dataesr/scientific-paragraphs-categorization huggingface dataset:
REAL DATASET: FMRI The results obtained for all methods on the real dataset FMRI are displayed in Table  6. In order to compare all methods, we focus here on the summary graph, evaluating as before the capacity of each method to retrieve a causal relation between two time series (i. e. to obtain a correct skeleton) and to orient such relations. We also evaluate the method through their capacity to detect causal relations between different time series (w/o self causes) and within a time series (self causes only). All methods but TCDF are able to retrieve the skeleton of the summary causal graph, tsFCI and VarLiNGAM being the two best methods here, reaching a F1 score above 0. 8. For the summary causal graph, VarLiNGAM is by far the best method which may suggest that the relations between time series in FMRI may be well approximated by linear relations.
Apart from that, the different families of approaches perform similarly (even though some methods are worse than others in the different families, as TCDF here). The same conclusion can be drawn when only causal relations between different times series are considered. When considering self causes only (which amount to roughly 50% of all causal relations) one can see that all methods perform very well (the methods with a 1. 00 in italics always assume self causes) except TCDF. Lastly, one can see that the standard deviations vary from one method to the other. They are more important without self causes than when considering self causes only and similar for the skeleton and the summary causal graph. All in all, all families of approaches obtain more or less the same results on the summary causal graph, with an advantage to the noise-based method VarLiNGAM on this dataset.
As mentioned before, this method relies on certain assumptions that seem to be appropriate for the FMRI dataset considered here. )), the orientation of the edges is not taken into account when computing the F1 score. The third column (Sum. caus. graph (details)) illustrates the capacity of the methods to detect causal relations between different time series (W/o self causes) and within a time series (Self causes only). In this latter case, a 1. 00 in italics indicates that the method assumes that self causes always exist. Best results are in bold and methods are grouped according to their family  (Granger, constraintbased, noise-based, score-based).
Conclusion We have presented in this survey different methods, pertaining to different families of approaches, for causal discovery in time series. We furthermore have illustrated their behaviour through ex-periments conducted on both artificial and real datasets for inferring either a window causal graph or a summary causal graph. The families we have retained correspond to approaches à la Granger, constraint-based approaches, noise-based approaches, score-based approaches logic-based approaches, topology-based approaches, and difference-based approaches. The main conclusions one can draw from this survey is that causal discovery in times series is an active research field in which new methods (in every family of approaches) are regularly proposed, and that no family or method stands out in all situations.
Indeed, they all rely on assumptions that may or may not be appropriate for a particular dataset. Constraint-based and noise-based methods often come with theoretical guarantees on their optimality. If this is clearly an interesting feature, these guarantees also rely on assumptions which are not always met in practice. Several extensions to the methods we have presented have been, and still are, investigated. For example,  Gong et al. (2015)  considers the problem of subsampling which amounts to recover relations between time instants that were not observed as their difference is smaller than the sampling rate of the time series. Hyttinen et al. (2017)  further studies the subsampling in the context of time series with hidden variables. Gong et al. (2017)  studies methods to infer causal relations on time series which correspond to aggregate (local averages or sums of observations) of other time series.
8 and 1) in terms of precision and comparable for all methods, TCDF and DYNOTEARS being slightly lower. The performance obtained for the summary causal graph (skeleton and oriented) and the window causal graph in terms of recall is a bit lower, but still on a good range for most of the methods (except for TCDF and VarLiNGAM and DYNOTEARS). On can in particular notice that tsFCI is one of the best methods in terms of recall, whereas it was one of the worst in terms of precision. The results obtained for all methods on the real dataset FMRI are displayed in Table  7. In order to compare all methods, we focus here on the summary graph, evaluating as before the capacity of each method to retrieve a causal relation between two time series (i. e. , to obtain a correct skeleton) and to orient such relations (providing the summary causal graph).
