Search Results (52)

The dynamic non-equilibrium effect (DNE) describes the non-unique character of saturation–capillary pressure relationships observed under static, steady-state, or monotonic hydrodynamic conditions. Macroscopically, the DNE manifests as variations in soil hydraulic characteristic curves arising from varying hydrodynamic testing conditions and is fundamentally governed by soil matrix particle size distribution. Changes in the DNE across porous media with discrete particle size fractions are investigated via stepwise drying experiments. Through quantification of saturation–capillary pressure hysteresis and DNE metrics, three critical signatures are identified: (1) the temporal lag between peak capillary pressure and minimum water saturation; (2) the pressure gap between transient and equilibrium states; and (3) residual water saturation. In the four experimental sets, with the finest material (Test 1), the peak capillary pressure consistently precedes the minimum water saturation by up to 60 s. Conversely, with the coarsest material (Test 4), peak capillary pressure does not consistently precede minimum saturation, with a maximum lag of only 30 s. The pressure gap between transient and equilibrium states reached 14.04 cm H₂O in the finest sand, compared to only 2.65 cm H₂O in the coarsest sand. Simultaneously, residual water saturation was significantly higher in the finest sand (0.364) than in the coarsest sand (0.086). The results further reveal that the intensity of the DNE scales inversely with particle size and linearly with wetting phase saturation (Sw), exhibiting systematic decay as Sw decreases. Coarse media exhibit negligible hysteresis due to suppressed capillary retention; this is in stark contrast with fine sands, in which the DNE is observed to persist in advanced drying stages. These results establish pore geometry and capillary dominance as fundamental factors controlling non-equilibrium fluid dynamics, providing a mechanistic framework for the refinement of multi-phase flow models in heterogeneous porous systems. Full article

Inverse problems involving time-fractional differential equations have become increasingly important for modeling systems with memory-dependent dynamics, particularly in biotransport and viscoelastic materials. Despite their potential, these problems remain challenging due to issues of stability, non-uniqueness, and limited data availability. Recent advancements in Physics-Informed Neural Networks (PINNs) offer a data-efficient framework for solving such inverse problems, yet most implementations are restricted to integer-order derivatives. In this work, we develop a PINN-based framework tailored for inverse problems involving time-fractional derivatives. We consider two representative applications: anomalous diffusion and fractional viscoelasticity. Using both synthetic and experimental datasets, we infer key physical parameters including the generalized diffusion coefficient and the fractional derivative order in the diffusion model and the relaxation parameters in a fractional Maxwell model. Our approach incorporates a customized residual loss function scaled by the standard deviation of observed data to enhance robustness. Even under 25% Gaussian noise, our method recovers model parameters with relative errors below 10%. Additionally, the framework accurately predicts relaxation moduli in porcine tissue experiments, achieving similar error margins. These results demonstrate the framework’s effectiveness in learning fractional dynamics from noisy and sparse data, paving the way for broader applications in complex biological and mechanical systems. Full article

This study proposes a standardized robustness measurement framework for comprehensive evaluation models based on the Intraclass Correlation Coefficient (ICC(3,1)), The framework aims to address two key issues: (1) the non-unique evaluation results caused by the abundance of such models, and (2) the lack of standardization and the arbitrariness in existing robustness testing procedures. Theoretical derivation and simulation confirm that ICC(3,1) exhibits a positive correlation with Kendall’s Coefficient of Concordance (Kendall’s W) and a negative correlation with Root Mean Square Error (RMSE) and Normalized Inversion Index (NII), demonstrating superior stability, discrimination, and interpretability. Under increased noise levels, ICC(3,1) maintains a balance between robustness and sensitivity, supporting its application in robustness evaluation and method selection. Full article

