Accurate Interpolation Research Articles

An explainable spatial interpolation method considering spatial stratified heterogeneity

Spatial interpolation is essential for handling sparsity and missing spatial data. Current machine learning-based spatial interpolation methods are subject to the statistical constraints of spatial stratified heterogeneity (SSH), normally involving separate modeling of each stratum and simple weighted averaging to integrate intra-stratum and inter-strata features. However, these models overlook the different contributions of inter-strata features to different locations within a stratum (heterogeneous inter-strata associations, HIA) and the explanation of spatial effects on the interpolation process, leading to suboptimal and unreliable interpolation outcomes. This article proposes a novel explainable spatial interpolation method considering SSH (X-SSHM). Spatial and environmental features are utilized to describe intra-stratum and inter-strata information, which are fed into random forest-based learners to achieve high-level semantic feature mapping. Geographically weighted regression is employed to integrate intra-stratum and inter-strata features to achieve a unified expression of SSH and HIA, obtaining the final interpolation result. Geographically weighted Shapley (GSHAP) is proposed to decompose the marginal contributions of intra-stratum and inter-strata features. Model performance is evaluated on simulated and soil organic matter datasets. X-SSHM outperformed five baselines regarding interpolation accuracy. Moreover, statistical methods validated X-SSHM’s ability to elucidate the mechanisms by which SSH, spatial autocorrelation and HIA affect the model interpolation process.

NIERT: Accurate Numerical Interpolation Through Unifying Scattered Data Representations Using Transformer Encoder

NIERT: Accurate Numerical Interpolation Through Unifying Scattered Data Representations Using Transformer Encoder

An improved subpixel measurement method for piezoelectric ceramic driving characteristics based on particle filter

Microscopic vision displacement calculation is crucial for its high precision and non-contact nature in measuring piezoelectric ceramic displacement. However, the inefficient global search limits its effectiveness. This paper proposes an improved sub-pixel algorithm (GKF-PFBM) based on particle filtering. Firstly, particle filtering (PF) is combined with block matching (BM) to enhance matching efficiency and accuracy by replacing global search with particle state prediction and update. Then, subpixel interpolation using a Gaussian kernel function (GKF) is better adapted to nonlinear variations, handling high-frequency variations while preserving clear edges, thereby improving interpolation accuracy. Finally, a high-precision experimental platform is used to measure the driving characteristics of piezoelectric ceramics. Experimental results show that the mean errors of the GKF-PFBM algorithm and the bilinear interpolation algorithm (BI-BM) are 0.0032pixels and 0.1269pixels, respectively. The average hysteresis displacement error was measured to be approximately 12 nm by this method, verifying its precise non-contact measurement capability.

Spatial Interpolation of Seasonal Precipitations Using Rain Gauge Data and Convection‐Permitting Regional Climate Model Simulations in a Complex Topographical Region

ABSTRACTIn mountainous areas, accurately estimating the long‐term climatology of seasonal precipitations is challenging due to the lack of high‐altitude rain gauges and the complexity of the topography. This study addresses these challenges by interpolating seasonal precipitation data from 3189 rain gauges across France over the 1982–2018 period, using geographical coordinates, and altitude. In this study, an additional predictor is provided from simulations of a Convection‐Permitting Regional Climate Model (CP‐RCM). The simulations are averaged to obtain seasonal precipitation climatology, which helps capture the relationship between topography and long‐term seasonal precipitation. Geostatistical and machine learning models are evaluated within a cross‐validation framework to determine the most appropriate approach to generate seasonal precipitation reference fields. Results indicate that the best model uses a machine learning approach to interpolate the ratio between long‐term seasonal precipitation from observations and CP‐RCM simulations. This method successfully reproduces both the mean and variance of observed data, and slightly outperforms the best geostatistical model. Moreover, incorporating the CP‐RCM outputs as an explanatory variable significantly improves interpolation accuracy and altitude extrapolation, especially when the rain gauge density is low. These results imply that the commonly used altitude‐precipitation relationship may be insufficient to derive seasonal precipitation fields. The CP‐RCM simulations, increasingly available worldwide, present an opportunity for improving precipitation interpolation, especially in sparse and complex topographical regions.