Figure15: Performance of all methods on the 5 artificial datasets. The results are computed over 10 runs for which we report the mean (± the standard deviation) of the F1 score without taking into account the orientation of edges for the skeleton of the summary causal graph (left column), and while taking into account the orientation of the edges for the summary (middle column) and window (right column) causal graphs. The results are computed for various lengths of the time series: 125, 250, 500, 1000, 2000 and 4000 time points (a log-scale is used for the x-axis).
Figure18: Performance of all methods on the 5 artificial datasets. The results are computed over 10 runs for which we report the mean (± the standard deviation) of the recall without taking into account the orientation of edges for the skeleton of the summary causal graph (left column), and while taking into account the orientation of the edges for the summary (middle column) and window (right column) causal graphs. The results are computed for various lengths of the time series: 125, 250, 500, 1000, 2000 and 4000 time points (a log-scale is used for the x-axis).
The development of high-fidelity mechanical property prediction models for the design of polycrystalline materials relies on large volumes of microstructural feature data. Concurrently, at these same scales, the deformation fields that develop during mechanical loading can be highly heterogeneous. Spatially correlated measurements of 3D microstructure and the ensuing deformation fields at the micro-scale would provide highly valuable insight into the relationship between microstructure and macroscopic mechanical response. They would also provide direct validation for numerical simulations that can guide and speed up the design of new materials and microstructures. However, to date, such data have been rare. Here, a one-of-a-kind, multi-modal dataset is presented that combines recent state-of-the-art experimental developments in 3D tomography and highresolution deformation field measurements.
As a consequence, a representative volume element (RVE) for deformation of polycrystalline metallic materials must encompass the 3D grain structure over a large field of view with accurate representation of the deformation fields at the sub-grain scale. Recent advances in scanning electron microscopy (SEM), 3D tomography and multi-modal data analysis have provided unique opportunities to measure and analyze, in a reasonable amount of time, slip activity over near mm 2 -scaled fields of view as a function of the 3D microstructure. In the present paper, slip localization measurements during monotonic loading have been performed by high resolution digital image correlation (HR-DIC) on a face centered cubic nickel-based Inconel 718 superalloy. Quantitative measurements were performed over large regions of interest on this multi-modal dataset for statistically significant correlations between the microstructure and slip event locations and amplitudes.
The grain structure at the sample surface was captured by conventional electron backscatter diffraction (EBSD) measurements. However, the full subsurface 3D grain structure was collected by TriBeam serial sectioning  3. Advanced data merging tools were used to produce a distortion-free multi-modal dataset. This dataset is one of a kind and will provide the scientific community a new means of investigating the effect of two-dimensional (2D) and 3D microstructure on slip localization, and a benchmark dataset for model development and validation. All raw measurement data are provided. In addition, the final reconstructions of the dataset, in the form of both voxelized and meshed 3D structures, are also provided to allow direct comparison between experimental data and computational modeling. Finally, the 3D volume mesh built from the voxelized 3D microstructural data fully renders the grain and grain boundary morphology and is prepared for finite element crystal plasticity analysis.
Backscatter electron (BSE) images are collected from the top surface of the pillar (0° tilt) and secondary electron (SE) images are collected at a 30° tilt angle. BSE images were also collected every 30 slices for use with dataset stack alignment. A set of 526 slices was obtained during the experiment and reconstructed into a 3D dataset using the DREAM. 3D software  15  (Fig. 5 (5)). Prior to reconstruction, each EBSD slice was aligned to match the corresponding BSE image using the procedure described above. The BSE images of the top surface of the pillar, collected 0° tilt were subjected to minimal distortions compared to the EBSD measurements, collected at 70° tilt  16  and experiencing longer beam dwell times per pixel and hence larger beam drift. GrainIDs and FeatureIDs were defined during the reconstruction process using a miorientation-based grain segmentation tolerance of 5°.