Energy efficiency (EE) is an important driver of quality of life (QoL), which is an overarching goal of sustainable development (SD). The levels of these phenomena in the European Union (EU) vary. Previous analyses presented in the literature have focused mainly on a one-dimensional view of EE and QoL. The authors of this article, given the multidimensional nature of the phenomena under study, present both categories from a holistic perspective. The purpose of this study was to identify the level of QoL in the context of EE and to compare the results of the classification of EU countries in terms of the analyzed phenomena. The study was conducted using the ELECTRE Tri method, one of the advanced techniques of multi-criteria decision analysis (MCDA). The classification procedure used made it possible to assign countries to predefined decision-making categories on the basis of preference threshold values and dominance relations to reference profiles. The 27 EU member states were analyzed on the basis of empirical data from 2023, using a set of 20 indicators characterizing EE and QoL. Countries were assigned to one of five classes, differentiating the level of development in both analyzed areas. Optimistic and pessimistic approaches were used to assess the stability of the classifications. The analysis showed the presence of countries with consistent results (e.g., Poland and Germany), extreme countries (Ireland and the Netherlands—high QoL with low EE; Romania and Croatia—inversely), as well as non-unique cases (e.g., Malta, the Czech Republic/Czechia, and Finland). The spatial approach indicated regions requiring special support. The results of the study can be a useful tool to support the process of designing public policies aimed at integrating social, economic, energy, and environmental goals within SD. Full article

Although various magnetic inversion techniques have been developed in geophysics, traditional methods are often constrained by inherent limitations such as low computational efficiency and pronounced non-uniqueness. In 3D magnetic inversion, multi-dimensional deep learning methods have shown promise in numerical simulations; however, their generalization capabilities and practical effectiveness in real-world geological applications, particularly in complex settings like gold exploration, remain underexplored. This study introduces MAGNETPRO, a residual convolutional neural network based on an encoder–decoder architecture, designed to accurately invert 2D magnetic field data into 3D magnetic susceptibility structures. To enhance the model’s generalization ability and inversion accuracy, an innovative data construction strategy was implemented to create a highly randomized training dataset incorporating complex geological features. Theoretical model tests demonstrate that MAGNETPRO achieves inversion accuracies of 97% across the entire region and 80% within magnetic structure areas, highlighting its excellent spatial resolution and structural recognition capabilities. To further validate its practical effectiveness, the method was applied to real exploration data from a gold mining area in Fujian Province. The results show a high degree of consistency between the inversion outcomes and drilling data, confirming the method’s reliability and practical value under real geological conditions. Full article

This study introduces a data-driven and machine learning (ML)-based methodology for converting the encounter wave frequency spectrum to the original wave spectrum, a critical process for navigating vessels with forward speed in various control and adjustment missions. The spectral conversion from the encounter- to original-frequency domain faces challenges under certain wave conditions due to the non-uniqueness of the inverse problem. To resolve these challenges, the authors developed an artificial neural network (ANN) model that transforms the encounter-frequency spectrum into the original wave spectrum at a given vessel speed and wave direction. The model was trained and validated using a large dataset mapped from various JONSWAP wave spectra to the corresponding encounter-frequency spectra for various vessel speeds and wave parameters. The hyperparameters of the ANN model were subsequently tested and optimized. The results demonstrate that the ANN model can effectively predict the original wave spectrum with high accuracy, as evidenced by a favorable R2 value and error distribution analysis. This approach not only enhances the reliability of wave spectrum estimation during maritime navigation but also broadens the capability of real-time operational controls and adjustments. Full article

Three-dimensional (3-D) magnetic inversion is an essential technique for revealing the distribution of subsurface magnetization structures. Conventional methods are often time-consuming and suffer from ambiguity due to limited observations and non-uniqueness. To address these limitations, we propose a novel inversion method under the machine learning framework. First, we design a training sample generation space by extracting the horizontal positions of magnetic sources from the analytic signal amplitude and the reduced-to-the-pole anomalies of magnetic field data. We then employ coordinate transformation to achieve data augmentation within the designed space. Subsequently, we utilize a broad learning network to map the magnetic anomalies to 3-D magnetization structures, reducing the magnetic inversion time. The efficiency of the proposed method is validated through both synthetic and field data. Synthetic examples indicate that compared to the traditional inversion method, the proposed method approximates the true model more closely. It also outperforms traditional and deep learning methods in terms of computational efficiency. In the field example of the Danzhukeng Pb-Zn-Ag deposit in South China, the inversion result is consistent with drilling and controlled-source audio frequency magnetotelluric survey data, providing valuable insights for subsequent exploration. This study provides a new practical tool for processing and interpreting magnetic anomaly data. Full article

