Computer implemented processing method optimized for dynamically computing, discovering and generating new materials

Abstract

Computer implemented processing method optimized for dynamically computing, discovery and generating new materials, comprising defining a material dataset including a property vector of emergent properties for each compound of the dataset, defining a target compound, defining a correlation matrix correlated to the compounds of the material dataset, applying a clustering algorithm identifying one or more communities close to the target compound and among them iteratively search or predict via ML a candidate compound that is closer to the target than a predetermined final threshold value reducing significantly the computational resources requested.

Description

[0001] Computer implemented processing method optimized for dynamically computing, discovering and generating new materials

[0002] Technical Background

[0003] Regarding the search and identification of new materials with specific properties, it is well known that pure combinatorial solutions are beyond the elaboration capabilities available nowadays. Indeed, considering that the number of possible combinations of material components exceeds the order of IO80, a combinatorial approach would require virtually infinite elaboration power.

[0004] Furthermore, the Applicant contends that existing approaches based on Machine Learning (ML) are unsatisfactory and mostly ineffective in identifying viable solutions. Several factors concur to such ineffectiveness.

[0005] Firstly, existing material datasets fail to provide reliable information about material properties: this is a severe limitation for ML algorithms, as it hinders the effectiveness of training and, consequently, the quality of the predictive performance.

[0006] In this sense, for example, US 2020176087 teaches how to adopt a variational autoencoder (VAE) to learn a continuous numerical representation of molecular structure.

[0007] Secondly, and because of this limitation, existing algorithms fail to grasp the intrinsic complexity of materials and of their emergent properties.

[0008] As an example, consider the peculiar behavior of silicon (Si): in its pure form silicon behaves substantially as an electrical insulator; when it is doped with an impurity density of the order of just 0.01% wt of some elements, it becomes a very good electrical conductor.

[0009] While such behavior can be explained and calculated by accurate physical models for this specific example, it is virtually impossible to predict similar effects for generic and arbitrary compound materials based on the relative atomic models and / or conductive / valence bands adopted by existing approaches. Finally, identifying the ideal candidates for an advantageous adoption in industrial applications requires the exploration and combination of material properties in ways that are beyond the capabilities of current frameworks taught in the state of the art.

[0010] Summary of the Invention

[0011] Based on the above considerations, the Applicant deems the technical solutions available from the state of the art inadequate for an effective discovery of new materials with specific emergent properties.

[0012] In the present application, the Applicant discloses a novel approach to counter the limitations of current solutions, by proposing a method for the iterative selection of favorite candidates for some specific emergent properties by reducing the required amount of elaboration resources and the time needed to identify the ideal solutions.

[0013] The new approach is based on an original computer-assisted process that employs:

[0014] - network theory to identify, within a material dataset, the communities (or clusters) of compounds that share (identically or proximally) a well-defined set of predetermined properties;

[0015] - Machine Learning algorithms trained on specific communities of the material dataset to optimize the prediction of new materials sharing the properties distinctive of the chosen communities;

[0016] - an active learning loop to extend the material dataset and inform the clustering and prediction algorithms by way of (i) the lab-conducted generation of the predicted materials and (ii) the subsequent characterization of the generated materials to trace their actual properties.

[0017] Preferably, the algorithms described herein use attribute vectors (a.k.a. embeddings) to describe the material compounds as it is standard in ML frameworks.

[0018] However, it is relevant to note that, unlike existing approaches in which the prediction algorithms are guided by material descriptors that trace the atomic composition and arrangement or other elemental properties, in the present application the embeddings provide a full characterization of the emergent properties of the compounds. This step represents a distinctive choice of the present invention approach, and a fundamental departure from existing methods. In fact, while current approaches start from the building blocks to predict materials with given properties, here it is proposed to learn the building blocks from the known emergent properties. This provides a much more informed training basis for the ML-guided prediction algorithms and, consequently, a substantially more efficient and effective prediction performance.

[0019] The generation and characterization processes are instrumental to the iterative construction of the material dataset used fortraining.

[0020] Main modules

[0021] According to an embodiment of the present invention, the main components and methods of the iterative process for the search of compounds with desired or predetermined properties are disclosed below.

[0022] A. Materials and material descriptors

[0023] The elemental constituents are represented as hot vectors of constant dimension, say dE, defining the maximum number of elements in a compound and each position indicates the (possibly zero) atomic number for the element in each compound. Let nE be the total number of elements considered.

