esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods  
### Sound Speed Profile Dimensionality Reduction Method  
An SSP is essentially a three-dimensional matrix, where different dimensions of the matrix reflect different distribution characteristics of the SSP. The first dimension of the SSP reflects the vertical distribution characteristics of the sound speed in seawater, and the other two dimensions reflect the spatiotemporal distribution characteristics of the sound speed. Analyzing SSPs in multiple dimensions requires the use of multidimensional variables for machine learning. However, to reduce the complexity of machine learning when fitting SSPs and avoid variables with smaller weights, the sEOF-r method is introduced to perform dimensionality reduction processing on the SSPs. In the SSP inversion problem, the general SSP can be expressed as [21]  
\[c(z)=c_{0}(z)+\sum_{m=0}^{m}a_{n}\psi_{n}(z), \tag{1}\]  
where z represents the depth distribution characteristics of the SSP; \(c_{0}\) represents the background profile, that is, the stable and unchanging part of the spatiotemporal sound speed; \(\psi_{m}\) represents the EOF, which is a basis function that changes with time, and its specific mode can be used to describe a certain disturbance form of the SSP; \(a_{n}\) are the EOF projection coefficients, reflecting the weight of each mode disturbance coefficient; and \(n\) represents the order of the EOF, reflecting the size and importance ranking of different modes in the data. In the mainstream acoustic inverse problem, due to the existence of noise, a too high EOF order will mistake noise for effective signals. Therefore, the EOF retains the first few orders of modes to obtain a high cumulative variance contribution rate. In the subsequent experiments of this paper, we use an order of 3 to obtain the highest inversion accuracy.  
As a typical basis function extraction method, the EOF can extract the main components of an SSP. Usually, an SSP sample is a two-dimensional matrix, \(W\), with dimensions of \(m\times n\), where \(m\) is the number of discrete depths in each SSP and \(n\) is the total number of SSP samples. The irregular matrix, \(K\), is obtained by subtracting the background profile from \(W\), and then the covariance matrix of \(K\) is solved as  
\[T=K\times K^{\prime}. \tag{2}\]  
The empirical orthogonal matrix is calculated using the covariance matrix, \(T\), and its eigenvalues:  
\[T\times s=s\times\lambda. \tag{3}\]  
In the above formula, \(\lambda\) represents the eigenvalue of the covariance matrix \(T\), and \(s\) represents the empirical orthogonal matrix, whose dimensions are \(m\times m\).  
The EOF can be applied to the principal component extraction of SSP disturbance modes. In order to perform SSP inversion effectively, it is necessary to explore the possible connection between the EOF projection coefficients and the SSP to strengthen the inversion accuracy.
## 2 Fracture Parameter Solution Method Based on the Postprocessing Routine of ABAQUS
### Computation of Interaction Integral
A program is then written to iterate over all Gaussian points within the integration domain, perform weighted accumulation, and ultimately output the interaction integral terms. \[I\ =\ \sum_{e\ =\ 1}^{e_{A}}\sum_{p\ =\ 1}^{p_{e}}\Big{\{}\Big{(}\sigma_{ij}^{ \text{aux}}u_{j,1}^{AB}+\sigma_{ij}^{AB}u_{j,1}^{\text{aux}}-\sigma_{jk}^{ \text{aux}}\varepsilon_{jk}^{AB}\delta_{1i}\Big{)}q_{j,i}+\sigma_{ij}^{AB}[S_{ ijkl}^{\text{tip}}-S_{ijkl}(x)]\sigma_{kl,1}^{\text{aux}}q\Big{\}}_{p}\ |J|_{p}w_{p} \tag{13}\]  
In the formula, \(e_{A}\) denotes the number of elements within integration area \(A\), and \(p_{e}\) represents the number of integration points within each element. \(|J|_{p}\) is the determinant of the Jacobian matrix, \(w_{p}\) is the weight coefficient for integration point \(p\), and \(u_{j,1}^{AB}\), \(\sigma_{ij}^{AB}\), \(\varepsilon_{ij}^{AB}\) are the derivatives of displacement, strain tensor, and stress tensor component data obtained via the post-processing of the ABAQUS finite element computation results. For three-dimensional cases, the interaction integral form for calculating stress intensity factors is similar to that in two-dimensional problems. The equivalent volume integral form of the interaction integral for a three-dimensional crack front is as follows:  
\[\overline{I}\ =\ \int_{V}\big{(}u_{ij}\sigma_{ij}^{\text{aux}}q_{l,j}+u_{i,l}^{ \text{aux}}\sigma_{ij}q_{l,j}-\sigma_{ij}^{\text{aux}}\varepsilon_{ij}q_{l, l}\big{)}dV+\int_{V}\big{(}u_{ij}\sigma_{ij,i}^{\text{aux}}+u_{i,lj}^{\text{aux}} \sigma_{ij}-u_{i,l}^{\text{aux}}f_{i}-\sigma_{ij,l}^{\text{aux}}\varepsilon_ {ij}\big{)}q_{l}dV, \tag{14}\]  
The interaction integral at point s on the crack front can be expressed as follows:  
\[I(s)\ =\ \frac{\overline{I}}{\int_{L_{c}\ \triangle a(p)dl}}, \tag{15}\]  
In the equation, \(\Delta a(p)\) represents the virtual extension length of the crack front.
