Method and device for processing experimental data by machine learning

Abstract

The invention relates to a computer-implemented method for processing the experimental data (4d) of a solid (4) to be characterised comprising atoms and comprising one or more faults, the experimental data (4d) coming from at least one sensor (40) and having a multimodal distribution, said method comprising: - representing, in a space referred to as a descriptor space having a size K between 10 and 108, one or more reference solids and the data; - calculating, for at least one portion of the atoms of the solid to be characterised (4d), an experimental confidence score in the descriptor space relative to the atoms of the reference solid; - classifying the atoms of the structure according to the experimental confidence score.

Description

[0001]DESCRIPTION Title: METHOD AND DEVICE FOR PROCESSING EXPERIMENTAL DATA BY MACHINE LEARNING TECHNICAL FIELD AND STATE OF THE PRIOR ART The invention relates to the field of processing experimental data from a measurement on a solid. In the case of measurements carried out using techniques such as Atom Probe Tomography (SAT) or by Synchrotron Radiation (SR) X-ray diffraction or Transmission Electron Microscopy (TEM), there is no technique available for efficiently analyzing the data resulting from the measurements. These measurements reproduce massive quantities of data, for which few analysis tools are available. The known tools do not allow for the exploitation of this data in a reproducible, unbiased manner and without human interpretation errors.A first problem is therefore that of exploiting such data in a reproducible, unbiased manner and without human interpretation errors. In another aspect, recent publications, and in particular the article by Goryaeva et al., Reinforcing materials modeling by encoding the structures of defects in crystalline solids into distortion scores, Nature Communications, (2020), exclusively propose analysis solutions for data from atomic-scale simulations, i.e. devoid of any uncertainty specific to experimental data. Moreover, as indicated in this document, the method proposed there is used only with unimodally distributed data. However, data from experience never satisfy this unimodal character, but are always multimodal, for reasons inherent, in particular, to the various sources of noise that the experiment involves.Furthermore, the interpretation of data from atomic-scale experiments has never been analyzed before. Figure 4 shows analysis results obtained by implementing the technique described in the article by Goryaeva et al. mentioned above, by implementing the distortion score of this document for a perfect solid, then for a solid with 30% missing atoms, and finally for a solid with 50% missing atoms (50% missing atoms is a situation frequently encountered in SAT-type experiments). It can be seen that the distributions obtained for this distortion score are very different from each other: thus, 100% of the results obtained for solids with many defects are considered as errors or outliers.In other words, if the technique described in this document gives satisfactory results for a perfect theoretical solid, it is not applicable to real solids, which may have significant defects and for experimental data distributed according to multimodal distributions. In other words, real data are too noisy and much more complex than "in silico" data, which, in comparison, are simple, Gaussian and clean; for the latter, the teaching of the prior art is suitable, but it is not suitable for real solid data, which are very noisy and disordered. There is therefore also the problem of processing and / or interpreting experimental data with atomistic resolution and the identification and / or classification of defects. There is also the problem of processing and / or interpreting experimental data with a very reduced or reduced or acceptable speed compared to known techniques.STATEMENT OF THE INVENTION The invention aims to solve one or more of these problems. It proposes a suitable method for analyzing experimental data and interpreting them based on the characteristics specific to each type of experiment. The invention firstly relates to a method for processing data, preferably implemented by computer, originating from at least one sensor used in the context of an experiment for characterizing a solid, this solid being made up of atoms and comprising one or more defects, this method comprising: - the calculation and / or the representation, in a so-called descriptor space, of dimension K > 3 or even K >> 3, for example between on the one hand 10 or 50 and on the other hand 10. 3 or 10 4 , or even 10 8, of one or more reference structure(s) or solid(s) and of said data; - the calculation, preferably in the space of descriptors, of an experimental confidence score of each atom of said solid to be characterized, with respect to at least the atoms of said structure(s) or of said reference solid; - the grouping and / or classification of the experimental data and / or of the atoms of the structure according to the experimental confidence score; thus it is possible, for example, to identify the atoms which group together in clusters of defects in the sample of material or solid analyzed. Such data, in particular the noise which affects them, have a multimodal distribution, unlike the unimodal data which are treated in the document by Goryaeva et al. already commented above.This type of multimodal distribution is typical of data from experimental analyses, in particular data obtained by techniques such as Atom Probe Tomography (SAT) or by Synchrotron Radiation (SR) X-ray diffraction or by Transmission Electron Microscopy (TEM). The invention implements the representation and analysis of experimental data, usually done in real 3D space, in a space of increased K dimension, from a few tens to thousands of dimensions, for example between 10 or 50 on the one hand and 10 on the other hand. 3 or 10 or even 10 8. This new representation of the data is ensured by one or more mathematical function(s) called “the descriptor functions”. The invention allows the processing and / or interpretation of experimental data with atomistic resolution and / or the identification and / or classification of defects which are or may possibly be present in the material or solid studied. According to one aspect, the invention implements an interpretation and / or an analysis of the data resulting from experiments, at the atomic scale, in the abstract space of the descriptors. The solid or material studied and / or to be characterized can be previously subjected to an experimental technique which allows access, thanks to a resolution at the atomic scale, to the arrangements of the atoms which may (or may not) comprise one or more defects.Experimental data can be obtained, for example, by Atom Probe Tomography (SAT) technique or by Transmission Electron Microscopy (TEM) or by X-ray diffraction, for example from Synchrotron Radiation. The invention makes it possible to accelerate the analysis of data from experiments, at the atomic scale; it also allows the exploitation of data in a reproducible, unbiased manner and without human interpretation error.A method according to the invention may be preceded by: - ​​a step of processing or preprocessing and / or preparation of the experimental data, preferably taking into account the experimental particularities: noise / detection uncertainty etc; - and / or a step of calculating or forming a space of descriptors, and / or one or more descriptor function(s), for example as a function at least of the distances between the atoms and / or the angles between the directions connecting each atom of the solid or sample studied to its different neighbors in its network. The atomic descriptors, of dimension K>3 or even K>>3, for example between on the one hand 10 or 50 and on the other hand 10. 