[0024] Then, each compound is represented by two vectors:

[0025] - the composition vector, a (tfe • ^-dimensional vector resulting from the concatenation of the nE hot-vector representations of all the elements in the compound, and

[0026] - the property vector, a / ^-dimensional vector whose real-valued entries measure the emergent properties of interest for the compound (electrical conductivity, bandgap, density, heat capacity, thermal conductivity, magnetization, electron-phonon coupling, to enumerate a non-exhaustive set)

[0027] Preferably, the computer implemented processing method herein described can be applied to any database where materials are listed with a set of their properties, and it allows to define patterns of similarities that can aid the discovery and design of innovative materials reducing and optimizing the computational resources required. Indeed, the Applicant has preferably found that the new materials search can be based on one or more of the electronic, structural or magnetic properties, or the combination thereof, contained in the database for every compound.

[0028] B. Dataset inception

[0029] As part of the search for materials with the desired properties, the methos comprises creating and iteratively growing the material dataset (henceforth, MDS) to include compounds represented by the material descriptors introduced above.

[0030] To create the material dataset, the method preferably comprises randomly start growing alloys. More preferably, in the proposed embodiment of the Application, the method comprises random generation enhanced by further materials identified through a process that (i) mines the scientific literature for known compounds, (ii) synthesizes the compounds and characterizes them to (iii) finally include them in the dataset.

[0031] C. Topology-derived dataset clustering

[0032] The task of the clustering module is to identify, within the material dataset MDS, the communities of materials with similar emergent properties.

[0033] The clustering module assumes that MDS includes N compounds, numbered from I to A and represented by the material descriptors introduced above.

[0034] Preferably, the method comprises defining a first N x N correlation matrix (equivalently, a correlation graph) C (with N vertices) whose entries (edges) measure the correlation value between compound i and compound j, wherein the compounds serve as indices of the N x A correlation matrix .

[0035] Several parameters can be considered to measure the correlation value on material compounds.

[0036] For the present Application according to one embodiment, the method comprises measuring the correlation value on material compounds adopting the concept of the cosine similarity Sc, computed on the / ^-dimensions (or a combination thereof) of the property vectors of the materials in the MDS dataset. Specifically, given two / -dimensional vectors of attributes, A(z) and A( / ), the method comprises computing the cosine similarity between the compounds i and j as the value cos(0) of the cosine of the angle between the two vectors. Preferably, the method comprises computing the cosine similarity between the compounds i and j as the dot product of the two vectors divided by the product of their lengths.

[0037] Such a relationship is expressed by the Equation 1 reported below: where Am(i) is the m-th component of vector A(z).

[0038] Preferably, the method comprises adopting normalized vectors.

[0039] Preferably, the method comprises weighting the vectors and or the cosine similarities values as a function of further possible correlations between different material properties taken into consideration using standard weighting procedures.

[0040] Preferably, the computer implementing processing method comprises defining a distance De between the two / -dimensional vectors of attributes as the following Equation 2:

[0041] Dc= ^2 (1 - SC) (2)

[0042] Preferably, the method comprises performing the clustering module (CM) executing the following steps:

[0043] 1 . Building the complete graph of compounds by filling the entries of the first correlation matrix , based on the cosine similarity for the properties of interest;

[0044] 2. Filtering the complete graph resulting from the above construction to remove the correlation links with lower values. To accomplish that, a Minimum Spanning Tree (or Forest) is preferably adopted.

[0045] 3. Identifying via the filtering a first set of communities of compounds in the form of subgraphs (i.e. a submatrix having a dimension smaller than the original correlation matrix) of the complete correlation matrix.

[0046] For the purpose of dynamically updating the clusters of the MDS dataset (cf. the Active Learning Loop described in point G below) preferably, the method comprises updating the Minimal Spanning Trees via algorithms such as Chin and Houck in “Updating Minimal Spanning Trees”. F. Chin, D. Houck. JCSS 16, 333-344 (1978) to achieve a linear complexity (i.e. O(N), with N number of vertices on the graph / ) for the update of the MSF.

[0047] D. Machine Learning driven prediction

[0048] Preferably, the method comprises adopting the prediction module to compute accurate predictions of new materials with specific emergent properties.

[0049] According to an embodiment of the present method, the module is preferably structured as Variational Autoencoder (VAE): alternative possible embodiments could be based on other deep-learning networks (e.g. Generative Adversarial Networks - GAN), or perturbation theory or genetic algorithms or else on materials-science informed combinatorics.

[0050] An autoencoder (AE), consists of a pair of deep neural networks, an encoder and a decoder: the former projects the input vectors into a reduced space (known as latent space) which is then converted back to its original dimension. The latent space is designed to learn the most statistically relevant information in the data, and the goal of the AE is to learn an identity function, minimizing the error incurred in the reconstruction of the input.