While grainIDs and FeatureIDs represent the same entities, grainIDs refer specifically to the grains in the meshed dataset. Figure  6  shows the final reconstruction of the 3D dataset from a subset of the specimen, where the free surface of the 3D dataset corresponds to the same surface where surface EBSD and HR-DIC measurements were collected. The black box in Fig. 6 (a) highlights the location of the area mapped in 3D. A cubic voxel resolution of 1 μm was used to create a representation of the 3D grain structure of the investigated region i. e. a RVE. A comprehensive review on RVE classification, generation and usage is provided by Bargmann et al. 17   The information provided by TriBeam serial sectioning is detailed in Fig. 7. At each voxel, the crystallographic orientation as described by Euler angles is given and displayed in "EulerAngles" in the h5 file (Hierarchical Data Format version 5 -See Data Records section) of the 3D dataset.
The convention for Euler angles representation is different than in the 2D EBSD data. Information on the conversion between the surface EBSD and 3D EBSD Euler angles is provided in the file "Transformation_EulerAngle_2d_3d. pptx". Crystallographic orientations are also provided using unit quaternions in the h5 file. More information about the conventions used to store EBSD data and conversions between reference frames is in the following references  18, 19. Figure  7  is colored according to the FeatureIDs, integer numbers that label continuous regions of voxels that have been identified as grains. A subset of the dataset with FeaturesIDs coloring is presented in Fig. 7(b). Grains (twin or parent grains) are identified as voxel regions that have been segmented using a tolerance angle of less than 5°.
Clusters of twin-related grains  20  and their associated parent features are indicated by an ID named ParentIDs. The FeatureIDs labeled as 0 are associated with the surface layer of the voxels with unassigned data at the free surface of the specimen. The reconstruction of the 3D dataset and alignment of EBSD slices (Fig. 5 (5)) produce alignment errors from the stacking of slices that result in non perfectly flat surface (X-Z) in the two axes orthogonal to the slicing direction. The offsets in the free surface are filled with unassigned data to obtain a planar surface where DIC data was collected, as shown in Fig. 7(d). The other surfaces were simply cropped to obtain flat faces. All the contained array values at each voxel within the HDF h5 file are described in Fig. 7(a). This dataset includes the grain reference orientation deviation (GROD) calculated at each voxel, which is shown for a subset of the 3D dataset in Fig.
7(c ). The value of the GROD, which is labeled as "FeatureReferenceMisorientation" in the. dream3d file, is the misorientation in degrees for each voxel in a grain, with respect to the average orientation of the grain. Correlative measurements: multi-modal data merging. The strain fields obtained from DIC corresponding to the investigated free surface of the 3D dataset are provided for the different loading steps. All fields have been aligned to fit the free surface of the 3D dataset as displayed in Fig. 8. The distortion between both datasets was modeled using a polynomial function of degree 3, described in Eq. (1). Individual slip traces were segmented from the DIC maps and indexed as individual features, using the iterative Hough transformation method presented in Charpagne et al. 13. The location of each slip band in the 3D volume (coordinates of its endpoints on the (X g -Z g surface), its inclination angle relative to the loading direction, its length and average in-plane slip intensity and direction are all calculated.
With the assumption of slip on any of the twelve {111} <110> slip systems, the recombination of the slip trace inclination angle on the DIC surface with the local crystallographic orientation enables the determination of the active {111} slip plane. Since at least one point within each slip band and its crystallographic slip plane are known, all the slip bands can be projected and reconstructed in the 3D volume, as shown in Fig. 9. An angular tolerance was applied to obtain 1 voxel thick slip bands to accommodate the voxelized nature of the data. The voxels were assigned number IDs that refer to the slip bands they belong to, and a readily observable in the 'SlipBands' entry in the. dream3d file of the merged dataset. Individual slip bands can be viewed in Paraview as voxelized objects, or as 'slice' objects, as shown in Fig.