## 4 Results and Discussion
### Object Height Differences  
For a clear height estimation, in our work we considered only single objects, located in free, open and smooth areas, without any other entities in their close surroundings. Assuming that in the free, open areas, the DSM coincide with DTM elevations, we inspected the vertical quality of the photogrammetric derived surface models by computing the vertical offsets from the reference LiDAR DTM (1 m resolution and \(\sigma_{Z}\) = 0.12 m). The results showed a good correspondence of the DSMs with the reference DTM, featuring a RMSE of 0.32 m for Pleiades and of 0.20 m for WorldView-3. When it comes to individual objects, we sometimes observed a constant offset, but it was always below 0.30 m. Therefore, it did not significantly impact our height investigations.  
The reconstructed individual object height was extracted from the interpolated surface models. Heights of buildings, vehicles and trees were computed by subtracting the DTM elevations from the elevations of the highest object points (located on roof ridges, on car roofs, and on treetops) at the same 2D location.  
We consider the reference height (\(H\)) as being the real object height, which was computed by subtracting the DTM elevation from the manual measurements (Section 3.2) at the same position.  
\[H=Z_{M}-Z_{DTM}\left(m\right) \tag{2}\]  
\[h=Z_{DSM}-Z_{DTM}\left(m\right), \tag{3}\]  
with \(H\) the reference object height, \(h\) the estimated object height, \(Z_{M}\) the manual elevation measurements, \(Z_{DTM}\) the elevation of the ground surface and \(Z_{DSM}\) the elevation of the reconstructed DSM.  
In Equations (2) and (3) the \(Z_{DTM}\) elevation values are identical, since for computing the reference and the estimated heights, the same ground elevation at the same 2D position was considered. Based on the defined equations, we obtained a reference height (\(H\)) and two estimated heights for each individual object (from Pleiades and WorldView-3 DSMs). These values will be employed in further analysis.
# Performance of Satellite-Based Evapotranspiration
## 4 Results
### In-situ and Modeled Grassland Evapotranspiration
The dashed red line represents the identity function, and the black line denoted the slope of the linear regression of each model. GLEAM and PML_V2 comparisons are shown as density scatterplots, with red and blue colors denoting high- and low-density areas, respectively.
## 3 Results and Discussions
### Effect of Operating Variables
#### 3.2.4 Effect of pH on Mn(II) Sorption  
The pH value affects the surface characteristics of soil particles and the fugitive form of heavy metals and has a strong influence on the sorption of the Mn(II) [42]. The effect of pH on the sorption capacity of DX manganese is shown in Figure 5. With the increase of pH from 5 to 8, the sorption and removal of Mn\({}^{2+}\) achieved an increase of 0.50 mg\(\cdot\)g\({}^{-1}\) and 9.97%, respectively, and finally up to 5.73 mg\(\cdot\)g\({}^{-1}\) and 77.51%. At pH 6-8, DX could achieve more than 70% of Mn\({}^{2+}\) sorption efficiency. Ion exchange is the main metal sorption mechanism in the solution. At low pH, most of the sorption sites were bound to H\({}^{+}\), which had a competitive sorption relationship with Mn(II). With the increase of pH, the decrease of H\({}^{+}\) makes the competitive relationship weaker, resulting in the significant improvement of Mn(II) sorption capacity and sorption efficiency. Meanwhile, the effect of pH on the surface potential of the sediment was also an important reason for the improvement of the sorption capacity. As the pH increases, the negative charge companions on the surface of clay minerals and soil organic matter in the soil increase, which facilitates the sorption of DX on manganese ions in the solution [43].  
