Limited Sampling Data Research Articles

Physics-Informed Fully Convolutional Networks for Forward Prediction of Temperature Field and Inverse Estimation of Thermal Diffusivity

Abstract Physics-informed neural networks (PINNs) are a novel approach to solving partial differential equations (PDEs) through deep learning. They offer a unified manner for solving forward and inverse problems, which is beneficial for various engineering problems, including heat transfer analysis. However, traditional PINNs suffer from low accuracy and efficiency due to the fully-connected neural network framework and the method to incorporate physical laws. In this paper, a novel physics-informed learning architecture, named physics-informed fully convolutional networks (PIFCNs), is developed to simultaneously solve forward and inverse problems in thermal conduction. The use of fully convolutional networks (FCNs) significantly reduces the density of connections. Thus, the computational cost is reduced. With the advantage of the nodal-level match between inputs and outputs in FCNs, the output solution can be used directly to formulate discretized PDEs via a finite difference method, which is more accurate and efficient than the traditional approach in PINNs. The results demonstrate that PIFCNs can flexibly implement Dirichlet and Neumann boundary conditions to predict temperature distribution. Remarkably, PIFCNs can also estimate unknown thermal diffusivity with an accuracy exceeding 99%, even with incomplete boundaries and limited sampling data. The results obtained from PIFCNs outperform those obtained from PINNs.

Global geologic expert system and database for predicting carbonate reservoirs from seismic: Application to the Upper Jurassic

Carbonate systems are influenced by a great variety of physical and biological controlling factors that operate from global to local scales. The resulting intrinsic complexity of carbonate platforms makes them difficult to predict, especially when data are limited. Predicting geologic geometries and properties based on limited sampling or uncalibrated seismic data generally relies on a priori knowledge and equivocal interpretations that are marked by geologist perception and personal experience. To overcome these uncertain interpretations of such a complex natural system, which can become critical in frontier exploration, we developed an expert system that relies on a process-based method and a standardized data set using normalized information and parameters. The main innovation relies on the realization of knowledge- and process-based synthetic carbonate stratigraphic architectures that support seismo-stratigraphic interpretations. The workflow consists of four steps: (1) bibliographic compilation of a geologic database for each case study supported by quantitative parameters (e.g., sedimentation duration and thickness) and qualitative parameters (geodynamic context, seismic architecture, and facies model); (2) statistical analyses to establish consistent geologic classes and spatiotemporal trends; (3) process-based modeling to simulate stratigraphic architectures associated with carbonate sedimentation processes in a physically constrained numerical environment and testing different geologic hypotheses; and (4) realization of a predictive palaeogeographic map representing the global distribution of carbonate stratigraphic architectures, and estimation of controlling parameters for unconstrained case studies. The expert system is based on 77 case studies of Upper Jurassic carbonate platforms, which reveal the resemblance of these carbonate systems, in response to uniform global palaeoclimatic conditions and sea level. Significant local differences in stratigraphic architectures are related to specific geodynamic contexts and subsidence trends. The thickest carbonate platforms are developed in extensive/passive geodynamic settings such as the Central Atlantic Ocean margins, while thinner platforms form in intra- and peri-cratonic settings such as those of the Arabian region.

OutcropHyBNet: Hybrid Backbone Networks with Data Augmentation for Accurate Stratum Semantic Segmentation of Monocular Outcrop Images in Carbon Capture and Storage Applications.