3 or 10 4 , or even 10 8, preferably preserve all or part of the symmetries and / or the chemical nature of the atomic structure(s) resulting from the experiment and / or used for reference. For example, after the acquisition of the data made by an experimental technique making it possible to analyze matter at the atomic scale (for example here SAT, but also TEM or DRX with synchrotron radiation) the invention makes it possible to transform these data from the real 3D space to a higher K-dimensional space (see indications above concerning K) of said descriptor space by using the mathematical descriptor functions. A descriptor function makes it possible to increase the dimensionality K of the data representation space while preserving the atomic arrangement symmetry inherent in the experimental analysis technique used, for example SAT.In a method according to the invention, the representation step is preferably carried out using a descriptor (of the so-called "FastGraph" type) which implements, for each atom j, a graph Gj whose nodes are neighbors, more or less close, of the atom j, this graph then being pixelated in the form of a matrix; the graph is preferably a dense, non-directional graph, the nodes or vertices of the graph being for example the, or corresponding to, the very atoms of the atomic environment of a central atom and for example with edges with weight weighted by the interatomic distances. The matrix is ​​preferably the pixel matrix of such a dense, non-directional graph. A method according to the invention may comprise a step of distributing or grouping the detected atoms by class of defects, by a method of the convolutional neural network (CNN) type.A method according to the invention may be preceded by: - ​​the choice of a cut-off radius, which defines the environment of each atom j (including all the atoms present in the close vicinity of atom j and which are included in the cut-off radius); - and / or the definition of at least one or more symmetries in the volume of radius ^^. ^^around each atom. In a method according to the invention, the set or class of reference structures may include environments of "perfect" solid and / or well-predefined structures, which may include point defects (dp) and / or clusters of point defects and / or extended defects such as dislocation lines. A method according to the invention may implement a comparison, for example in the descriptor space, between one or more reference structures and the structure of interest (on which a study or analysis is carried out, for example in SAT). This comparison may be made by calculating statistical distances, for example in the descriptor space. This statistical distance, which measures the difference between the descriptor(s) of the reference structure(s) and the descriptor of the structure of interest,will then allow the identification of the defect(s) in the structure of interest. We can therefore locate the structures of the defects (“unusual” or “anomaly” structures) by eliminating the environments close to the reference structures (if the reference is represented by the perfect solid, without defect). Advantageously, in the space of descriptors, we can compare the experimental or interest structure (object of the analysis carried out) with respect to one or more reference structures, which can for example come from data acquired during an experimental measurement on a sample without defect (which can be similar to a perfect solid). This comparison can be made objective, reproducible, unbiased and without human interpretation error by using the notion of statistical distance associated with each atom which constitutes the two classes of structure. In statistical mathematics,the notion of statistical distance is used to measure the difference between two probability distributions: in the context of the present invention, we compare the distributions of the atomic descriptors of the reference on the one hand and of the experiment on the other. Therefore this comparison can be made by calculating the statistical distances, also called experimental confidence score between the two classes of experimental and reference structures. This distance is ambiguous and mathematically difficult to define in 3D real space. In contrast, in the space of increased K dimension (the space of descriptors),This distance is less ambiguous and more mathematically robust. This statistical distance measures the difference between the descriptor(s) of the atoms that constitute the reference structure(s) and the atomic descriptor(s) of the structure of interest analyzed by the experiment. Thanks to this experimental confidence score, we can therefore locate the atoms that are part of defect structures ("unusual" structures or "anomalies"), for example by eliminating environments close to the reference structures (if the reference is represented by the perfect solid, without defects). Using, for example, the similarity of the experimental confidence score of the "unusual" atoms, we can then group similar atoms and classify each grouping or cluster. As indicated above,the descriptors can take into account the distances between neighboring atoms in the lattice of the reference solid and / or the angles between the directions which connect an atom to its different neighbors in this lattice, in particular in the case where the experimental data are obtained by the Tomographic Atom Probe (SAT) technique. A method according to the invention can further comprise a step of learning a method of calculating, for example a statistical distance, said experimental confidence score. Such a step can implement a machine learning or deep learning method or even a method of detecting anomalies or detecting novelty, for example a calculation of physical statistical distance with a technique of the SVM type or a neural network. The classification of the atoms can itself implement a classification algorithm of the DBScan type or neural network or SVM,or MCD or any other "clustering" method. A method according to the invention may further comprise a step of distributing or grouping the detected atoms by class of defects, by a multimodal method of the machine learning or deep learning type or a clustering and classification method such as DBSCAN or a "Gaussian Mixtures" or neural network type method. The invention also relates to a device for processing experimental data of solids to be characterized, consisting of atoms and comprising one or more defects, this device implementing, or being adapted or programmed for, a method as described above or in the present application. The invention also relates to a device for processing experimental data of a solid to be characterized, consisting of atoms and comprising one or more defects, this device comprising: - suitable means oet / ouu programmed to represent,in a so-called descriptor space, of dimension K >>3, at least one reference solid, or data from this