Mesh generation with xtalmesh. One version of a mesh structure was created with XtalMesh 21 , and can be seen in Fig. 10. XtalMesh is used to create smooth representations of voxelized microstructures and leverages the state-of-the-art tetrahedralization algorithm fTetWild  22  to generate an analysis-ready, boundary conforming tetrahedral mesh. The base workflow of XtalMesh was modified to better preserve the many small and thin features (mainly twins) of the Inconel 718 dataset from the effects of excessive smoothing (shrinkage and/or thinning). XtalMesh works by first receiving as input the triangle surface geometry of all grains in the microstructure, in this case obtained via the QuickSurfaceMesh filter in DREAM3D  15. Once received, XtalMesh smooths all   grain boundary interfaces and triple junctions in a sequential manner using a constrained Laplacian smoothing algorithm.
The final mesh contains 19. 9 million tetrahedral elements. Geometric reconstruction and mesh generation using simmetrix' software suite. Accurate representation of the material structure at the mesoscale level in the finite element domain is one requirement to model grain-level deformation process and to attempt fulfilling any validation requirements. Existing geometric representation and mesh generation capabilities  25  can close the technological gap in converting EBSD serial-sectioning stacks to high-definition volumetric meshes suitable for finite element analysis. While it is possible to directly generate a mesh from a voxel dataset it is advantageous to introduce a geometric model, specifically a non-manifold boundary representation  26  as an intermediate representation of the analysis domain  27.
Such a model provides an unambiguous representation of the analysis domain and provides a mechanism to associate information such as material properties in a manner that is independent of the mesh. Assigning meshing attributes on the topology of this model (e. g. , interfaces between grains or the boundary of the domain) or based on geometry (mesh refinement in areas of interest) allows multiple meshes to be automatically generated from this representation  27. To be able to build a valid and appropriate (based on the needs of the simulation) finite element model from a voxel dataset assembled from a serial sectioning EBSD measurement, various procedures to remove artifacts are required. This includes the elimination of small groups of disconnected voxels, and removing noise from the grain boundaries (e.
g. , through the use of erosion and dilation filters  28  ). This process is followed by the elimination of physically undesirable voxel configurations (e. g. , voxel clusters of the same material connecting at a single voxel corner) that could create singularities in the finite element solution. The resulting geometric model represents each grain as a region (volume) with geometric faces (surfaces) representing grain boundaries. Attributes attached to each region allow the user to retrieve the grain ID as it was defined in the originating DREAM3D  15  dataset. At this stage, the face geometry still reflects the stair-stepped boundaries between the individual voxels, therefore a geometric based algorithm is used to create smooth geometric faces while preserving the overall shape of the grain boundaries.
The resulting geometric model can be tagged with meshing and analysis attributes to generate a run-ready input deck for the finite element solver. For the In718 RVE, features smaller than 50 connected voxels were removed followed by an erosion/dilation step using a 3x3x3 block structuring element. Many of the grains in this dataset were rather thin (often only one or two voxels thick). These were not processed using the erosion/dilation algorithm since it would completely remove them from the data. Figure  13  shows a twin grain (identified as grain ID 105 in the DREAM3D dataset) with a cut plane showing that the grain is at times only one voxel thick. Figure  14  shows pictures of that grain as it goes through the reconstruction and meshing process, from the original voxel dataset to the voxel structure after artifacts were removed, followed by the smoothed grain surface representation and the associated volumetric mesh.
Data records SEM Images. The raw SEM images used for HR-DIC calculations are 16-bit tiff images and can be downloaded from the DRYAD repository  29. The nomenclature and location of the images are detailed in Fig. 2. The image origin is located for the pixels within the tiff images, which is set as the first top-left pixel, with the x-tiff (Xg) proceeding to the right, and y-tiff (Z g ) proceeding down the image. Full-field measurements from HR-DIC. The HR-DIC data are provided as 32-bit tiff images. The images can be viewed using software such as ImageJ. The values at each pixel in the images are the quantitative physical value of the displayed full fields given in unit length for the strain field ε xx , in pixels for the in-plane slip amplitude, and in radians for the in-plane slip direction.