The rapid advancement of climate change and global warming have widespread impacts on society, including ecosystems, water security, food production, health, and infrastructure. To achieve significant global emission reductions, approximately 74% is expected to come from cutting carbon dioxide (CO2) emissions in energy supply and demand. Carbon Capture and Storage (CCS) has attained global recognition as a preeminent approach for the mitigation of atmospheric carbon dioxide levels, primarily by means of capturing and storing CO2 emissions originating from fossil fuel systems. Currently, geological models for storage location determination in CCS rely on limited sampling data from borehole surveys, which poses accuracy challenges. To tackle this challenge, our research project focuses on analyzing exposed rock formations, known as outcrops, with the goal of identifying the most effective backbone networks for classifying various strata types in outcrop images. We leverage deep learning-based outcrop semantic segmentation techniques using hybrid backbone networks, named OutcropHyBNet, to achieve accurate and efficient lithological classification, while considering texture features and without compromising computational efficiency. We conducted accuracy comparisons using publicly available benchmark datasets, as well as an original dataset expanded through random sampling of 13 outcrop images obtained using a stationary camera, installed on the ground. Additionally, we evaluated the efficacy of data augmentation through image synthesis using Only Adversarial Supervision for Semantic Image Synthesis (OASIS). Evaluation experiments on two public benchmark datasets revealed insights into the classification characteristics of different classes. The results demonstrate the superiority of Convolutional Neural Networks (CNNs), specifically DeepLabv3, and Vision Transformers (ViTs), particularly SegFormer, under specific conditions. These findings contribute to advancing accurate lithological classification in geological studies using deep learning methodologies. In the evaluation experiments conducted on ground-level images obtained using a stationary camera and aerial images captured using a drone, we successfully demonstrated the superior performance of SegFormer across all categories.

Adaptive source localization for mobile robots based on Kriging prediction

This paper addresses the source localization for mobile robots under the assumption of spatio-temporal invariance. Two kriging-based source localization methods, namely global traversal and adaptive gradient extremum, are proposed and implemented using limited sampling data. The global traversal method controls the robot to traverse the whole region according to a fixed trajectory, and finally fits the information distribution of the sources in the whole target region, so as to obtain the location and number of sources. The adaptive gradient extremum method initially controls the robot to collect data by traversing the target search area. Simultaneously, it uses the collected data to fit the source distribution across the entire region. Then, it utilizes gradient and extremum principles to determine the next target point iteratively, eventually reaching the positions of the sources. The simulation results show that the global traversal can obtain more field distribution information, and the adaptive gradient extremum method is more efficient.

Dynamic Security Assessment of Small-Signal Stability for Power Grids Using Windowed Online Gaussian Process

The online small-signal stability assessment of electrical power grids is typically a challenging problem due to uncertainties and parameter variations of power system dynamics as well as the incurred high computational complexity. This paper proposes a novel theoretical framework for dynamic small-signal stability assessment of power grids by estimating the region of attraction (ROA) for operating states in real time. By analyzing the latest sampling data of power grids in a fixed time window, an up-to-date training set is constructed with the aid of converse Lyapunov function, which enables us to develop an online learning approach based on Gaussian Process (GP) to assess the stability level of power grids. As a result, an iteration algorithm is designed to update the assessment parameters by learning the input-output pairs in the training set. Theoretical analysis is conducted to ensure the existence of converse Lyapunov function for differential-algebraic system that serves to describe power system dynamics, as well as to estimate the region of attraction for operating states with a given confidence level. In particular, a practical method is proposed to leverage time series of phasor measurement unit (PMU) measurements including voltage/current magnitude, phase and frequency (i.e., PMU data) of real power grids for validating the online GP approach. Moreover, validations are taken to substantiate the proposed approach by using PMU data of real smart-grid infrastructure and IEEE test cases. The proposed assessment approach contributes to situational awareness of human operators in the control station, thereby taking proactive remedial actions prior to emergencies. Note to Practitioners—This paper was motivated by the problem of online assessment of power systems security but it also applies to other industrial control systems that have stable state trajectories. Existing approaches to security assessment of power systems generally focus on the adoption of various machine-learning algorithms by treating power grid as a “black box,” which ignores the intrinsic characteristics of power systems and thus restricts the inference performance. This paper proposes a new approach using limited sampling data and system dynamics to construct a domain of stability for power grids, which can reflect the evolution of security zones and provide more accurate predictions. In this work, we mathematically characterize the domain of stability for a practical power grid by analyzing and learning its state trajectories. Then we show how the proposed approach can be efficiently implemented online, which can timely alert human operators to abnormalities. Preliminary validations suggest that this approach is feasible and effective. In future research, we will incorporate it into an energy management system and test it in other industrial processes.