A Novel Interpolation Method for Soil Parameters Combining RBF Neural Network and IDW in the Pearl River Delta

Soil fertility is a critical factor in agricultural production, directly impacting crop growth, yield, and quality. To achieve precise agricultural management, accurate spatial interpolation of soil parameters is essential. This study developed a new interpolation prediction framework that combines Radial Basis Function (RBF) neural networks with Inverse Distance Weighting (IDW), termed the IDW-RBFNN. This framework initially uses the IDW method to apply preliminary weights based on distance to the data points, which are then used as input for the RBF neural network to form a training dataset. Subsequently, the RBF neural network further trains on these data to refine the interpolation results, achieving more precise spatial data interpolation. We compared the interpolation prediction accuracy of the IDW-RBFNN framework with ordinary Kriging (OK) and RBF methods under three different parameter settings. Ultimately, the IDW-RBFNN demonstrated lower error rates in terms of RMSE and MRE compared to direct RBF interpolation methods when adjusting settings based on different power values, even with a fixed number of data samples. As the sample size decreases, the interpolation accuracy of OK and RBF methods is significantly affected, while the error of IDW-RBFNN remains relatively low. Considering both interpolation accuracy and resource limitations, we recommend using the IDW-RBFNN method (p = 2) with at least 60 samples as the minimum sampling density to ensure high interpolation accuracy under resource constraints. Our method overcomes limitations of existing approaches that use fixed steady-state distance decay parameters, providing an effective tool for soil fertility monitoring in delta regions.

Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations

Radial kernel interpolation is an advanced method in approximation theory for the construction of higher order accurate interpolants for scattered data up to higher dimensional spaces. In this manuscript, we formulate a radial kernel collocation approach for solving problems involving the Volterra integro-differential equations using two radial kernels: The Generalized Multi-quadrics and the linear Laguerre-Gaussians. This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. Two examples were used to illustrate the process; the numerical results are shown as tables and graphs. MATLAB 2018a was employed in the process.

Evaluating Spatial Interpolation Maps of the Age Structure of the Population of Thi Qar Governorate Using Geographic Information Systems (GIS) Technologies

The research aims to harness spatial interpolation techniques to produce maps with a high level of perceptual accuracy in representing the population data of the study area. This is achieved after exploring the statistical and spatial nature of the databases used, analyzing them, and determining their distribution using a variety of spatial data exploration tools available within the GIS (Geographic Information Systems) environment. These tools contribute to evaluating the characteristics, distribution, and analysis of data, including testing data distribution, identifying its direction, and uncovering its spatial correlations. This highlights the importance of the study and understanding the distribution pattern of the population data in the study area, thereby facilitating the preparation of future that serve spatial organization by building spatial models for the numerical distribution of the data for age groups: young, middle-aged, and elderly, at the level of administrative units of the study area by relying on the inductive approach and the quantitative analysis approach. This is done using Geostatistical Analysis methods within the concept of spatial interpolation in GIS. The research also seeks to predict the population maps for Thi Qar Governorate by comparing spatial interpolation methods, namely Inverse Distance Weighting (IDW) and Simple Kriging (SK). The study concluded, after verifying the accuracy of the results using the Cross-Validation curve, that the Simple Kriging (SK) method is the most accurate model in spatial prediction of population data for representing the data of the young age group in the study area, as it had the lowest Root Mean Square Error (RMSE) of 10.012. It was followed by the Inverse Distance Weighting (IDW) method for representing the data of the elderly age group with an RMSE of 350.48. This indicates that the use of statistical criteria improves the accuracy of spatial interpolation and that the spatial prediction of the population data for the study area using the Simple Kriging (SK) method was more accurate than the Inverse Distance Weighting (IDW) method based on statistical indicators.

Heterogeneous Transfer Learning of Electrohydrodynamic Printing Under Zero-Gravity Toward In-Space Manufacturing

Abstract As we continue to commercialize space and mature in-space manufacturing (ISM) processes, there is a strong need to transfer the knowledge we learn from experiments on the ground to zero-gravity environments. Physics-motivated manufacturing processes, like additive manufacturing, experience a shift in fabrication parameters due to the absence of gravity and the change of environments. Thus, we found traditional machine learning methods are not capable of addressing this domain shift and present a transfer learning scheme as a solution in this paper. We tested a kernel ridge regression model built for heterogeneous transfer learning (KRR-HeITL) on data from the electrohydrodynamic inkjet printing (EHD printing) process. EHD printing is a process that uses electrical force to control material flows, thus achieving the fabrication of electronics without requiring gravity. Our team has successfully conducted three rounds of parabolic flights to validate this technology for ISM. We trained on multiple datasets built from on-ground experiments and tested using zero-gravity printing data obtained from parabolic flight tests. Measurements of the Taylor cone both on-ground and in zero-gravity were taken and exploited as a part of the training data. We found that our method obtains good interpolation accuracy (MAPE 3.85%) compared to traditional machine learning methods (MAPE 16.84%) for predicting the printed line width. We concluded that the KRR-HeITL method is well suited for zero-gravity domain shifts of EHD printing parameters. This study paves the way for future predictions of ISM parameters when there are only on-ground experiments or very limited zero-gravity datasets for a given process.