Figure 4: Effect of different temperatures on the sorption effect of manganese.
## 5 Conclusions  
Focusing on the problem of time-varying formation control, this paper introduces algebraic graph theory to abstract the connection topology between agents. Combining the concept of affine transformations with universal rigidity, the relation is unique regardless of how the topology graph is affine transformed in linear space. To achieve the minimum fuel consumption, the improved Hungarian algorithm is used to reallocate the target position after topology switching. Moreover, the corresponding model library has been built to rapidly establish new target formation configurations in a collaborative environment. Our method can save the whole system energy and improve the efficiency of multi-agent reconstruction after failure. A distributed control law based on consensus theory and leader-follower is designed for the linear model, and its global stability is proved using the Lyapunov function. In the end, the feasibility of the proposed approach was proved by the numerical simulations in the time-varying target configuration case.  
Plenty of appealing directions for future research remain. The time-varying topological formation control considered in this paper is only for a single disabled agent. For a more complex and realistic collaborative environment, it is necessary to study the system with heterogeneous dynamics and when multiple agents are randomly disconnected. In the process of large-scale multi-agent reconstruction, how to avoid dynamic obstacles and how to face unknown external disturbances is another important research topic. In addition, the time-varying topology formation reconfiguration method in this paper can also be applied in three-dimensional or higher-dimensional spaces in the future.  
Writing--original draft, [PERSON] ([PERSON]); methodology, M.C.; project administration, M.C.; writing--review and editing, [PERSON] ([PERSON]) and C.C.; supervision, J.C.; funding acquisition, J.C. and C.C.; validation, H.Y.; formal analysis, [PERSON] ([PERSON]); software, X.D. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China (Grant No. U21B6002) and Interdisciplinary Innovation Fund for Doctoral Students of Nanjing University of Aeronautics and Astronautics (Grant No. KXKCXJJ202203).  
Data Availability Statement: Data availability is not applicable to this article as no new data were created in this study.  
We thank all the scientists and principal researchers who prepared and provided the research data. We would also like to thank our colleagues from the College of Astronautics who provided profound insights and expertise to our research.  
The authors declare no conflict of interest.  
Figure 8: Comparison of time-varying topological formation tracking errors.
###### Abstract  
Precise prediction of short-term electric load demand is the key for developing power market strategies. Due to the dynamic environment of short-term load forecasting, probabilistic forecasting has become the center of attention for its ability of representing uncertainty. In this paper, an integration scheme mainly composed of correlation analysis and improved weighted extreme learning machine is proposed for probabilistic load forecasting. In this scheme, a novel cooperation of wavelet packet transform and correlation analysis is developed to deal with the data noise. Meanwhile, an improved weighted extreme learning machine with a new switch algorithm is provided to effectively obtain stable forecasting results. The probabilistic forecasting task is then accomplished by generating the confidence intervals with the Gaussian process. The proposed integration scheme, tested by actual data from Global Energy Forecasting Competition, is proved to have a better performance in graphic and numerical results than the other available methods.  
probabilistic forecasting; integration scheme; correlation analysis; improved weighted extreme learning machine; switch algorithm; Gaussian process +
Footnote †: journal: Applied Sciences
## 5 PPO-Attention Algorithm
### Attention Model Architecture
#### 5.2.1 Encoder  
The encoder comprises two parts: the linear layer and the attention layer. The linear projection serves as the initial layer to embed all the original vertices, while the attention layer is responsible for passing weighted messages. Unlike the encoder in the Transformer Model [30], the encoder in our model does not include a positional encoding module.  
