dataesr/scientific-paragraphs-categorization huggingface dataset:
fullwave time-Domain Solver In this work, we consider a general modelling approach for the numerical characterization of metasurfaces based on rectangular and cylindrical nanopillars by solving the full system of 3D time-domain Maxwell equations. The most widely used numerical method for this purpose is the Finite Difference Time-Domain (FDTD) method  42  rooted on Yee's scheme  43. The FDTD method is highly popular in the computational nanophotonics community, in particular due to its simplicity and computational efficiency. It is available in several commercial software such as the Lumerical suite, which has been used here for comparison with the alternative numerical method that we consider in our study. Let us first recall that in the FDTD method, the whole computational domain is discretized using a structured (cartesian) grid, which is a strong asset from the point of view of computational efficiency.
g the type of polynomial interpolation). This is a striking difference with classical, continuous FETD formulations. Finally, such a time explicit DGTD method is naturally adapted to parallel computing. In this study, we exploit a high order DGTD-based solver that we have recently developed, and which has been specifically designed for the simulation of nanoscale light-matter interaction problems  45. This DGTD fullwave solver is implemented in the DIOGENeS  41  software suite, which is programmed in Fortran 2008 and is adapted to high performance computing systems. It is worth mentioning that the a metasurface device can also be modeled in the frequency-domain, especially when one is interested in assessing its performance at a few frequency points. In this context, the most widely used simulation approach is the Rigorous Coupled Wave Analysis (RCWA) method  2.
The results are used to construct a surrogate model, of interest to search for the next design. The latter is simulated using the fullwave DGTD solver, and the corresponding objective value enrich the database, repeating these steps until the convergence is obtained. The major difference between the CMA-ES and EGO methods essentially relies on the utilization of a surrogate model for EGO that drastically reduces the number of evaluations N DOE by an order of magnitude. Algorithm 1. Baseline CMA-ES steps (e. g. Latin Hypercube Sampling)  57. After simulation of the corresponding designs, all fitness values obtained are considered as observations and are stored in a database. In the second step, this database is iteratively refined towards the most promising areas. This is performed using a Gaussian Process (GP) model, constructed using all the database points.
This is basically an interpolating or approximating model, whose internal parameters are calibrated according to a maximum likelihood principle  58. Once this GP model is defined, one can estimate at any point of the design space the fitness value (model mean) and an uncertainty value (model variance). Both are used to define a statistical merit function, e. g. the expected improvement, whose maximum defines the next design parameters set to evaluate. After simulation of this new point, the database is updated accounting for this new observation and the second step of the algorithm repeats until convergence. The algorithm is illustrated in Fig. 1(b ). As explained, this approach based on the iterative construction of a database and an associated model can be considered as a statistical learning strategy, like for instance Artificial Neural Networks (ANNs).
Its main characteristic is the use of internal uncertainty estimation (variance) to drive both the search for the optimum and the improvement of the model accuracy. Contrary to the approaches based on ANNs, that often aims at constructing a model accurate in the whole design space before optimization, EGO focuses on the most promising areas regarding the optimization criterion. It is therefore far less expensive in terms of solver calls, making it very well suited to the context of expensive simulations. In practice, only a few hundreds of simulations are typically required for EGO, whereas the database used to train ANNs usually requires tens of thousands of solver calls. As an example, in ref. 32  a database of 90 000 simulations has been achieved in order to train an ANN to optimize 16 parameters.
As seen, both methods reach a very satisfactory function value, CMA-ES being clearly more expensive converging after about 180 solver calls, compared to 30 (including training data) for the EGO method. Below, we demonstrate the evolution of the two methods. π π π =      -. + -      +     -      + f x y y x x x minimize ( , ) 5 For CMA-ES, the yellow points shown in Fig. 2(d-g ) show the evolution of all samples tested at generations ranging from 0 to 30, the red points corresponding to the last generation (size N = 6). CMA-ES sampling points are essentially exploring only the vicinity of the population mean, which progressively moves towards the best objective function values to converge on a local minimum. For EGO, Fig. 2(h-k ) show both the Gaussian Process model and the underlying database generated from iteration 0 to 30.