reference solid, and said data, - means adapted and / or programmed to calculate an experimental confidence score, in the descriptor space, for example as defined above or in the remainder of this application, for at least a portion of the atoms of said solid to be characterized, relative to the atoms of said reference solid; - means adapted and / or programmed to classify atoms of a solid and / or data to be analyzed from this solid, as a function of said experimental confidence score. A device according to the invention may further comprise means adapted and / or programmed to: - form or calculate a descriptor space from the experimental data,for example from data of at least one reference sample as a function at least of the distances between the atoms and the angles between the directions connecting the atoms of this solid; - and / or forming or calculating a space of descriptors, and / or one or more descriptor function(s), for example as a function at least of the distances between the atoms and / or the angles between the directions connecting each atom of the solid or sample studied to its different neighbors in the lattice of the solid to be characterized or studied; the atomic descriptor(s) may have the properties already explained above and / or detailed subsequently in the present application; - and / or to implement a step of processing or preprocessing and / or preparation of the experimental data, preferably taking into account the experimental particularities: noise / detection uncertainty etc; - and / or implementing a step of learning a calculation method,for example of a statistical distance, of said experimental confidence score; for example such a step may implement a machine learning or deep learning method or an anomaly detection or novelty detection method, for example a statistical distance calculation or a method of the MCD or Mahalanobis type (if the multimodal nature of the experimental data is well established and known and exploitable) or a physical statistical distance calculation adapted to the multimodal experimental data by a technique of the SVM type or a neural network; - and / or, for the classification of atoms, implement a multimodal classification algorithm of the DBScan type or neural network or SVM, or MCD or any other "clustering" method; - and / or a distribution or grouping of the atoms detected by class of defects,by a machine learning or deep learning type method or a clustering and classification method such as DBSCAN or a “Gaussian Mixtures” or neural network type method; - make a choice of a cut-off radius, which defines the environment of each atom (including all atoms present in the close neighborhood included in the cutoff radius - and / or enter or select one or more symmetries, at least in a volume of radius ^^ ^^around each atom. A device according to the invention may comprise suitable and / or programmed means for implementing a representation step using a descriptor (of the so-called “FastGraph” type) for which, for each atom j, a graph Gj whose nodes are neighbors, more or less close, of atom j, this graph then being pixelated in the form of a matrix, preferably a matrix of pixels of a dense, non-directional graph, the nodes or vertices of the graph being for example the, or corresponding to, the very atoms of the atomic environment of a central atom and for example with edges with weight weighted by the interatomic distances. A device according to the invention may comprise suitable and / or programmed means for implementing a machine learning or deep learning method or even a method for detecting anomalies or detecting novelty, by a convolutional neural network.In a method or device according to the invention, the implementation of a “FastGraph” type descriptor (based on graphs and matrices) allows rapid learning by a convolutional neural network (CNN) of the experimental multimodal noise. By using this “FastGraph” descriptor, the noise of the experiment (including the missing atoms) is perceived by the CNN network as variations in contrast on the matrix elements M of the atomic neighborhood. Each element of the matrix becomes a pixel of an image, and can therefore be used by the CNN network. A device according to the invention can be connected to a detector, for example a detector of an Atom Probe Tomographic (SAT) system or an X-ray detector associated with a Transmission Electron Microscopy (TEM) system or an X-ray diffraction system, for example of a Synchrotron Radiation. BRIEF DESCRIPTION OF THE DRAWINGS [Fig. 1] represents steps of a method according to the invention. [Fig.2a-2d] represent aspects of a “FastGraph” type descriptor. [Fig. 3] represents results obtained with a “FastGraph” type descriptor coupled with a convolutional neural network. [Fig. 4] represents results obtained with a prior art method. [Fig. 5] and [Fig. 6] represent data acquisition and processing means that can be used in the context of the present invention. DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS The invention will first be explained in connection with a specific technique for analyzing a material, namely the atom probe tomography (SAT) technique. This technique is for example described in the book “Atom probe Tomography”, ISBN 978-0-12-804647-0, Editors Williams Lefebvre-Ulrikson, François Vurpillot, Xavier Sauvage, Academic Press, 2016.But the invention can be applied to other techniques for analyzing a material, for example to the analysis of images in transmission electron microscopy or to an X-ray analysis technique, for example by diffraction, the X-ray radiation being able to come from Synchrotron radiation. In all these techniques, and in many others, the experimental data obtained are never unimodal in distribution, but are always multimodal, for reasons inherent, in particular, to the various sources of noise that each experiment involves. The solid material analyzed has a crystalline structure made up of atoms arranged in a network. This network can contain defects that need to be identified and / or characterized.Any two neighboring atoms in this lattice are separated by an interatomic distance, and the directions connecting an atom to each of its neighbors are separated by different angles; see for example: In addition, real samples may have defects in significant proportion, for example up to 30 or 50% of missing atoms as already mentioned above, which reinforces the very more complex nature of the data obtained, which are very far from the theoretical data used in the article by Gorayeva et al. already mentioned above. Steps of an exemplary embodiment of a method according to the invention are illustrated in Figure 1. In a first step (S1) one or more structures or solids to be analyzed and one or more reference structures 2 are defined. The reference structures 2 can be of different natures.They can for example come from data acquired during an experimental measurement (same experimental method as the method to obtain structure 4) on a defect-free sample. This step S1 can therefore be preceded by an experimental measurement step, by SAT technique in the example considered, generating data from at least one structure to be analyzed and / or data from a defect-free sample. In addition, at least part of the reference structure(s) 2 can also come from in silico data obtained by numerical simulation. Part of this in silico data can be generated by numerical simulations