First, for all the input vertices with \(d_{x}\)-dimensional representation, the linear layer embeds each node from \(d_{x}\)-dimensional to \(d_{h}\)-dimensional:  
\[h_{i}^{0}=W^{X}x_{i}+b^{X} \tag{32}\]  
Next, the embedded information is passed to the attention layer, which may consist of \(N\) layers. Each attention layer consists of two sublayers: a multi-head attention (MHA) layer for exchanging weighted messages between vertices and a fully connected feed-forward (FF) layer. Empirical tricks such as skip-connection [35] and batch normalization (BN)[36] are utilized. Let \(h_{i}^{\ell}\) denote the vertex embedding result produced by layer \(\ell\in\{1,\dots,N\}\). Therefore, we have:  
\[\hat{h_{\ell}}=BN^{\ell}(h_{i}^{\ell-1}+MHA_{i}^{\ell}(h_{1}^{\ell-1},\dots,h _{n}^{\ell-1})) \tag{33}\]  
\[h_{i}^{\ell}=BN^{\ell}(\hat{h_{\ell}}+FF^{\ell}(h_{i})) \tag{34}\]  
These equations describe the forward pass through the attention layer, where \(h_{i}^{\ell-1}\) is the input to the layer, \(\hat{h_{\ell}}\) is the intermediate result after the MHA layer, and \(h_{i}^{\ell}\) represents the output after applying the FF layer. By stacking multiple attention layers, the encoder captures the dependencies and interactions between vertices in the road network.
# Numerical Coupling between a FEM Code and the FVM Code OpenFOAM Using the MED Library
## 4 Numerical Results
### Buoyant-Driven Cavity
#### 4.1.1 Volume Data Transfer Algorithm  
Following Algorithm 1, we outline the procedure employed for the coupling application involving volume data transfer. In both coupling cases \(c_{1}\) and \(c_{2}\), the init_interface() and create_mesh() are used to create a MED mesh object of the entire domain. The FEMuS problem can use either a 2D or a 3D mesh, according to the problem dimension. In contrast, OpenFOAM can handle only 3D meshes, even for 2D problems. Since we are addressing this latter mesh dimension in this context, the volume mesh used by FEMuS consists of a 2D computational grid. Consequently, the MED meshes employed in this scenario consider a 2D mesh for FEMuS and a 3D mesh for OpenFOAM with a single cell across the third dimension.  
The initialization of MED fields over the MED meshes involves calling the routine init_med_field_on_cells() to initialize a cell-wise temperature field and a cell-wise velocity field for both codes throughout the entire computational domain. We name the \(P_{0}\) temperature field over MED meshes as temp_P0_2 Dmesh for FEMuS and temp_P0_3 Dmesh for OpenFOAM. Similarly, the \(P_{0}\) velocity field is denoted by vel_P0_2 Dmesh and vel_P0_3 Dmesh for FEMuS and OpenFOAM, respectively.  
We describe the algorithm for the coupling case \(c_{1}\) since the \(c_{2}\) case is entirely similar but with the fields swapped. Once the time loop is started, FEMuS solves the temperature equation as described in (1). Then, the get_field_from_femus() function is called to extract the temperature solution. Given that FEMuS solves for a biquadratic temperature field, an interpolation from \(P_{2}\) to \(P_{0}\) is performed to correctly pass the data to OpenFOAM, which works with \(P_{0}\) fields. Following this, the fill_med_array() and update_med_field() functions are used to set the temp_P0_2 Dmesh field. At this point, the interpolation() routine is used to interpolate temp_P0_2 Dmesh into the MED mesh from OpenFOAM to obtain the target MED field temp_P0_3 Dmesh. The function set_field_to_OpenFOAM() sets the interpolated field into the OpenFOAM temperature field, used to compute the buoyancy term within the Navier-Stokes equation. Once OpenFOAM has solved the system of equations, the velocity field is extracted using the get_field_from_OpenFOAM() routine and set to the vel_P0_3 Dmesh field. Then, the interpolation function computes the vel_P0_2 Dmesh to be passed to the FEMuS code. This field must be first interpolated using the \(P_{0}\) to \(P_{2}\) interpolation scheme and then written into the velocity field of FEMuSusing the routine set_field_to_femus(). In the following time iteration, FEMuS uses this updated velocity field in the advection term of the temperature equation.
# Computational Investigations and Control of Shock Interference +
## 3 Model Validation
### Numerical Methods  
All computational results were obtained using the Viscous Upwind aLgorithm for Complex flow ANalysis (VULCAN) Navier-Stokes code. Pseudo-time-step advancement was achieved using an incomplete LU factorization scheme with planar relaxation. A Courant-Friedrichs-Lewy (CFL) number of 100 was utilized. The inviscid flux differencing was evaluated using a Low-Diffusion Flux Splitting Scheme of [PERSON], with cell interface variable reconstruction achieved via the \(k=\frac{1}{3}\) Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) [25]. The Korean flux limiter was utilized to avoid spurious oscillations during this reconstruction process. The viscous fluxes were evaluated using 2 nd-order accurate central differences with the viscosity of air computed from Sutherland's Law [26]. The molecular and turbulent Prandtl numbers were set to 0.72 and 0.9, respectively.  