[0051] VAEs enhance AEs by encoding the input vectors as a probability distribution (rather than as discrete points) over the latent space: this ensures that the latent space has a regular structure and thus enables a more effective generative process.

[0052] According to an embodiment of the present application the method comprises:

[0053] - Training the VAE on the compounds of one (or more) of the communities of the MDS dataset, as identified by the clustering module, sharing similar emergent properties;

[0054] - Defining a loss function for the learning process which is, as customary in VAEs, the sum of the reconstruction loss improving the quality of the resulting components (evaluated based on their composition vectors) and the Kullhack-Leihler divergence acting as a regularizer of the latent space (again evaluated on the composition vectors). - Preferably, the method comprises balancing efficiently the two elements via suitable techniques such as those described in A. Asperti, M. Trentin: Balancing Reconstruction Error and Kullback- Leibler Divergence in VAEs. IEEE Access (8) 2020;

[0055] - Once the VAE is trained, the decoder is used to predict new materials.

[0056] The Applicant has noted in this way that insisting on the communities identified by the clustering module has a two-fold beneficial effect.

[0057] Firstly, it ensures a significant reduction of the training set, hence a corresponding reduction of the computing power required fortraining and material generation.

[0058] Secondly, it provides a very reliable dataset for training and informing the prediction process, as the properties expected of the generated materials are the same as those distinctive of the compounds in the training set.

[0059] E. Material growth

[0060] Preferably, the method comprises synthesizing the candidate materials generated by the prediction module via a growth module.

[0061] According to an embodiment of the present Application, materials are grown using proven technology such as RF magnetron sputtering with multiple targets. Each target is made of pure elements of choice, which can be combined in arbitrary manner by a computer-controlled routing. Alternative method can be Chemical Vapor deposition, Atomic Layer Deposition or similar technologies.

[0062] F. Material characterization

[0063] Preferably, the method comprises assessing the emergent properties of material synthesized by the growth module via a characterization module.

[0064] According to an embodiment of the present Application, the materials will be characterized using laserbased techniques. Varying the wavelength and the intensity of the laser light, as well as the measurement geometry and technique, different properties can be evaluated, such as electrical conductivity, infrared and optical properties, UV reflectivity, thermal properties, magnetic anisotropy and coercivity, crystalline phase.

[0065] G. Active learning loop According to an embodiment of the present application, the computer implemented method comprises an iterative process of active learning for the search and generation of compounds with given properties. Preferably, the active learning loop comprises defining the parameter t as the target compound with the desired emergent properties traced by its -dimensional property vector.

[0066] Preferably, the active learning loop comprises adopting the following constants:

[0067] - A = the predetermined eligibility threshold value, i.e. the distance from the target which determines, within the dataset communities, the set of compounds used to train the predictor;

[0068] - P = the predetermined size of the batches of new compounds (nc) generated in the active learning loop before upgrading the prediction module by performing a new training

[0069] - 5 = the predetermined final threshold value of the distance employed to assess the adequacy of the new candidate compounds nc with respect to and the target compound t.

[0070] Preferably, the active learning process comprises the following steps:

[0071] 1. Execute the inception module to initialize the material DATASET and inserting the target desired properties;

[0072] 2. Execute the clustering module to (i) create the correlation matrix, (ii) build MSF(DATASET), the Minimum Spanning Forest for DATASET and (iii) compute PROXY (t), the set of the compounds that are at distance lower than or equal to A from t m MSF (DATASET) with respect to the distance measure adopted by the clustering module;

[0073] 3. Train the prediction module on the community PROXY^(t);

[0074] 4. Initialize (to zero) the counter b measuring the size of the next batch of candidate compounds;

[0075] 5. Execute the prediction module to compute the new candidate compound nc;

[0076] 6. Execute the grow module to synthesize the new candidate compound nc; execute the characterization module to compute the new candidate compound property vector and add to MSF(DATASET) a new vertex corresponding to the generated compound nc;

[0077] 7. Preferably, the active learning process comprises evaluating if Dc(nc,t) < 5 then stop the process;

[0078] 8. Otherwise, the active learning process comprises evaluating if b < then jump back to STEP 5 (Executing the prediction module to compute the new candidate compound nc) to repeat the prediction loop, else jump back to STEP 3 (Training the prediction module on the community PROXY ^t)) to refine the training and enter a new prediction loop.

[0079] The composition and interrelations of these communities defined via correlation submatrix obtained with the above procedure on a given database allows a fast and efficient mapping of the multidimensional material space of compounds.