taking into account the particularity of the experiments.In the example of the atom probe tomography (SAT) technique, these numerical data take into account: - the specific characteristics of this analysis technique, for example spatial and chemical uncertainties; these parameters are inherent to the experimental technique as described in the book "Atom probe Tomography" already cited above; - and / or the different behaviors of atoms during their evaporation (linked to the SAT technique), such as the crystallographic direction and / or the presence of another phase (clusters, or defects, etc.) within the sample analyzed. These parameters are also inherent to the experimental technique and are described in the book "Atom probe Tomography" (cited above). In a second step (S2) we define a space of descriptors, which is a unique mathematical space for the representation of the data of experiment 4 and reference 2 named below 2d and 4d respectively.In particular, each atom can be defined by its geometric environment with all atoms present in the close neighborhood included within a certain cutoff radius. . This neighborhood of atom i can be completely described by the positions of the set of [Math 1] where each is a 3-dimensional vector representing the Cartesian coordinates of k éme neighbor of the i éme atom: An atomic descriptor function can transform and project the environment [Math 2] into a K-dimensional space (see the indications above concerning the value of K). These functions can take into account all the neighborhood symmetries or at least one or more of them. Preferably, the mathematical functions of the descriptors preserve the topology of the experimental atomistic data by keeping the physical symmetry(s) associated with the crystalline structure of the material, for example the rotations, and / or the translations and / or the permutations of the atoms. This space of descriptors, which is a Euclidean mathematical space, is preferably of dimension K much larger than 3 (3 is the dimension of the real space of the data 2 and 4); it can be generated for example by applying one or more descriptor functions to each atom from the experimental data 4 and from the reference 2. In other words, each atom of a sample 2 and 4 can be described using its representation in the space of descriptors, i.e. a vector in a space of dimension K, K > 3 or even K >>3, for example K between on the one hand 10 or 50 and on the other hand 10 3 or 10 4 or even 10 8 . (10 or 50 < K < 103 , 10 4 or 10 8). The descriptor functions preferably preserve the geometric (including crystallography) and chemical symmetries of the solid (i.e., the invariance to permutation of atoms of the same chemical species), for example by taking into account the coordinates of the atoms in the lattice and / or the distances between neighboring atoms in the lattice and / or the angles between the directions that connect an atom to its different neighbors in the lattice of the solid and / or the structural symmetries of the material or the solid and / or the density(ies) of atoms in the lattice. Examples of descriptors that use the distances and / or angles between atoms are given in J. Behler et al., Phys. Rev. Lett.98, 146401 (2007). Examples of descriptors that use spectral analysis of atomic densities are given in A.P. Bartok's thesis "Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics", Ph.D.Thesis, University of Cambridge (2009) or in the article by A.P. Bartok et al., Phys. Rev. B 87, 184115 (2013), or in the article by M. Eickenberg et al., in Advances in Neural Information Processing Systems 30, edited by I. Guyon, UV Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., 2017) p. 65406549. Examples of descriptors that use a tensor description of atomic coordinates are given in the article by A. Shapeev, Multiscale Model. Sim.14, 1153 (2016) or in the article by E.V. Podryabinkin et al., Comput. Mater.Sci.140, 171 (2017). Examples of descriptors that preserve symmetry with respect to rotations and permutations are given in CvdOord et al., Machine Learning: Science and Technology 1, 015004(2020), Y. Lysogorskiy et. al. npj Computational Materials volume 7, article 97 (2021).In order to best handle complex experimental data, a special descriptor class (named "FastGraph") is used. This descriptor class allows for a fast evaluation of a high-dimensional system of, for example, 10. 6 at 10 9atoms, including results from atom probe tomography (SAT) experiments, with the limited computing capacity of a typical desktop computer. This type of descriptor will first be explained in connection with Figures 2a-2d. Figure 2a represents the local neighborhood of a central atom j, in the form of a graph Gj, which is then encoded in the form of a pixelated matrix M. This method is numerically efficient and allows, as illustrated in Figure 2b, an acceleration of up to 10000 in computing speed, compared to a BSO(4) spectral descriptor used in the article already commented above by Gorayeva et al. In addition, the design of a descriptor of the FastGraph class allows the convolutional neural network (CNN) to quickly learn the experimental multimodal noise.Using a FastGraph descriptor, the noise from the experiment (including missing atoms) is perceived by CNN networks as contrast variations on the matrix elements M of the atomic neighborhood. Each element of the matrix becomes a pixel of an image, thus easily usable by the CNN network. See also Neural Networks and Deep Learning: A Textbook, Charu Aggarwal, Springer International Publishing AG (2018). Figures 2c and 2d are examples of pixel maps (the intensity of the pixel is related to its value) of a FastGraph descriptor for an atom in different crystallographic structures: body-centered cubic (BC), face-centered cubic (FCC), hexagonal close-packed (HCP) and cubic diamonds (diam), showing the visual differences that can be exploited for this classification phase.Further details regarding this descriptor are given later in this description; for example, the 1st line describes the atomic environment of a central atom, the 2nd the environment of 1. er atom closer to the central atom and so on and the kth line the environment of the k èmeatom closer to the central atom. Within the scope of the present invention, other descriptors could be used, for example of the type which are numerically very heavy (and involve the implementation of very high computational resources) but which are precise, or of the type which are imprecise, but more efficient and faster from a numerical point of view. For example, one can use the SO4 (bSO4) descriptor described in the article by Gorayeva et al. already commented above, this descriptor being numerically very heavy but precise. It can be used with a classifier implementing a dense neural network (NN) in order to identify the crystallographic structure of each atom under conditions close to those encountered in SAT-type experiments.A solution according to the present invention, combining a "FastGraph" type descriptor with a convolutional neural network (CNN), is much faster and offers the same accuracy as the SO4 descriptor. Figure 4 illustrates the accuracy obtained with a method according to the invention with the four crystallographic structures (mentioned above) most common in materials science. An in silico database was created with these 4 types of crystallographic structures: CC (Fe), CFC (Cu), HCP (Fe at very high pressure) and diamond (Si). Preferably, these structures are in a highly perturbed state, with a high temperature, up to 2 / 3 of the melting temperature. Atoms were progressively removed, up to 50%, which is a situation frequently encountered in SAT type experiments.It was then noted that: -classical methods, with unimodal distribution or not, such as Ovito PTM or CNA, fail, even with a small fraction of missing atoms; -the "FastGraph" method with a convolutional neural network (CNN) gives 100% accuracy, even with 50% missing atoms, at the same level as the BSO(4) descriptor, which is about 5000 times heavier, combined with a dense neural network. In this same step, a statistical pre-analysis can be carried out for the experimental data to take into account the multi-modal character of the data. Since the subadjacent statistical distribution of data in the descriptor space is multimodal, the reference data are distributed into several groups. Each group is for example made up of data that can be described with a single Gaussian distribution. A concrete example is the distribution of atomic positions measured in SAT which have two systematic errors inherent to the SAT technique itself: an error associated with the normal detection direction Z (also the evaporation direction) and another error (about 10 times larger) associated with the lateral directions X and Y. This step can also allow obtaining the values ​​of these systematic errors. The same analysis can also be carried out for the reference samples This analysis can be done using a Gaussian Mixture type method (as described in CM Bishop: Mixture density networks (1994) or MP Deisenroth et al. Mathematics for machine learning, Cambridge University Press, (2020)). Depending on this pre-analysis, the experimental confidence score, discussed below (step 3) will have one or more dimensions, depending on the number of groups. In a third step (S3) we proceed to a step of calculating the experimental confidence score (based on "learning" the statistical distribution of the data, from step This method is for example a learning method automatic or deep learning, it can be for example a Mahalanobis type statistical distance calculation (PC Mahalanobis, Proceedings of the National Institute of Sciences of India, 2, 49–55 (1936)), or the MCD method (described for example in M.Hubert et al., Minimum covariance determinant and extension, 10, e1421, WIRES Comp. Stat. (2018) or in PJ Rousseeuw et al. A fast algorithm for the Minimum Covariance Determinant estimator, Technometrics 41, 212–223 (1999)) or Mahalanobis (PC Mahalanobis, Proceedings of the National Institute of Sciences of India, 2, 49–55 (1936)) if the multimodal aspect of the experiment is well known and exploitable. Alternatively, one can implement a technique of the SVM type (“Support Vector Machine”, see for example Vapnik, VN The Nature of Statistical Learning Theory, Speinger-Verlag, New York, 1998) or a neural network (see in particular: CM Bishop: Mixture density networks (1994) or MP Deisenroth et al.Mathematics for machine learning, Cambridge University Press, (2020)). In order to best process experimental data with multimodal distributions, a highly non-linear artificial intelligence model is preferably used, such as a neural network or SVM (support vector machine). This step therefore makes it possible to associate an experimental confidence score with each atom. The dimension of this score can be defined by the statistical pre-analysis mentioned above, in relation to the number of groups identified in step S2, following the pre-analysis of the statistical distribution of descriptors using, for example, the "Gaussian Mixture" method. The amplitude of the experimental confidence score distortion, according to each dimension, is calculated in relation to the corresponding group. In a fourth step (S4) anomaly detection is carried out (at the scale of atoms or domains which potentially correspond to defects).Depending on the experimental confidence score established in the previous step, using a classification algorithm, we can "label", for example for atoms from SAT data, the "normal" and "unusual" cases. We can therefore stratify the scores obtained with respect to a threshold which will ultimately make it possible to detect the differences between the noise and the real clusters. The classification algorithm implemented can be, for example, of the following type: - DBScan; see for example M. Ester et al. A density-based algorithm for discovering clusters in large spatial databases with noise, Proceedings of the 2nd International Conference on Knowledge Discovery and Data mining, 1, 226–231 (1996); - or neural network; see on this subject, in addition to the references already cited, for example Neural Networks and Deep Learning: A Textbook, Charu Aggarwal, Springer International Publishing AG (2018); or AP Dempster et al.: Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B (Methodological), 39, 1-22 (1977); or G. Heinz et al.: Exploring Relationships in Body Dimensions. Journal of Statistics Education, 11, 2 (2003); or KP Murphy: Machine learning: a probabilistic perspective., MIT press (2012)) - or SVM "Support Vector Machine", Vapnik, VN The Nature of Statistical Learning Theory (Springer-Verlag, New York, 1998)., or MCD (see references already cited for this method) or any other "clustering" method. In a fifth step (S5) we can proceed to a distribution or a grouping of the detected atoms by class of defects.To do this, a clustering method using machine learning or deep learning is implemented: DBSCAN (see reference already cited above regarding this method), or a “Gaussian Mixtures” or neural network method (see the references already cited above on this subject). It is then possible, during a sixth step (S6), depending on the morphology and / or geometry of the clusters identified in the previous steps, to carry out a physical interpretation: for example, 2D clusters can be interpreted as loops or dislocation lines, 3D clusters as precipitates or cavities. As already indicated above, the experimental data processed by a method according to the invention can be obtained other than by the Tomographic Atom Probe (SAT) technique.They can be obtained by Transmission Electron Microscopy (TEM) or by X-ray Diffraction (XRD), for example from Synchrotron Radiation (SR). With the SAT technique, we access the positions of atoms, whereas in the TEM or XRD techniques: - we work on images, the atoms being replaced by pixels (data obtained on the TEM or XRD detectors); - the atomic descriptors are replaced by image descriptors. It is therefore possible to perform detection and / or morphological characterization of defects such as irradiation loops, or the detection and identification of clusters of segregated elements within a homogeneous solid solution.For each of the techniques implemented, the digital data preferably take into account: - the specific characteristics of this analysis technique, for example spatial and chemical uncertainties; - and / or the different behaviors of the atoms during the implementation of the technique considered, such as the crystallographic direction and / or the presence of another phase (clusters, or defects, etc.) within the sample analyzed. The data implemented during each of the steps of a method according to the invention can be processed by a system such as a processing unit or