At iteration 0, the database is composed of 6 points obtained from the DOE phase. Then, the database is enriched in most promising areas, yielding an improvement of the corresponding model. At iteration 30, the three regions around the global minima have been found. Moreover, a Gaussian Process model has been constructed, which is very close to the true function seen in Fig. 2(a) , in which the three global points have been identified by the EGO (see black points in Fig. 2 (k) and the analytical function given in Fig. 2(a ). This simple analytical example illustrate the different optimization mechanisms involved in CMA-ES and EGO algorithms. In the following, we exploit these two methods to optimize metasurface geometries for improved light deflection efficiency at λ = 600 nm.
One fullwave simulation with these mesh and solver configurations cost 26 minutes using 48 cores. A numerical convergence is provided in Fig. 8 (a). The results shown in Fig. 4 (a,b) have been obtained using a finer mesh and a DGTD- 2 solver. The same optimization has also been realized using the EGO method, still considering the rectangular nanopillar setting shown in Fig. 3(a). As explained previously, this optimization approach build a DOE database in a first phase. In this example, we built a database with 80 design points represented by the blue points in Fig. 3(c ). In a second phase, based on these 80 design points, a surrogate model is constructed and used during the optimization process to find a global minimum, i. e. that could achieve a better result than the actual best point found in the DOE process (represented by the pink point in Fig.
CMA-ES: distance between elements (center to center) EGO: distance between elements (center to center) between (1-2) 308. 6 nm between (1-2) 293. 9 nm between (2-3) 255. 7 nm between (2-3) 279. 4 nm between (3-4) 249. 3 nm between (3-4) 236. 9 nm Table  2. CMA-ES and EGO optimized parameters for the cylindrical nanopillars shown in Fig. 5 (a). The optimized heights obtained from CMA-ES and EGO are h ≈ 735 nm and h ≈ 708 nm, respectively. which a global point with diffraction efficiency around 85% for TM polarized waves (results for TE polarization is also around 85%, data not shown) is obtained after 300 fullwave solver calls. For the EGO method, we consider a DOE database with 50 design points (see blue points in Fig. 5(c) ). Then, a surrogate model is constructed and a global optimum is clearly obtained after nearly 180 iterations with efficiency 85%.
Our future works will aim at improving the computational performances of these optimization strategies by leveraging the different levels of parallelism underlying their algorithmic structures one one hand, and extending their capabilities in view of dealing with multi-objective problems. numerical validation. In this section, we discuss about the numerical validation of some of the results obtained in our work. First, we start by studying the influence of the mesh size/type using our DGTD fullwave solver from the DIOGENeS software suite  41  on some of the optimized designs. In Fig. 8 (a), we study the influence of the mesh and the polynomial order on the optimized solution obtained in the rectangular nanoantennas case (the results obtained from the CMA-ES method are shown in Fig. 3 ). As it can be seen in Fig.
In Fig. 9 , we provide another validation of our numerical results by simulating the optimized structure given in Table  3  using the FDTD fullwave solver from Lumerical commercial software, and comparing the results with the ones obtained from our DGTD solver. As it can be seen from Fig. 9 , we have a very good agreement between the results obtained using the two methods for both the total transmission and the deflection efficiency of the first order mode. However, in the case of the DGTD method, we show the results using curvilinear elements with fourth order polynomial using only 13 000 cells (same results can be obtained with classical linear elements with 109000 cells as we have seen in Fig. 7 ). On the other hand, for the FDTD results, we consider a very fine mesh with nearly 10 5 cells in order to get accurate results that can be compared with the DGTD method.