Recent advancements in geophysical exploration have highlighted the importance of integrating electromagnetic (EM) and magnetic data to enhance subsurface target detection. Conventional inversion techniques often struggle with the non-uniqueness of solutions and sensitivity to noise when relying on a single data modality. In this study, we introduce a novel deep learning framework, MagEMNet, designed to jointly invert EM and magnetic responses. This convolutional neural network (CNN)-based model effectively combines these two complementary data types, improving the estimation of target characteristics such as location, orientation, and physical properties. Trained on synthetic datasets generated through forward modeling, MagEMNet leverages the adaptive moment estimation (Adam) optimizer and a dynamic learning rate strategy to enhance convergence. Our results show that MagEMNet not only outperforms traditional inversion techniques in terms of accuracy but also accelerates the inversion process, offering an efficient solution for real-world applications, including unexploded ordnance (UXO) detection and subsurface resource assessment. Full article

Magnetization vector inversion (MVI) is an effective method for simultaneously determining the distribution of magnetization intensity and direction without knowing the direction of magnetization beforehand. Nevertheless, the presence of serious non-uniqueness in MVI imposes challenges in achieving accurate and reliable results. To improve the accuracy of MVI, we propose a method that incorporates a modulus constraint, informed by an analysis of the model constraints in two different frameworks. We employ a sparse operator on the magnetization magnitude and obtain an explicit expression for the magnetization components, establishing correlation constraints among them. Synthetic test results show that this method can achieve models with clear boundaries and consistent magnetization directions. Furthermore, the application of a sparse operator to the gradient’s modulus of the magnetization magnitude helps recover inclined structures. However, the dispersed magnetization directions suggest that we should also constrain the magnetization direction, simultaneously. The inversion of magnetic data measured over the Zaohuohexi iron-polymetallic deposit in Qinghai Province, northwest China, verified the proposed approach’s effectiveness. Full article

A major challenge in accidental or unregulated releases is the ability to identify the pollutant source, especially if the location is in a large industrial area. Usually in such cases, only a few sensors provide non-zero signal. A crucial issue is therefore the ability to use a small number of sensors in order to identify the source location and rate of emission. The general problem of characterizing source parameters based on real-time sensors is known to be a difficult task. As with many inverse problems, one of the main obstacles for an accurate estimation is the non-uniqueness of the solution, induced by the lack of sufficient information. In this study, an efficient method is proposed that aims to provide a quantitative estimation of the source of hazardous gases or breathable aerosols. The proposed solution is composed of two parts. First, the physics of the atmospheric dispersion is utilized by a well-established Lagrangian stochastic model propagated backward in time. Then, a new algorithm is formulated for the prediction of the spacial expected uncertainty reduction gained by the optimal placement of an additional sensor. These two parts together are used to construct an adaptive decision support system for the dynamical deployment of detectors, allowing for an efficient characterization of the emitting source. This method has been tested for several scenarios and is shown to significantly reduce the uncertainty that stems from the insufficient information. Full article

The traditional approach to optical design faces limitations as photonic devices grow increasingly complex, requiring advanced functionalities. Recently, machine learning algorithms have gained significant interest for extracting structural designs from customized wavelength spectra, surpassing traditional simulation methods known for their time-consuming nature and resource-demanding computational requirements. This study focuses on the inverse design of a reflectionless multilayer thin-film structure across a specific wavelength region, utilizing a tandem neural network (TNN) approach. The method effectively addresses the non-uniqueness problem in training inverse neural networks. Data generation via the transfer matrix method (TMM) involves simulating the optical behavior of a multilayer structure comprising alternating thin films of silicon dioxide (SiO₂) and silicon (Si). This innovative design considers both reflection and absorption properties to achieve near-zero reflection. We aimed to manipulate the structure’s reflectivity by implementing low-index and high-index layers along with Si absorption layers to attain specific optical properties. Our TNN demonstrated an MSE accuracy of less than 0.0005 and a maximum loss of 0.00781 for predicting the desired spectrum range, offering advanced capabilities for forecasting arbitrary spectra. This approach provides insights into designing multilayer thin-film structures with near-zero reflection and highlights the potential for controlling absorption materials to enhance optical performance. Full article