a calculator (for example: a computer, or a microcomputer, or a server). A more detailed description of the “FastGraph” descriptor will now be given. An approach can be based on the representation of the local neighborhood of a central atom j in a 2D image which is invariant in rotation and permutation.It is the visual representation by a pixel matrix of a dense, non-directional graph, with the nodes or vertices of the graph being the, or corresponding to, the atoms themselves in the atomic environment of a central atom and with edges with weight weighted by the interatomic distances. Consider the set v(j) of neighbors of atom j with a cutoff radius (for example as defined above) rcut (“v (j) = {i|rji ≤ rcut, i ̸= j}”). The cardinal n(j) of this set (n(j) = |v (j)|) is the number of neighbors of atom j. We denote by α. j : v (j) → {1, ... , n(j)} the bijective relation which transforms the elements of v (j) into a 1 sequence of integers from 1 to n(j). The relation α j assigns the number “1” to the atom closest to atom j, the number 2 to the second nearest neighbor and so on up to n(j), which is the n(j) ème nearest neighbor of atom j. We denote G jthe graph which has the n(v ) + 1 nodes noted from 0 to n(v ) (node ​​0 of the graph is the atom itself) and whose edges represent the connections between the atoms. We note r j:0k the distance, in the graph G j from the central node 0 of G j to the nearest neighbor k of node 0. In the same way, we can measure the distance rj:lk which is the distance between the l èmeneighbor of node 0 and the kth neighbor, in Gj , of the lth neighbor of node 0 in the same graph Gj. We choose, from the set v (j), nG - 1 atoms (the first nG - 1 neighbors). Preferably, we choose nG - 1 between 35 or 31 on the one hand and 15 or 10 on the other hand (optimal value or range); in general, this number is chosen less than the average number of n(j) (in the database). We can first treat the case of (nG − 1) ≤ n(j) for any atom j. The graph Gj is in the form of an nG x nG matrix. The 1st row contains nG pixels, each of which has a value representing, or related to, the inverse of rj:0k (with k ranging from 1 to nG ). The lth row (1 < l ≤ nG) of matrix Mj concerns the neighbor of order (l − 1) of node 0 of graph Gj, again with nG pixels that are inversely proportional to rj:(l−1)k (with k from 1 to nG ). The case (nG − 1) > n(j) can be handled by assigning the elements of matrix M the values ​​zero.An implementation with a single chemical element has been described above. A multi-element version, suitable for alloys or molecules, can be deduced from what is explained above: the intensity of each pixel of the matrix can be modified proportionally with a given weight factor for each chemical element. The usefulness of this description appears in Figures 2a-2d, which have already been commented on above. The unique design of this descriptor allows the easy implementation of a convolutional neural network (CNN) that can classify the "FastGraph" descriptor of each atom. The combination of this descriptor with a CNN allows efficient and fast processing of experimental data. The multimodal character of experimental data is explained below, in particular in the case of atom probe tomography (ATP) experiments.In this type of analysis, the material is examined and prepared in the form of a very fine tip evaporated under the action of an electric field; it is the best characterization technique for performing measurements providing information on a 3D image at the atomic scale and / or the chemical composition of the material, with spatial resolution at the atomic scale. In principle, this technique would provide the position of each atom in a structure with sufficient precision to determine the atomic arrangement in the material. However, as with any microscopy technique, there are many obstacles to overcome to achieve the optimal spatial resolution. Accurate 3D images are impaired by the quantum nature of atom detection, which means that approximately every two seconds an atom is missing from the ultimately detected structures.Furthermore, the results of the experiments generally contain geometric reconstruction artifacts related to the shape of the SAT tip (sample for SAT analysis, sharp-edged). As a result, in the best SAT experiments it is possible to detect the 3D arrangements of atoms with a near-atomic spatial resolution, which is 3 Å in the lateral detection direction and 1 Å in depth in the long direction of the SAT tip. An example of such a system is shown in Figures 5 and 6. It comprises, for example, means 50, for example a computer or a calculator or microcomputer, to which a sensor 40 transmits measurement data via a connection 41.For example, in the case of the implementation of a tomographic atom probe technique, the sensor 40 is an ion detector, which makes it possible to measure the flight time of the ions and their positions; in the case of an analysis by transmission electron microscopy this sensor 40 is a camera; The same applies in the case of an analysis by X-rays, for example from Synchrotron radiation. According to one embodiment, the means 50 comprise (figure 6) a microprocessor 52, a set of RAM memories 53 (for data storage), a ROM memory 55 (for storing program instructions). Optionally, means, for example a data acquisition card 59, transform the analog data supplied by one or more sensors into digital data and put this data in the format required by the means 50. These various elements are connected to a bus 58.Peripheral devices (screen or display means 54, mouse 57) allow an interactive dialogue with a user. In particular, the display means (screen) 54 make it possible to provide a user with a visual indication. In the means 50, the data or instructions are loaded to implement data processing according to the invention, and in particular to carry out the training of one or more models and / or to carry out any prior processing of the data.These data or instructions for training a model and / or for carrying out any prior processing of the data and / or the experimental measurement data, the reference structure data and / or the descriptor space (or the data for generating it) and / or one or more descriptor functions and / or for carrying out the calculation of an experimental confidence score and / or a classification (in particular the data relating to one or more machine learning method(s)) and / or any other data for implementing the invention, may be in a memory area of ​​the means 50, into which they may have been transferred for example from any medium that can be read by a microcomputer or a computer (for example: USB key, hard disk, ROM read-only memory, DRAM dynamic random access memory or any other type of RAM memory, compact optical disk, magnetic or optical storage element).The invention allows: - the processing and interpretation of experimental data with atomistic resolution and the identification and / or classification of defects; - to accelerate data analysis; - an exploitation of the data in a reproducible, unbiased manner and without human interpretation error. The invention relates to a method and a device suitable for the analysis of experimental data as well as their interpretation based on the characteristics specific to each type of experiment. The interpretation of data from experiments at the atomic scale has never before been analyzed in an abstract space of descriptors.