The green line represents the best, optimized, results obtained during optimization phase, as explained in Fig. 1(b). (d-g) Evolution of the points tested by CMA-ES, as a function of the generation numbers (for each generation we simulate 6 designs). The yellow points represent all samples evaluated so far, the red points correspond to the last generation of size N = 6. This illustrates the search by progressive sampling and convergence. (h-k) Evaluation of the Gaussian process model (surrogate model) and the underlying database generated from iteration 0 to 30. Notice that the model converge to the analytical function shown in (a) after 30 iterations. The design points from the DOE phase are shown in blue, the black points represent the database progressively enriched during the optimization.
18 The parameters involv-ing the Zn atoms were derived by fitting to experimental lattice constants. In 2013 the same group published a refined version of their original FF in order to be able to model the sorption-induced structural transition by hybrid MC/MD simulations. 19 The crucial torsions around the Zn atom were fitted to a single experimental N 2 isotherm. In a parallel effort, several FFs for ZIF-8 were developed by Demontis et al. In 2011 they published partial charges for several ZIF systems derived from cluster calculation and periodic DFT calculations. 20 In 2012 the first FF based on these partial charges was published,  21  which is again based on Amber. Missing parameters for the organic linker were obtained via the parmcal software,  22  which calculates bond length and bond angle parameters based on empirical rules.
Methods The basic idea behind the MOF-FF parameterization procedure is visualized in Fig. 1. The reference information i. e. DFT optimized structure and the curvature information represented in the the matrix of the second derivatives of the energy in respect to the coordinates -→ ∇ 2 E called Hessian H are calculated for a given reference system and serve as input for the FFgen code (written in Python). The code is then used to find the best matching bonded parameter set P of the predefined force field energy expression in respect to the provided reference information for a given set of a priori defined van der Waals (vdW) potentials and charges. Whereas charges were calculated by a fit to the electrostatic potential of the optimized reference structure, vdW parameters were taken from the well known MM3 force field,  38, 39  and used within the dispersion damped Buckingham potential, as implemented in MOF-FF.
One limitation of this approach is thus that it is necessary to define these ranges a priori. If the solution is outside of the range it must be readjusted manually. Furthermore, the periodic reference systems used in this study are substantially larger than the cluster models employed before. The primitive cell of ZIF-8 consists of 138 atoms and is more than a factor of two larger than e. g. a benzoate paddle-wheel unit. We thus needed to change the optimizer to reduce the computational cost of the parameterization process. We implemented in our FFgen code an algorithm called Covariance Matrix Adaption Evolution Strategy (CMA-ES), which was developed by Hansen for optimization problems on continuous variables. 42, 43 CMA-ES has previously been applied for force field development, namely for deriving coarse grained FFs for MOFs  33  and recently for the parameterization of ReaxFF.
45 A more elaborate description of the optimizer can be found in the supporting information. CMA-ES is implemented in FFgen using the ask-and-tell interface of the pycma library. 46 We accelerated the parameterization process by distributing the evaluation of the fitness function over parallel processes. Using CMA-ES instead of PIKAIA leads to a substantially faster convergence. To validate this claim we fitted a force field for ZIF-8(Br), using the same setup as described in Sec. 4. 1. 3, with both optimizers. The convergence behavior is visualized in a logarithmic scale in Fig. 2a. One evaluation of the objective function takes around 2 s on a single core of a current desktop GNU/LINUX workstation. A further advantage of CMA-ES is that it is not necessary to define a priori any ranges for the parameters as needed in PIKAIA.
Obtaining the Reference Information The reference information needed for the FF optimization was obtained with periodic DFT calculations using the QUICKSTEP/CP2K package. 47 QUICKSTEP/CP2K is based on a hybrid Gaussian plane-wave approach combining a Gaussian basis for the wave-functions with an auxiliary plane wave basis set for the representation of the density. We found that it is crucial to use a high plane-wave cutoff E cut to obtain accurate Hessians, since in the QUICKSTEP module, the computation of Coulomb and exchange-correlation energies is performed on a real space grid. This representation breaks the translational invariance of the system, which can lead to spurious forces on the atoms (egg box effect), which can have a large influence on the Hessian calculated by a finite difference approach based on the atomic forces.