Performance-Enhanced Static Modulated Fourier Transform Spectrometer with a Spectral Reconstruction

A static modulated Fourier transform spectrometer has been noted to be a compact and fast evaluation tool for spectroscopic inspection, and many novel structures have been reported to support its performance. However, it still suffers from poor spectral resolution due to the limited sampling data points, which marks its intrinsic drawback. In this paper, we outline the enhanced performance of a static modulated Fourier transform spectrometer with a spectral reconstruction method that can compensate for the insufficient data points. An enhanced spectrum can be reconstructed by applying a linear regression method to a measured interferogram. We obtain the transfer function of a spectrometer by analyzing what interferogram can be detected with different values of parameters such as focal length of the Fourier lens, mirror displacement, and wavenumber range, instead of direct measurement of the transfer function. Additionally, the optimal experimental conditions for the narrowest spectral width are investigated. Application of the spectral reconstruction method achieves an improved spectral resolution from 74 cm-1 when spectral reconstruction is not applied to 8.9 cm-1, and a narrowed spectral width from 414 cm-1 to 371 cm-1, which are close to the values of the spectral reference. In conclusion, the spectral reconstruction method in a compact static modulated Fourier transform spectrometer effectively enhances its performance without any additional optic in the structure.

Measuring lake carbon dioxide from space: Opportunities and challenges

<p>Inland waters such as lakes are important CO<sub>2</sub> emitter, however, accurately estimate the emissions is still a big challenge, leading to large uncertainty to the terrestrial carbon sinks estimation. Compared to the abundant lakes with diverse types, the limited sampling data with strong randomness at global, national, regional-scale contributed to large uncertainly of lake CO<sub>2</sub> emissions estimation. Satellites have accumulated a large amount of long-term data at large spatial coverage with high temporal resolution, which not only can depict the current situation but also can reconstruct the past, and then play crucial role in lake CO<sub>2</sub> emissions estimation via mapping. In this perspective, we highlight the key opportunities and challenges of lake CO<sub>2</sub> estimation with satellite. We believe that satellite remote sensing holds the potential to address the existing knowledge gap in lake CO<sub>2</sub> emissions.</p>

High-resolution mapping and driving factors of soil erodibility in southeastern Tibet

Quantifying the spatial distribution of soil erodibility (K factor) in the Qinghai-Tibet Plateau is essential for global soil erosion management. However, many K factor maps have a coarse spatial resolution at the regional scale, and high-resolution mapping is still a challenge. Quantitative analysis of the influence of environmental factors such as soil, topography, climate, and vegetation, and human activities on the K factor is also lacking. Therefore, we mapped the high-resolution (90 m) spatial distribution of the K factor values in southeastern Tibet using a random forest model with multiple environmental variables, based on remote sensing, ground observations (114 sampling points), and gridded datasets. The K factor estimates based on soil particle size composition and organic carbon content ranged from 0.09 to 0.35, showing moderate variation. The random forest model yielded a coefficient of determination > 0.9 and provided detailed information on the spatial distribution of K factor values, especially in large unsampled areas. The predicted K factor values tended to be high in the eastern area and low in the western area. Partial least squares path modeling showed that soil physical properties such as fractal dimension and mean weight diameter of aggregates had the largest influence on the K factor (path coefficient 0.695). Climate and topography also had a considerable influence on the K factor (path coefficient −0.489 and −0.469, respectively), while the influence of vegetation and human activities was minimal. Accordingly, the random forest model is an effective tool for high-resolution spatial distribution mapping of the K factor with limited sampling data.