Ray-tracing versus Born approximation in full-sky weak lensing simulations of the MillenniumTNG project

ABSTRACT Weak gravitational lensing is a powerful tool for precision tests of cosmology. As the expected deflection angles are small, predictions based on non-linear N-body simulations are commonly computed with the Born approximation. Here, we examine this assumption using DORIAN, a newly developed full-sky ray-tracing scheme applied to high-resolution mass-shell outputs of the two largest simulations in the MillenniumTNG suite, each with a 3000 Mpc box containing almost 1.1 trillion cold dark matter particles in addition to 16.7 billion particles representing massive neutrinos. We examine simple two-point statistics like the angular power spectrum of the convergence field, as well as statistics sensitive to higher order correlations such as peak and minimum statistics, void statistics, and Minkowski functionals of the convergence maps. Overall, we find only small differences between the Born approximation and a full ray-tracing treatment. While these are negligibly small at power-spectrum level, some higher order statistics show more sizeable effects; ray-tracing is necessary to achieve per cent level precision. At the resolution reached here, full-sky maps with 0.8 billion pixels and an angular resolution of 0.43 arcmin, we find that interpolation accuracy can introduce appreciable errors in ray-tracing results. We therefore implemented an interpolation method based on non-uniform fast Fourier transforms (NUFFT) along with more traditional methods. Bilinear interpolation introduces significant smoothing, while nearest grid point sampling agrees well with NUFFT, at least for our fiducial source redshift, $z_s=1.0$, and for the 1 arcmin smoothing we use for higher order statistics.

Interpolation of microbiome composition in longitudinal data sets.

Since missing samples are common in longitudinal microbiome dataset due to inconsistent collection practices, it is important to evaluate and benchmark different interpolation methods for predicting microbiome composition in such samples and facilitate downstream analysis. Our study rigorously evaluated several such methods and identified the K-nearest neighbors approach as particularly effective for this task. The study also notes significant variability in interpolation accuracy among individuals, influenced by factors such as age, sample size, and sampling frequency. Furthermore, we developed a predictive model for estimating interpolation accuracy at a specific time point, enhancing the reliability of such analyses in future studies. Combined, our study, thus, provides critical insights and tools that enhance the accuracy and reliability of data interpolation methods in the growing field of longitudinal microbiome research.

Research on engine dynamic torque modeling for torsional vibration analysis of vehicle powertrain

In order to improve the accuracy of dynamic torque model of engine, a simulation model of quasi-transient engine dynamic torque under all operating conditions was established considering the influence of throttle opening. Firstly, the calculation model of engine output torque and cylinder pressure is established according to the kinematic relation of crank linkage mechanism. Secondly, BP neural network is used to establish the mapping relationship model of throttle opening, rotational speed, and cylinder pressure ratio data. In order to solve the contradiction between calculation accuracy and efficiency of engine cylinder pressure interpolation, a quadratic interpolation method is proposed, which refines data to improve interpolation accuracy, and improves calculation efficiency by online adjacent interpolation, and completes the construction of dynamic torque simulation model of engine in all working conditions. Finally, the experimental data of dynamic torque characteristics of the engine at different speeds are used to verify the accuracy of the model calculation. By using the verified engine model, the dynamic operating characteristics of variable valve opening and variable speed are simulated and analyzed. The results show that the model established in this paper can effectively reflect the dynamic characteristics of the engine, and the model is suitable for the simulation of the torsional vibration of the vehicle powertrain under steady and unsteady conditions.

A comparison of interpolation methods to predict chill accumulation in a Mediterranean stone fruit production area (Región de Murcia, SE Spain)

One of the most important agroclimatic variables for stone fruit production is winter chill accumulation. To estimate chill accumulation in locations where climatic data is not recorded, spatial interpolation is necessary. In this study, we compare different interpolation methods for mean and Safe Winter Chill (SWC) in a Mediterranean stone fruit production area (Region of Murcia, SE Spain) using data from 49 climatic stations. To choose the most accurate interpolation method, as its choice may substantially influence the prediction accuracy, the predictive capability of several interpolation methods with different parameterizations (for a total number of 32 instances) was compared through out-of-bag bootstrap cross-validation, concluding that the best ones were Radial Basis Functions applied on the altitude-dependent regression residuals for mean winter chill and the altitude+latitude linear regression for SWC. The incorporation of altitude in the interpolation increased greatly the accuracy of the estimation. In fact, most of the chill accumulation spatial dependency was explained through altitude. The accuracy of the interpolation was not homogeneous across the study area. Chill accumulation in warmer coastal localities was overestimated by all the methods, possibly due to the proximity to the sea, highlighting the importance of microclimatic variables at higher-resolution spatial interpolations. Differences between methods were more notable in higher locations, where distance-only based methods underestimated chill accumulation and methods that consider altitude slightly overestimated it. This study demonstrates the importance of comparing the performance of multiple spatial interpolation methods before applying any for chill accumulation data.