Claims

CLAIMS 1. A computer-implemented method for processing experimental data (4d) of a solid (4) to be characterized, comprising atoms and having one or more defects, said experimental data (4d) originating from at least one sensor (40) and having a multimodal distribution, this method comprising: - the representation, in a space called the descriptor space, of dimension K, between 10 and 10 8of one or more reference solid(s) and said data; - the calculation, for at least a portion of the atoms of the solid to be characterized (4d), of an experimental confidence score in the descriptor space, relative to the atoms of said reference solid; - the classification of the atoms of the structure according to the experimental confidence score.

2. Method according to claim 1, the experimental data being obtained by Atom Probe Tomography (SAT) technique or by Transmission Electron Microscopy (TEM) or by X-ray diffraction, for example of Synchrotron Radiation. 3.A method according to claim 1 or 2, comprising a preliminary step of forming the descriptor space and / or one or more descriptor function(s), for example, as a function of at least the distances between atoms and / or the angles between the directions connecting each atom of the solid or sample under study to its various neighbors in the lattice of the solid (4) to be characterized. A method according to any one of claims 1 to 3, wherein the representation, in the descriptor space, of dimension K, preserves the symmetry(ies) and the chemical nature of the atomic structure(s) obtained from the experiment (4) and / or used for reference (2).