Classical Molecular Dynamics Simulations Classical molecular dynamics simulations were performed using our in-house developed PYDLPOLY code on 2 × 2 × 2 crystallographic unit cells of the material, employing the same lattice constants as used for the AIMD simulations. Simulations were run in the canonical ensemble (N, V, T ) using a Berendsen thermostat for equilibration runs of 0. 1 ns and a Nosé-Hoover thermostat for sampling runs of 1 ns. Thermostat relaxation times were set to 0. 2 ps and 2. 0 ps.
Calculation of Elastic Constants Elastic constants C ij , which are the coefficients of the second-order elastic tensor C, were computed by using the numerical first derivative of the cell gradients corresponding to the each elastic coefficient C ij. For this purpose the optimized structure was deformed in each possible direction, applying both negative and positive strain (corresponding to compression and tension), and for each deformation the atomic coordinates were energy-minimized. For deformations along the normal coordinates strains of -1. 0 % to 1. 0 % in steps of 0. 5 % were applied, whereas for shear deformations, strains from -4. 0 % to 4. 0 % in steps of 2. 0 %. The PYMATGEN package was used to deform the structures and to perform the final analysis,  58  using the crystallographic unit cell as a reference configuration.
Acknowledgement J. P. D. is grateful for the financial support by the  Fonds der Chemischen Industrie (FCI)  and by the  Research School Plus  from the  Ruhr-Universität Bochum. Further financial support from the  Deutsche Forschungsgemeinschaft (DFG)  is acknowledged (grants  SCHM1389/8-1  and  SCHM1389/10-1 ). Access to HPC platforms was provided by a  GENCI grant  ( A0050807069 ). We thank  Hendrik Heenen  for implementing MOF-FF in LAMMPS.
Constant Rule: We calculate the standard deviation for a set of successive observations. If this value is equal to zero, the set is declared as an anomaly. • Density-based method that consists in comparing the density around a point with respect to the density of its local neighbors. It can detect local and global anomalies (abnormal change). (Breunig et al. , 2000)  proposed the LOF algorithm. In this method, the anomaly scores are measured using a local outlier factor, which is the ratio of the local density around this point to the local density around its nearest neighbor. The data point whose LOF value is high is declared anomaly. The effectiveness of LOF is strongly depends on the choice of the number of closest neighbors. • Statistics-based method: First, we used ESD method for the automatic detection of anomalies and more precisely the abnormal change such as positive or negative peaks.
Secondly, we used the point change method to detect the level shift. AnomalyDetection is an open source R package for detecting anomalies in the presence of seasonality and an underlying trend. This package is based on the SH-ESD (Seasonal Hybrid ESD) algorithm, developed by  (Hochenbaum et al. , 2017) , which first uses the STL time series decomposition (Seasonal and Trend decomposition using Loess) developed by  (Cleveland et al. , 1990)  to divide the time series signal into three parts: seasonal, trend and residue. Secondly, it applies residual anomaly detection techniques such as ESD  (Rosner, 1983 ) using statistical metrics. For point change detection, this is the name given to the problem of estimating the point at which the statistical properties of a sequence of observations change  (Aminikhanghahi and Cook, 2017).
Description of the Case Study The field o f a pplication t reated i n t his p aper, i s the sensor network of the Management and Exploitation Service (SGE) of Rangueil campus attached to the Rectorate of Toulouse. This service exploits and maintains the distribution network from the data related to the different installations. More than 600 sensors of different types of fluids ( calorie, water, compressed air, electricity and gas), which are scattered in several buildings, are managed by the SGE supervision systems. For this paper, we focus on calorie data and we processed 25 sensors. Thus, we analyze calorie measurements collected every day for more than three years collected from the 25 sensors deployed in different buildings: 1453 data per sensor which is 36325 data points in total. The measurements of these sensors are reassembled at a regular frequency and represent the indexes (readings of sensors) which are used to measure the quantities of energy consumed (by successive value differences, consumption).