For the model validation study, an adiabatic no-slip condition was applied at all solid surfaces. An extrapolation boundary condition was used at the isolator exit for all variables (except for static pressure). The static pressure was set to 304.5 kPa, which was a value obtained by averaging the 20 surface pressure measurements taken around the periphery of the isolator duct at the x = 22 h station, as mentioned earlier in this paper. Details regarding the isolator dimensions, mesh, solution methodology, and turbulence modeling are summarized in Table 1.  
Figure 6: Computational Domain: Schematic of quarter section of the backpressured isolator with boundary conditions.  
In the experimental work presented in [PERSON] et al. [22], facility flow conditions used for model validation were presented. These values are shown in Table 2 alongside the flowfield conditions used in this current work. It should be mentioned that this 2013 work contained multiple facility conditions. However, in a later publication of [PERSON] et al. [8], the conditions corresponding to the model validation were presented, which are utilized in this work. Due to the absence of a nozzle in this work, isentropic relations were utilized to calculate the total pressure and temperature at the nozzle exit using the plenum conditions reported in earlier work. The nozzle exit conditions served as isolator entrance conditions in this current work. All variables are consistent between the two, other than the minor variation in total temperature at the entry.
## 4 Measured Data of the Temperature Field in the Open-Excavation Section  
Due to the nearly symmetrical positioning of the T1 and T2 temperature measurement orifices, the alterations in temperature experienced by each are approximately equivalent. Therefore, the thermal changes at the T1 and T3 temperature measuring holes within the burial depth of the soil (2 m to 16 m) in the open-excavation section were observed for 99 days. Figure 5 shows the 3D thermal variations. Based on these thermal diagrams, the initial ground temperatures of the fine and medium sand layers were approximately 8.3 \({}^{\circ}\)C and 12 \({}^{\circ}\)C, respectively. The T1 temperature measuring holes were located between the P and Q rows, where the cooling capacities of both rows were combined, causing the temperature at these holes to decrease rapidly. During the 13 th day of freezing, the temperature of the fine sand layer dropped to nearly 0 \({}^{\circ}\)C. When the freezing reached 20 days, the temperature of the medium sand layer decreased to approximately 0 \({}^{\circ}\)C. The temperature of the fine sand layer declined faster than that of the medium sand layer due to its lower initial temperature and higher thermal conductivity. Notably, the T1 temperature measuring holes were located between the P and Q rows and following the intersection between the freezing walls, an enclosed freezing wall isolated the hydraulic connection between the inner and outer regions of the soil. The water within the soil could no longer flow to the surrounding area but instead froze, releasing solidification heat during phase transition. This heat offsets the cold energy released by the freezing holes, maintaining the soil temperature at approximately 0 \({}^{\circ}\)C for a short phase-transition platform period. By day 27 of the freezing, this platform period was completed, and the soil temperature decreased rapidly. When the freezing reached day 50, the overall soil temperature decreased to approximately \(-\)20 \({}^{\circ}\)C, with the soil temperature then decreasing slowly and gradually stabilizing.  
The T3 temperature measuring holes, located outside the P-row side-row holes, experienced a lower temperature drop rate compared with the T1 temperature measuring holes due to the external heat source provided by the soil. After approximately 30 days of freezing, the temperature of the fine sand layer at the T3 measuring points declined to approximately 0 \({}^{\circ}\)C. Later, on day 37 of the freezing, the temperature of the medium sand layer also decreased to 0 \({}^{\circ}\)C. As a result of the ultra-fine water pressure [26], water seepage and migration occurred within the soil, which expanded to other regions. Consequently, the heat released due to phase change was reduced, and no evident phase change platform was observed. After 60 days of freezing, the overall soil temperature dropped to approximately \(-\)8 \({}^{\circ}\)C, with the soil temperature gradually stabilizing as it continued to decrease gradually.  
Figure 4: Measured brine temperature change diagram.