5. A method according to any one of claims 1 to 4, wherein the representation step is performed using a descriptor that implements, for each atom j, a graph Gj whose nodes are neighbors, more or less close, of atom j, this graph then being pixelated in the form of a matrix Mj.

6. A method according to claim 5, the graph being a dense, non-directional graph, the nodes or vertices of the graph corresponding to the atoms in the atomic environment of a central atom and, for example, with edges weighted by interatomic distances.

7. A method according to claim 5 or 6, the lth row (1 < l ≤ nG) of the matrix Mj relating to the neighbor of order (l − 1) of node 0 of the graph (Gj). 8.A method according to any one of claims 1 to 7, comprising a preliminary step of selecting a radius Rc, called the cutoff radius, which defines the environment of one or more atoms or of each atom j, this environment including all atoms present in the vicinity of atom j or of each atom j and which are included within the cutoff radius Rc.

9. A method according to any one of claims 1 to 8, further comprising a step of learning a method for calculating, for example, a statistical distance, said experimental confidence score. 10.Method according to claim 9, the learning step of a method for calculating an experimental confidence score implementing a machine learning or deep learning method or an anomaly detection or novelty detection method, for example a statistical distance calculation or a method of type MCD or Mahalanobis or a physical statistical distance calculation or a technique of type SVM or a neural network.

11. A method according to any one of claims 1 to 10, classifying atoms using a classification algorithm such as DBScan, a neural network, an SVM, an MCD, or any other clustering method.

12. A method according to any one of claims 1 to 11, further comprising a step of distributing or grouping the detected atoms by defect class, using a machine learning or deep learning method, a clustering and classification method such as DBScan, a Gaussian Mixture method, or a neural network method.

13. A method according to any one of claims 1 to 12, further comprising a step of distributing or grouping the detected atoms by defect class, using a convolutional neural network method. 14.Device (40, 50) for processing experimental data of solids to be characterized, comprising atoms and comprising one or more defects, said data having a multimodal distribution, this device comprising: - means (50) adapted to represent, in a space called descriptors, of dimension K between 10 and 10. 8, of at least one reference solid and said data, - means (50) adapted to calculate an experimental confidence score, in the descriptor space, for at least a portion of the atoms of said solid to be characterized, with respect to the atoms of said reference solid; - means (50) adapted to classify atoms of a solid according to said experimental confidence score.

15. Device according to claim 14, connected to a detector (40), for example a detector of an Atom Probe Tomography (APT) system or an X-ray detector associated with a Transmission Electron Microscopy (TEM) system or an X-ray diffraction system, for example a Synchrotron Radiation system.

16. A device according to claim 14 or 15, further comprising means (50, 52, 53, 55) adapted for forming or calculating a descriptor space from experimental data, for example, from data of at least one reference sample as a function of at least the distances between atoms and the angles between the directions connecting the atoms of that solid.

17. A device according to any one of claims 14 to 16, further comprising means (50, 52, 53, 55) adapted for implementing a representation step using a descriptor for which, for each atom j, a graph Gj is formed whose nodes are neighbors, more or less close, of atom j, this graph then being pixelated in the form of a matrix. 18.Device according to claim 17, the graph being a dense, non-directional graph, the nodes or vertices of the graph corresponding to the atoms of the atomic environment of a central atom and, for example, with edges weighted by interatomic distances.

19. Device according to claim 17 or 18, the lth row (1 < l ≤ nG) of the matrix Mj concerning the neighbor of order (l − 1) of node 0 of the graph (G. j20. A device according to any one of claims 14 to 19, further comprising means (50, 52, 53, 55) adapted for implementing a processing or preprocessing and / or preparation step for experimental data.

21. A device according to any one of claims 14 to 20, further comprising means (50, 52, 53, 55) adapted for implementing a learning step for a calculation method, for example, for a statistical distance, of said experimental confidence score.

22. A device according to claims 14 to 21, further comprising means (50, 52, 53, 55) adapted for implementing a machine learning or deep learning or anomaly detection or novelty detection method, for example, statistical distance calculation or a method of the MCD or Mahalanobis type or a physical statistical distance calculation or a technique of the SVM type or a neural network.

23. Device according to claims 14 to 21, comprising means adapted for implementing a machine learning or deep learning method or an anomaly detection or novelty detection method, by a convolutional neural network.

24. Device according to any one of claims 14 to 23, further comprising means (50, 52, 53, 55) adapted for implementing a classification algorithm of the DBScan type or a neural network or SVM, or MCD or any other "clustering" method. 25.A device according to any one of claims 14 to 24, further comprising means (50, 52, 53, 55) adapted to perform a distribution or grouping of the detected atoms by defect class, using a machine learning or deep learning method, or a clustering and classification method such as DBSCAN, or a Gaussian Mixture or neural network method. A device according to any one of claims 14 to 25, comprising means for selecting a radius Rc, called the cutoff radius, which defines the environment of one or more atoms j or of each atom j, this environment including all atoms present in the vicinity of atom j or of each atom j and which are included within the cutoff radius Rc.

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