We were able to identify the types of anomalies that exist in the calorie data through the knowledge gained from the SGE experts by visually inspecting the data sets. The examples of faults presented in the figure  1  are taken from these same data sets. The predominant anomaly in these readings is the constant values, nearly 8578 observations on all the data and this is following the stopping of the sensors. We also found among these values, several constants with an offset. Typically, a constant with a level shift that begins with a positive or negative peak. Then, there is a lot of for more visibility. These methods are not fully automated and therefore we need to select the parameters such as the threshold for the short rule, the neighbor number for LOF or the model type for ARIMA etc.
To further evaluate our algorithm and to demonstrate the effectiveness of the anomaly detection methods, we used SGE consumption data. So, we took the measurements that come from 25 sensors. Consumption data are seasonal data and their daily evolution, unlike index data, are somewhat variable. We have manually inspected these data to understand how these data work and to create patterns of anomalies that may exist. The anomalies we have seen in the data are: positive and negative peaks, constant anomalies, constants that start and end with a big peak. Since the data is not stationary, we did not ap- According to the results presented in figure  6 , we can say that the number of neighbors equal to 20 is the most appropriate choice to detect the most anomalies in LOF algorithm. However, for the Constant rule, it is important to use a window size small enough to handle data sets containing a large number of constant values.
Experimentation on Benchmark Data Set Euro area. Also, we explored the data of IPI (Industrial Production Indices ). It represents the industrial production indices in the manufacturing sector of European Monetary Union countries(López-de Lacalle, 2016). Each of these data sets contains several time series which present monthly data from 1995 to 2013. We tested two time series of these two data sets. Each of them contains 229 measurements with 5 anomalies in HIPC and 4 anomalies in IPI. These anomalies are a mix of AO (Additive Outlier), TC (Temporary Change) or LS (Level Shift). Thus, we analyzed the characteristics of these data and the curve that represents the time series to be able to specify the patterns. So, we first created a different patterns to detect the remarkable points in the time series.
Then we made a composition of these patterns to detect anomalies. Table  4  is a comparison between the literature algorithms and our algorithm, on the data used in the ARIMA package. We did not test the constant rule in the HIPC and IPI datasets because the anomalies observed in these data do not contain a constant anomalies. Therefore, we applied CoRP, ARIMA, LOF with a number of neighbors equal to 20, S-H-ESD, Change Point and the Short rule on these data. The algorithm based on the Short rule and Change Point are the worst among these algorithms, while our algorithm is the best among them and can detect the majority of anomalies observed with few errors.
Complexity In this part, we focus on the computing time required by the different methods of literature and our algorithm. The experiments are performed on machine running windows 10 professional and optimized by an Intel (R) Core (TM) i5 processor and 16GB of RAM. We used the Python 3. 7 Anaconda open source distribution to turn our algorithm and R 3. 5 to turn the algorithms of the literature. We calculated the execution time of index data for each algorithm we evaluated to compare it with the execution time of our algo-In order to evaluate the algorithm in another context, different to our case study, we used the data sets used in the package developed in R and implements ARIMA method (López-de Lacalle, 2016). Among this data, we explored the data of HIPC (Harmonised Indices of Consumer Prices).
CONCLUSION Anomaly detection in supervisory applications is very important especially in the field of sensor networks. This paper represents the CoRP approach based on patterns applied to the univariate time series of sensor data. This method is very effective at simultaneously detecting different types of anomalies observed during actual deployments. Our algorithm is composed of two steps: it marks (labels) all the remarkable points present in the time series on the basis of patterns of detection. Then, he precisely identifies the multiple anomalies present by label compositions. This approach requires application domain expertise to be able to efficiently define patterns. Our case study is based on a real context: sensor data from the SGE (Rangueil campus management and operation service in Toulouse).