that the proposed method can accurately and efficiently simulate the MCIL responses in the horizontally layered TI formations with the large contrast resistivity.

An adaptive regularization iterative inversion of array multicomponent induction well logging datum is established to simultaneously reconstruct the horizontal and vertical conductivities of both invasion zone and origin formation, invasion radius, and the interface depth of each bed in the horizontally stratified inhomogeneous transversally isotropic (TI) formation. Applying numerical mode matching method, we can obtain a much compact semianalytic expression of the electromagnetic tensor Green's functions by magnetic current source in the inhomogeneous TI formation. Then, using the perturbation principles, an efficient computation of Fréchet derivatives of the multicomponent induction logging response is set up with respect to all the model parameters. After that, the combination of Morozev's discrepancy principle with Cholesky's decomposition is applied to adaptively select regularization factor during inversion so that stabilization of inversion solution is assured as well as realization of best fit of the input data with the modeling logs. Finally, the numerical tests validate the algorithm.

In this paper, we present an efficient algorithm to simulate the response of a multicomponent induction well-logging (MCIL) tool in a cylindrically layered anisotropic formation (transversely isotropic media). The tool consists of three pairs of orthogonally arranged transmitter-receiver coils for measuring the magnetic field around a borehole for oil and gas exploration. First, we will derive the EM field components to present the coupled transverse magnetic and transverse electric modes in the spectral domain for an arbitrary observation layer from the Maxwell equation and obtain the spectral-domain Green's function. The new local transmission and both the local and generalized reflections for the media are given. After that, we use a cubic spline interpolation to realize the inverse Fourier transformation and obtain the spatial-domain Green's function for the investigation of the response characteristics of the MCIL tool. Finally, we give some numerical results to explore the response characteristics of the tool in several different environments.

In this paper, we advance a fast iterative inversion algorithm of multicomponent induction well-logging (MCIL) datum to simultaneously reconstruct a total model vector in a deviated well in the horizontally stratified transversally isotropic (TI) formation (TI medium) with the case-neglecting borehole. The model vector consists of the horizontal and vertical conductivities, the interface depth of each bed, and a borehole dipping angle. Because an electromagnetic field emitted by a horizontal magnetic dipole is no longer axially symmetrical, we first decompose the horizontal magnetic dipole located at borehole axis as the sum of two harmonics only so that the computation of MCIL responses can be entirely transformed into three axially symmetrical problems. Therefore, we solve them through the numerical mode matching method and obtain the semianalytic (SA) solution of an EM field in an arbitrary bed. Then, based on the perturbation principle and spatial distribution of formation conductivity related to the model vector, we set up an efficient SA algorithm of Frechet derivatives of the MCIL response with respect to the model vector. Then we extract an initial model from synthetic logs for the inversion through a special blocking technique. Finally, we give an iterative process to simultaneously reconstruct all model parameters from the logs through a combination of a normalization and singular value decomposition technique. Numerical tests validate the algorithms.

The new multiarray induction logging tool consists of eight different spacing three-coil arrays, operates at three frequencies, and measures both in-phase and quadrature signals to provide more information on the distribution of conductivity around the borehole than the conventional induction tool. A horizontally layered medium with a step-profile invasion per bed is used to describe the formation model. In this paper, we will establish a regularized iterative inversion algorithm to simultaneously reconstruct geometric parameter and resistivity per bed from the multiarray induction logging data. During the inversion, the Frechet derivative matrix with respect to the model parameters is efficiently calculated in terms of the perturbation principle, and the hybrid approach of Maxwell's equations and the two-order Langrange function is used to determine the eigenmode solution in the radial direction in order to further enhance efficiency of forward modeling and calculation of the Frechet derivative matrix. Normalizations are used to transform the model vector, log data, and the Frechet matrix into dimensionless variables. Regularization and exponential damping factors are used to enhance inversion stability. We will also analyze and reduce the inversion errors originating from the noise in input data and the errors in bed thicknesses.

The expression and algorithm of the Born approximation of dual-laterolog (DLL) are different from nonfocusing resistivity tools because the currents and potentials on the surfaces of the electrodes must be satisfied with the special focusing conditions. The Born approximation is described by a linear integral equation about the changes in current density, bucking currents, and potentials on the surfaces of all the electrodes, caused by small perturbations in the formation conductivity. Using the complex forward modeling of DLL, and the semi-analytic solution of the Green's function, we advance the fast algorithm of the Frechet derivative matrix containing the partial derivatives of both the apparent resistivities and bucking currents with respect to all components of the model vector. A normalization approach is used to transform the matrix into a dimensionless matrix. We then develop a multiparameter iterative inversion technique to simultaneously reconstruct all model parameters. Furthermore, we analyze the influence of both noises in data and errors of some model parameters on the inversion solution and give a method to choose the regularization factors. Finally, numerical result tests show the characteristics of the normalized Frechet matrix, the influence of errors of both bed thickness and flushed zone resistivity, etc, on the inversion solution when they are fixed, and the great improvement of the inversion quality when all model parameters are simultaneously reconstructed from both the apparent resistivities and bucking currents.

A microspherically focused log is a focused microresistivity device used for evaluation of the electrical property of the subsurface rock formation for oil and gas exploration. The electrodes are mounted on a flexible rubber pad that is applied against the borehole wall to be in close proximity to the formation. Unlike other nonpad-focused electrode tools that are centered in the borehole such as Dual-Laterolog, the modeling of the microspherically focused log is much more complex and requires three-dimensional (3-D) code in general because the electric field is no longer axially symmetric. However, in a horizontally layered medium, the axial symmetry of the earth formation makes the problem two-and-a-half-dimensional (2.5-D), which is much simpler. In this paper, the authors apply the semi-analytic method to tackle this 2.5-D problem and establish a fast-modeling algorithm. First, they expand the Green's function as a Fourier series in order to transform the 2.5-D problem into a sequence of the axially symmetric (2-D) problems. The semi-analytic method is used to obtain the expression of the Green's function. Applying the focusing conditions of the tool and the solution of the Green's function, we then establish the boundary integral equation with respect to the current density, currents, and potentials on the electrode surfaces, and study its numerical solutions. Then, they compare results computed from the semi-analytical method with those from the finite element method (FEM) to verify its accuracy. Finally, they study the response characteristics of the tool in several different environments by the semi-analytical method.