A time window averaging method to mitigate the impact of shell growth trends on Tridacna δ18O records

Tridacna shells have become valuable archives for high-resolution paleoclimate reconstructions due to their daily-to-annual bands. The δ18O, influenced by temperature and salinity, serves as a key geochemical proxy for Tridacna. Traditionally, linear interpolation has been the go-to method for creating evenly spaced Tridacna δ18O timeseries. However, the accuracy of this method can be influenced by the prominent negative shell growth trends. Given that Tridacna shells exhibit significantly faster growth rates during the juvenile stage than in adulthood, constant sampling intervals may lead to overly dense sampling during the juvenile phase, which could potentially introduce errors in the linearly interpolated Tridacna δ18O record. In this study, we proposed a time window averaging method to mitigate the influence of growth trends in Tridacna δ18O records from the northern South China Sea (SCS). The time window averaging method calculates the average of measured Tridacna δ18O data within a time window, whose length is determined by the sampling resolution for each year and the expected temporal resolution. Pseudo-Tridacna experiments, using the newly developed proxy system model for Tridacna δ18O, were conducted to assess the accuracy of both interpolation and averaging methods. Results indicate that the averaging method outperforms the interpolation method, especially in seasonality estimation. The pseudo-Tridacna experiments recommend employing the averaging method for monthly Tridacna δ18O records when sampling density exceeds ∼20 samples/year. Two real Tridacna δ18O records from the northern SCS demonstrate consistency with pseudo-Tridacna experiments, supporting the efficacy of the averaging method in reducing bias in Tridacna δ18O records associated with growth trends. Our results show the potential of the time window averaging method to improve Tridacna-based paleoclimate reconstructions.

Manifold learning-based reduced-order model for full speed flow field

Reduced-order models (ROMs) can effectively balance the accuracy and efficiency of computational fluid dynamics (CFD). The nonlinear flow field characteristics cannot be captured accurately by traditional ROMs, such as proper orthogonal decomposition (POD). Combining isometric mapping (ISOMAP) and local linear embedding (LLE), a novel manifold learning method (ISOMAP-Local LLE) is proposed, performing global and accurate reconstruction of the nonlinear flow field. First, the nonlinear dimensionality reduction is derived by considering the global isometric characteristic and the local reconstruction relationship simultaneously. Then, the local interpolation model is constructed to improve the interpolation accuracy introduced by the global interpolation model. Finally, the flow field reconstruction is accomplished based on the inverse mapping. Furthermore, the criteria of hyperparameters have been established to achieve high-precision prediction. Several examples covering full speed flow field are carried out to demonstrate the accuracy and efficiency of ISOMAP-Local LLE. The proposed manifold learning-based ROM achieves prediction accuracy that surpasses that of other ROMs (such as POD, ISOMAP, LLE, etc.), resulting in significant time cost savings for CFD simulations.

On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon

Artificial Neural Networks (ANNs) are a tool in approximation theory widely used to solve interpolation problems. In fact, ANNs can be assimilated to functions since they take an input and return an output. The structure of the specifically adopted network determines the underlying approximation space, while the form of the function is selected by fixing the parameters of the network. In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. Given that the ANN is interpolating, the error incurred occurs outside the sampling interpolation nodes provided by the user. In this study, various choices of nodes are analyzed: equispaced, Chebychev, and randomly selected ones. Then, the focus is on regular target functions, for which it is known that interpolation can lead to spurious oscillations, a phenomenon that in the ANN literature is referred to as overfitting. We obtain good accuracy of the ANN interpolating function in all tested cases using these different types of interpolating nodes and different types of neurons. The following study is conducted starting from the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when the number of interpolation nodes increases, we increase the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge’s function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays, and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training. Then we can conclude that the use of such an ANN defeats the Runge phenomenon. Our results show the power of ANNs to achieve excellent approximations when interpolating regular functions also starting from uniform and random nodes, particularly for Runge’s function.