3D Compressed Spectrum Mapping With Sampling Locations Optimization in Spectrum-Heterogeneous Environment

Spectrum mapping has emerged as an important problem in wireless communications, which generates a spectrum map for the spectrum resource analysis and management. Given the constrained transceiver volume and the limited energy consumption, how to effectively reconstruct the spectrum situation by the limited sampling data is a pressing challenge for spectrum mapping. In this paper, by exploiting the sparse nature of spectrum situation, we firstly attempt to solve the three-dimensional (3D) compressed spectrum mapping problem in the way of compressed sensing. Then, we develop a quadrature and right-triangular (QR) pivoting based measurement matrix optimization algorithm. By iteratively selecting new dominant sampling locations, it promotes the recovery accuracy compared to random measurement. After that, we propose a 3D spatial subspace based orthogonal matching pursuit (OMP) algorithm to recover spectrum situation for 3D compressed spectrum mapping. Finally, simulations are presented to show the comparisons in terms of localization, source signal strength recovery, recovery success rate and situation recovery. Results show our proposed 3D spectrum mapping scheme not only effectively reduces the sampling number, but also achieves a high level of spectrum mapping accuracy.

Mapping soil erodibility in southeast China at 250 m resolution: Using environmental variables and random forest regression with limited samples

Soil erodibility (K factor) mapping has been accomplished mainly by soil map-linked or geo-statistical interpolation. However, the resulting maps usually have coarse spatial resolution at a regional scale. The objectives of this study were a) to map the K factors using a set of environmental variables and random forest (RF) model, and b) to identify the important environmental variables in the predictive mapping on a regional scale. We collected 101 surface soil samples across southeast China in the summer of 2019. For each sample, we measured the particle size distribution and organic matter content, and calculated the K factors using the nomograph equation. The hyperparameters of RF were optimized through 5-fold cross validation (mtry = 2, ntree = 500, p = 63), and a digital map with 250 m resolution was generated for the K factor. The lower and upper limits of a 90% prediction interval were also produced for uncertainty analysis. It was found that the important environmental variables for the K factor prediction were relief, climate, land surface temperature and vegetation indexes. Since the existing K factor map has an average polygonal area of 6.8 km2, our approach dramatically improves the spatial resolution of the K factor to 0.0625 km2. The new method captures more distinct differences in spatial details, and the spatial distribution of the K factor derived from RF prediction followed a similar pattern with kriging interpolation. This suggests the presented approach in this study is effective for mapping the K factor with limited sampling data.

Research on ADMM Reconstruction Algorithm of Photoacoustic Tomography With Limited Sampling Data

Photoacoustic imaging is a new non-destructive biomedical imaging method. When limited independent data is available, the restoration of the initial pressure rise distribution is often an ill-posed problem. In this paper, based on the study of photoacoustic effects, the sparse prior information of photoacoustic images is integrated into the reconstruction process by using the compressed sensing (CS) theory and the L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> norm optimization technique, combining the augmented Langrange weighting of the alternating direction method of multipliers (ADMM) with the total variation (TV) minimization problem, and the reconstruction artifacts are effectively eliminated. The simulation data from the real numerical model show that compared with the common time reversal algorithm, interpolation algorithm and truncated back projection algorithm, the total variational regularization method based on ADMM can effectively improve the quality of reconstructed images under the condition of limited viewing angles and incomplete projection data.

Rapid in situ assessment of radiocesium wood contamination using field gamma-ray spectroscopy to optimise felling

The Chernobyl nuclear power meltdown that took place in 1986 has left a radioactive contamination legacy that currently severely limits the economic potential of impacted regions including the Polessie State Radioecology Reserve in Southern Belarus. Extensive areas of forested land could potentially become economically viable for firewood and building materials if radioactive contamination, notably 137Cs, could be characterised faster, whilst closely adhering to regulatory limits. Currently, laboursome tree coring and unreliable transfer factors derived from limited soil sampling data are routinely employed in felling decision making, which has financial repercussions owed to the large amounts of waste produced and unnecessary transportation costs. In this study, it is demonstrated that a combination of targeted mobile gamma-ray spectrometry and a newly developed, lead shielded, in situ gamma-ray spectrometry method can significantly speed up the process of characterisation of 137Cs wood activity in the field. For the in situ method, Monte Carlo calibration routines were developed alongside spectral processing procedures to unfold spectra collected in the field allowing for separation of ground and tree spectral components. Isolated contributions from the tree could then be converted to activity. The method was validated at a test facility and then demonstrated at three separate sites with differing contamination levels. This technique showed that single trees could be measured within approximately 20% of the activity compared to conventional tree core data. However, some discrepancies were found which were attributed to under sampling using the tree corer and low count rates at the lowest activity site, prompting the need for further data collection to optimise the method. It was concluded that this real-time approach could be a valuable tool for management of contaminated forested areas, releasing valuable timber and ultimately reducing the risk associated with living and working in these areas.