We refer the reader to  10, 12  for more information about the physical meaning of these quantities. The data can be downloaded from the DRYAD repository  29. Adjacent pixels in all maps represent a physical distance of 100. 34 nm. The values in the in-plane slip amplitude maps are given in pixels, where one pixel represents a shearing/displacement induced by slip of 33. 45 nm. The image origin is located for the pixels within the tiff images, which is set as the first top-left pixel, with the x-tiff (X g ) proceeding to the right, and y-tiff (Z g ) proceeding down the image. 2D Crystallographic orientation data. The IPF maps along the loading direction X (see Fig. 4 ) from the raw EBSD measurements and after cleaning and distortion (to match the DIC full field maps) are provided in a tiff format in a RGB color type and labeled as IPF_Raw X.
tif and IPF_DistordedDIC_X. tif, respectively. The IPF map along the transverse direction Zg (see Fig. 4 ) is also provided and labeled as IPF_Raw_Z. tif. The raw crystallographic orientation data (Euler angle and grain structure) are provided in the. osc and. ang format and labeled as Euler_Orientation_Raw. osc and Euler_Orientation_Raw. ang. The. osc and. ang format are labeled as Euler Orientation Raw. osc and Euler Orientation Raw. ang. The. osc format can be opened using the TSL software from EDAX. The. ang format is a ASCII text format where the first three columns displayed the Euler angles φ 1 , Φ and φ 2 in radians. Columns 4 and 5 display the coordinate X g and Z g , respectively, for a given measurement point. It should be noted that the actual data column 5 in the. ang file are incorrectly labeled Y.
Again, the label Y in column 5 corresponds to the global direction Z g. Columns 7 and 8 display the image quality (IQ) and confidence index (CI) associated with the collected Kikuchi patterns. 3D Dataset -voxelized structure. The raw Kikuchi patterns obtained from EBSD measurement are provided in the. up2 binary file format for each EBSD slice from the TriBeam tomography measurement, these files can be opened using EMsoft dictionary indexing  30, 31  , EMSphInx 32 spherical pattern reindexing or with the Macroscopic strain 0. 69% 0. 91% 1. 23% 1. 83% Average ε xx strain from HR-DIC 0. 68% (1. 5%) 0. 87% (4. 4%) 1. 16% (5. 7%) 1. 70% (7. 1%) Table  1. Comparison between macroscopic total strain and average ε xx from the HR-DIC measurements. The absolute difference between average ε xx from HR-DIC measurements and macroscopic strain is given in parentheses.
commercial EDAX or Oxford EBSD analysis software. The data can be downloaded from the DRYAD repository  29  ; however, the up2 datafiles are each 3. 26 GB resulting in a large approximately 1. 71 TB download. The reconstructed DREAM3D dataset can be downloaded independently from DRYAD  29  for the interested reader who does not require the raw up2 EBSD patterns. The indexed data from each slice are also provided in the EMsoft HDF. h5 formatted files. The BSE and SEM images obtained after each slice during the TriBeam experiment are provided in 8-bit tiff images. The reconstructed 3D data with the distortion correction applied is provided in the. dream3d file (h5 structure). The Hierarchical Data Format version 5 (h5), is an open source file format that supports large, complex, heterogeneous data.
H5 file uses a "file directory" like structure that allows one to organize data within the h5 file in many different structured ways, as one might do in a standard computer file system. The h5 format also allows for embedding of metadata making it self-describing. The associated. xdmf file provides the container data descriptions. Such files can be opened using the open-source software Paraview (https://www. paraview. org/) for visualization. For more information about the different conventions used to store the 3D EBSD data, we encourage the reader to consult the following references  18, 19. 3D Dataset -meshed structures. The mesh generated with XtalMesh is provided in two file formats,. inp and. vtk. The. inp file, labelled XtalMesh. inp, is used as input into ABAQUS. The. inp file format is standard to ABAQUS and is an ASCII data file that consists of a series of ABAQUS keyword and data lines.