The probing depth of the transient electromagnetic method (TEM) refers to the depth range at which the underground conductivity changes can be effectively detected. It typically ranges from tens of meters to several kilometers and is influenced by factors such as instrument parameters and the conductivity of the subsurface structure. Rapid and accurate probing depth is useful for the selection of appropriate inversion parameters and improving survey accuracy. However, mainstream methods suffer from issues such as low computational precision, large uncertainties, or high computational requirements, making them unsuitable for processing massive airborne electromagnetic data. In this study, we propose a prediction model based on deep learning that can directly compute the probing depth from the TEM responses, and its effectiveness and accuracy are validated through synthetic models and field measurements. We compared the performance of classic deep learning models, including CNN, RESNET, and RNN, and found that RNN performed the best overall on both synthetic and field data. Furthermore, we apply this algorithm to deep learning-based ATEM inversion by constraining the one-dimensional resistivity model depths in the training set, to reduce the non-uniqueness of the inversion, accelerate the convergence, and improve its prediction accuracy. Full article

Mobile observation has been widely used in the monitoring of air pollution. However, studies on pollution sources and emission characteristics based on mobile navigational observation are rarely reported in the literature. A method for quantitative source analysis for industrial air pollutant emissions based on mobile observations is introduced in this paper. NO_x pollution identified in mobile observations is used as an example of the development of the method. A dispersion modeling scheme that fine-tuned the meteorological parameters according to the actual meteorological conditions was adopted to minimize the impact of uncertainties in meteorological conditions on the accuracy of small-scale dispersion modeling. The matching degree between simulated and observed concentrations was effectively improved through this optimization search. In response to the efficiency requirements of source resolution for multiple sources, a random search algorithm was first used to generate candidate solution samples, and then the solution samples were evaluated and optimized. Meanwhile, the new index $S_{match}$ was established to evaluate the quality of candidate samples, considering both numerical error and spatial distribution error of concentration, in order to address the non-uniqueness of the solution in the multi-source problem. Then, the necessity of considering the spatial distribution error of concentration is analyzed with the case study. The average values of NO_x emission rates for the two study cases were calculated as 69.8 g/s and 70.8 g/s. The $S_{match}$ scores were 0.92–0.97 and 0.92–0.99. The results were close to the online monitoring data, and this kind of pollutant emission monitoring based on the mobile observation experiment was initially considered feasible. Additional analysis and clarifications were provided in the discussion section on the impact of uncertainties in meteorological conditions, the establishment of a priori emission inventories, and the interpretation of inverse calculation results. Full article

Surface gravity inversion attempts to recover the density contrast distribution in the 3D Earth model for geological interpretation. Since airborne gravity is characterized by large data volumes, large-scale 3D inversion exceeds the capacity of desktop computing resources, making it difficult to achieve the appropriate depth/lateral resolution for geological interpretation. In addition, gravity data are finite and noisy, and their inversion is ill posed. Especially in the absence of a priori geological information, regularization must be introduced to overcome the difficulty of the non-uniqueness of the solutions to recover the most geologically plausible ones. Because the use of Haar wavelet operators has an edge-preserving property and can preserve the sensitivity matrix structure at each level of the multilevel method to obtain faster solvers, we present a multilevel algorithm for large-scale gravity inversion solved by the re-weighted regularized conjugate gradient (RRCG) algorithm to reduce the inversion computational resources and improve the depth/lateral resolution of the inversion results. The RRCG-based multilevel inversion was then applied to synthetic cases and airborne gravity data from the Quest-South project in British Columbia, Canada. Results from synthetic models and field data show that the RRCG-based multilevel inversion is suitable for obtaining density contrast distributions with appropriate horizontal and vertical resolution, especially for large-scale gravity inversions compared to Occam’s inversion. Full article

Understanding the subsurface is of prime importance for many geological and hydrogeological applications. Geophysical methods offer an economical alternative for investigating the subsurface compared to costly borehole investigations. However, geophysical results are commonly obtained through deterministic inversion of data whose solution is non-unique. Alternatively, stochastic inversions investigate the full uncertainty range of the obtained models, yet are computationally more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) for the stochastic inversion of time-domain electromagnetic data (TDEM). First, we analyse the impact of the accuracy of the numerical forward solver on the posterior distribution, and derive a compromise between accuracy and computational time. We also introduce a threshold-rejection method based on the data misfit after the first iteration, circumventing the need for further BEL1D iterations. Moreover, we analyse the impact of the prior-model space on the results. We apply the new BEL1D with a threshold approach on field data collected in the Luy River catchment (Vietnam) to delineate saltwater intrusions. Our results show that the proper selection of time and space discretization is essential for limiting the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distribution has a direct impact on fitting the observed data and is crucial for a realistic uncertainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach, as it allows us to estimate the uncertainty at a limited cost. Full article