Data-driven prediction of fracture toughness size effect in ductile-to-brittle transition using Two-Step-Scaling procedure

The fracture properties of ferritic steels in transition temperature region are usually statistically treated by models that presuppose the existence of various forms of quenched disorder (critical cleavage triggers). In this study, the fracture toughness from the Euro fracture toughness dataset (stress intensity factor used in the master curve KJc) for reactor steel 22NiMoCr37 is used with the aim of outlining a methodology for using the recently proposed two-step scaling (2SS) method. Three widely different temperatures (−154 °C, −91 °C, and 0 °C), which cover the entire range from lower shelf to upper shelf fracture, are selected to demonstrate the accuracy of extrapolation and interpolation of the fracture toughness CDF (cumulative distribution function) and the pertinent issues related to the procedure application. The obtained predictions at the two lower temperatures are in good agreement with the experimental results and well within the inherent experimental data scatter, while 2SS method is shown not to be applicable in upper-shelf transition region. Special attention is devoted to the effect of statistical sample size on prediction accuracy/reliability along with the minimum sample size requirement. Moreover, the reduction in random sample size affects the Weibull parameters, which in turn impacts the accuracy of predictions, introducing a degree of uncertainty and highlighting limitations in the method.

A New Integrated Interpolation Method for High Missing Unstable Disease Surveillance Data - 12 Urban Agglomerations, China, 2009-2020.

The prevalence of unstable and incomplete monitoring data significantly complicates syndromic analysis. Many data interpolation methods currently available demonstrate inadequate effectiveness in overcoming this issue. To improve the accuracy of interpolation, we propose the integration of the SHapley Additive exPlanation model (SHAP) with the structural equation model (SEM), forming a combined SHAP-SEM approach. A case study is then performed to assess the enhanced performance of this novel model compared to traditional methods. The SHAP-SEM model was utilized to develop an interpolation model employing data from the Chinese respiratory syndrome surveillance database. We executed three distinct experiments to establish the model datasets, comprising a total of 100 replicates. The performance of the model was evaluated using the root mean square error (RMSE), correlation coefficient (r), and F-score. The findings demonstrate that the SHAP-SEM model consistently achieves superior accuracy in data interpolation, which is evident across different seasons and in overall performance. We conclude that the SHAP-SEM model demonstrates an exceptional capacity for accurately interpolating volatile and incomplete data. This capability is crucial for developing a comprehensive database that is essential for conducting risk assessments related to syndromes.

Kriging Interpolation for Constructing Database of the Atmospheric Refractivity in Korea

This paper presents a Kriging interpolation method for constructing a database of atmospheric refractivity in Korea. To collect as much data as possible for the interpolation, meteorological data from 120 regions of Korea, including both land and sea areas, are examined. Then, the normalized atmospheric refractivity Nn is calculated for an altitude of 0 m, because the refractivity tends to vary depending on the altitude of the observation site. In addition, the optimal variogram model to obtain the spatial correlation required for the Kriging method is investigated. The estimation accuracy of the Kriging interpolation is compared with that of the inverse distance weighting (IDW) and the bi-linear methods. The average and maximum estimation errors when using the Kriging method are 0.24 and 1.32, respectively. The result demonstrates that the Kriging method is more suitable for the interpolation of atmospheric refractivity in Korea than the conventional methods.

On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures

For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF2- or UF4-bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. The primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.

DSE-NN: Discretized Spatial Encoding Neural Network for Ocean Temperature and Salinity Interpolation in the North Atlantic

The precise interpolation of oceanic temperature and salinity is crucial for comprehending the dynamics of marine systems and the implications of global climate change. Prior neural network-based interpolation methods face constraints related to their capacity to delineate the intricate spatio-temporal patterns that are intrinsic to ocean data. This research presents an innovative approach, known as the Discretized Spatial Encoding Neural Network (DSE-NN), comprising an encoder–decoder model designed on the basis of deep supervision, network visualization, and hyperparameter optimization. Through the discretization of input latitude and longitude data into specialized vectors, the DSE-NN adeptly captures temporal trends and augments the precision of reconstruction, concurrently addressing the complexity and fragmentation characteristic of oceanic data sets. Employing the North Atlantic as a case study, this investigation shows that the DSE-NN presents enhanced interpolation accuracy in comparison with a traditional neural network. The outcomes demonstrate its quicker convergence and lower loss function values, as well as the ability of the model to reflect the spatial and temporal distribution characteristics and physical laws of temperature and salinity. This research emphasizes the potential of the DSE-NN in providing a robust tool for three-dimensional ocean temperature and salinity reconstruction.