Effective design space exploration of gradient nanostructured materials using active learning based surrogate models

Inspired by gradient structures in the nature, Gradient Nanostructured (GNS) metals have emerged as a new class of materials with tunable microstructures. GNS metals can exhibit unique combinations of material properties in terms of ultrahigh strength, good tensile ductility and enhanced strain hardening, superior fatigue and wear resistance. However, it is still challenging to fully understand the fundamental gradient structure-property relationship, which hinders the rational design of GNS metals with optimized target properties. In this paper, we developed an adaptive design framework based on surrogate modeling to investigate how the grain size gradient and twin thickness gradient affect the strength of GNS metals. The Gaussian Process (GP) based surrogate modeling technique with adaptive sequential sampling is employed to develop the surrogate models for the gradient structure-property relationship. The proposed adaptive design integrates physics-based simulation, surrogate modeling, uncertainty quantification and optimization, which can efficiently explore the design space and identify the optimized design of GNS metals with maximum strength using limited sampling data generated from high fidelity but computational expensive physics-based simulations.

Constructing total suspended solid modelling on Agathis Lake by employing resource modelling associates program

This research uses Resource Modelling Associate (RMA) program to conduct a two-dimension model of Agathis Lake to analyse velocity and sediment transport distribution. The main programs are RMA-10 for velocity distribution and RMA-11 for the pollutant distribution. The sediment transport focuses on total suspended solids (TSS) pollutant. The research aims to construct total suspended solid model. Firstly, RMA Generation produces mesh of Agathis Lake. Next, RMA-10 and RMA-11 would perform both velocity and TSS simulation model to represent the actual condition. This research still gives temporary result due to limited sampling data. Calibration analysis of the model is needed to make the result of the program more accurate and more representative to the real condition.

A 3D Multi-scale geology modeling method for tunnel engineering risk assessment

A method for 3D multi-scale geology modeling is proposed for assessing tunnel engineering risk. Risk assessments have varying requirements at various different construction stages, therefore the proposed model can be modified for different scales. The regional scale 3D geological model, based on regional field surveys of geological boundary and attitude, is proposed for conducting preliminary evaluations with limited geological sampling data and the Hermite radial basis function (HRBF). The project scale geological model, based on updating and refining the regional scale model with dense drilling and geological prediction data, couples the geological body model for surrounding rock and the tunnel model. This project scale model is appropriate for performing pre-evaluations of tunnel construction. Once construction has begun, continuous rock structure surface information from the newly exposed tunnel face is incorporated into the outcrop scale geological model. It is based on a Monte-Carlo algorithm for conducting dynamic evaluations during construction. These modeling methods are applied to a case study, railway tunnel engineering of the Yuelongmen tunnel in China.

An Integrated H-G Scheme Identifying Areas for Soil Remediation and Primary Heavy Metal Contributors: A Risk Perspective

Traditional sampling for soil pollution evaluation is cost intensive and has limited representativeness. Therefore, developing methods that can accurately and rapidly identify at-risk areas and the contributing pollutants is imperative for soil remediation. In this study, we propose an innovative integrated H-G scheme combining human health risk assessment and geographical detector methods that was based on geographical information system technology and validated its feasibility in a renewable resource industrial park in mainland China. With a discrete site investigation of cadmium (Cd), arsenic (As), copper (Cu), mercury (Hg) and zinc (Zn) concentrations, the continuous surfaces of carcinogenic risk and non-carcinogenic risk caused by these heavy metals were estimated and mapped. Source apportionment analysis using geographical detector methods further revealed that these risks were primarily attributed to As, according to the power of the determinant and its associated synergic actions with other heavy metals. Concentrations of critical As and Cd, and the associated exposed CRs are closed to the safe thresholds after remediating the risk areas identified by the integrated H-G scheme. Therefore, the integrated H-G scheme provides an effective approach to support decision-making for regional contaminated soil remediation at fine spatial resolution with limited sampling data over a large geographical extent.

Post-processing for uncertainty reduction in computed 3D geological models

Computer aided geological modeling is always subject to uncertainty because it results from interpolation of sample data. Sample data are subject to uncertainties coming from location error, stochastic nature of the geological variable and imprecise knowledge. The lack of knowledge due to limited sampling data can be viewed as the main source of uncertainty. Besides, in terms of computer modeling another source of uncertainty is the shape complexity shown by geological units. Considering that just few drill holes are available the constructed model is going to present large uncertainties. However, an uncertain model cannot be used for a precise interpretation of geological setting. To overcome this problem, this paper proposes a novel approach for uncertainty reduction and enhancement of the reliability of the geological model. This procedure is based on resampling the computed model and post-processing using this new sample. Results of post-processing are much better than the first interpolated geological model. Besides, this procedure can be repeated until the final result is considered acceptable within the limited extent of the sample data.

A sparse sampling strategy for angular superresolution of real beam scanning radar

This paper investigates techniques for angular superresolution using limited data of real beam scanning radar (RBSR). In order to improve the angular resolution of RBSR, many algorithms have been proposed. However, for most algorithms, large amounts of sampling data is necessary. The requirement of data increases the burden of the radar system. Fortunately, the sparse signal reconstruction techniques provide a new train of thought for us. It has been proved in array signal processing and image processing that the techniques only need limited sampling data to realize DOA estimation and image superresolution. This paper describes the sparse sampling model of RBSR as an underdetermined equation-solving problem, the received signals are sparsely recovered in target domain. Two algorithms, including smooth approximation algorithm and focal underdetermined system solver (FOCUSS), based on different optimization ideas, are adopted to solve the problem. Simulation results show that compressive sampling methods can recover the target domain accurately, especially under the condition of high signal-to-noise ratio (SNR).

Estimation of phosphorus export from a Mediterranean agricultural catchment with scarce data

Knowledge of the amount of nutrient input to receiving waters by their catchments is often mandatory for water managers. In this study, we estimated the export of phosphorus from a Mediterranean catchment into a downstream reservoir under the constraint of limited sampling data availability. We calibrated the physically- based catchment-scale model ZIN-Sed 2D to a regionalized flow duration curve and scarce event mean sampling data of dissolved and particulate phosphorus. The model results were further confirmed by discussion of soft data from the literature. Our modelling approach differs from commonly applied models by using a time step of less than 1 day, and a Langmuir isotherm for phosphorus sorption instead of the linear isotherm. The successful model application showed that this combination of methods is applicable under data-scarce conditions and the long-term phosphorus export from the study site is below average for this region.Editor D. Koutsoyiannis; Associate editor T. OkruszkoCitation Gassmann, M., Brito, D., and Olsson, O., 2013. Estimation of phosphorus export from a Mediterranean agricultural catchment with scarce data. Hydrological Sciences Journal, 59 (1), 221–233.

Genetic variability of the tokay gecko based on mitochondrial and nuclear DNA

With largely allopatric distribution, the black tokay and the red tokay are two distinct morphs of the subspecies Gekko gecko gecko. In consideration of their different morphological characteristics, the taxonomic status of G. g. gecko is disputed. Through detailed morphological comparison, it has been proposed that the black tokay should be elevated to species ranking, but without strong genetic evidence. In order to further investigate the taxonomic status of the tokay gecko (G. gecko), we used one mitochondrial marker (ND2) and three nuclear markers (RAG1, c-mos, and ITS2) to explore the phylogenetic and taxonomic relationship of the tokay gecko. Our results revealed a deep phylogeographical divergence in tokay gecko and at the same time provided us with the evidence of possible introgressive hybridization or/and incomplete lineage sorting between the black tokay and the red tokay. The elevation of the black tokay to species level is also supported by our results. However, due to limited sampling and genetic data, this elevation should be further corroborated by more genetic evidence.