[0080] In other words, according to a first aspect, the invention is addressed to a computer implemented processing method optimized for dynamically computing, discovery and generating new materials. Preferably, the method comprises starting and defining a material dataset comprising N compounds, wherein each compound is represented by a composition vector, which is a (d| -n| ) - dimensional vector resulting from the concatenation of UE hot-vector of all the elements in the compound, and a property vector, which is a p-dimensional vector whose real-valued entries measure a predetermined plurality of emergent properties for each compound of the N compounds.

[0081] Preferably, the method comprises defining a target compound having predefined emergent properties and being expressed by a p-dimensional property vector.

[0082] Preferably, the method comprises defining a N x N dimensional first correlation matrix correlated to the N compounds of the material dataset as indices and whose edges measure a correlation value between compound i and j .

[0083] Preferably, the correlation value is a function of a cosine similarity computed on the p-dimensions of the property vectors of the N compounds of the material dataset according to the formula

[0084] Preferably, the method comprises defining a complete graph of the N compounds by filling the entries of the first correlation matrix. Preferably, the method comprises defining a complete graph of the N compounds by calculating the Euclidean distance Dc(i,j) of the p-dimensions of the property vectors between compound i and j and defined by

[0085] Preferably, the method comprises storing the material dataset, the target and the complete graph in a storage medium operatively connected to an elaboration unit.

[0086] Preferably, the method comprises applying a clustering algorithm configured to cluster the complete graph identifying one or more communities, each having a sub-correlation matrix having a dimension Nk x Nk smaller than the N x N dimension of the first correlation matrix and being close, preferably according to the Euclidean distance Dc(i,j), to the target compound.

[0087] Preferably, the method comprises further identifying within each of such community an eligible group consisting of the eligible compounds that are the closest preferably according to the Euclidean distance Dc(i,j), to the target having a Euclidean distance Dc(i,j) smaller than a predetermined eligibility threshold value.

[0088] Preferably, the method comprises saving the resulting eligible group in the storage medium.

[0089] Preferably, the method comprises initializing to zero a counter measuring the size of the next batch of eligible compounds.

[0090] Preferably, the method comprises executing a prediction module comprising actuating a train predictor. Preferably, the method comprises actuating the train predictor which is an autoencoder comprising a pair of deep neural networks, an encoder and a decoder, configured to be trained on at least one of the eligible compounds of at least one of the one or more communities.

[0091] Preferably, the method comprises using the decoder to predict a new candidate compound once the train predictor is trained.

[0092] Preferably, the method comprises executing a growth module comprising synthesizing the new candidate compound. Preferably, the method comprises executing a characterization module assessing the predefined emergent properties of the new candidate compound comprising computing the new candidate compound p-dimensional property vector.

[0093] Preferably, the method comprises calculating the normalized distance Dc(nc,t) between the new candidate compound and the target.

[0094] Preferably the method comprises evaluating if

[0095] Dc(nc,t) < 6 where 5 is a predetermined final threshold value, smaller than the predetermined eligibility threshold value A, employed to assess the adequacy between the new candidate compounds and the target. Preferably, the method comprises then identifying the new candidate compound as the desired solution, saving it in the storage medium and end the computer implemented processing method.

[0096] Otherwise, the method preferably comprises increasing the counter by 1 and modify the first correlation matrix extending it by adding the new candidate compound as a vertex increasing its dimension to N+l x N+1.

[0097] Then the method preferably comprises evaluating if b < p, where is a maximum value correlated to batches of new candidate compounds, then perform an active learning sub-loop returning to running the predictor, else returning to building the clusters and identifying the communities.

[0098] Thanks to this technical solution the advantageous benefit previously described can be obtained.

[0099] The invention as addressed by the claims can comprise in one or more embodiments any of the preferred features hereby disclosed.

[0100] Furthermore, the characteristics and advantages of the present invention will be better disclosed in the followings by the detailed description of one of his preferred embodiments, illustrated by way of mere example and not limited with reference to the united drawings, in which:

[0101] - Figure 1 represents a flow chart of the computer implemented processing method according to the present invention,

[0102] - Figure 2 is a schematic representation of the creation of the correlation matrix using the cosine similarity approach, - Figure 3 is a schematic representation of the filtering of the matrix using a minimal spanning tree approach wherein the identified communities form branches extending around similar and proximal compounds,

[0103] - Figure 4 is a schematic representation of the computer implemented processing method according to the present invention applied to approximately 40 000 compounds stored in an organic materials database,

[0104] - Figure 5 represents a plot of number of communities versus tree size according to an embodiment of the present invention.

[0105] Detailed description

[0106] With reference to figure 1 it is shown a flowchart of an embodiment of the computer implemented processing method 100 optimized for dynamically computing, discovery and generating new materials according to the present invention. As previously discussed, such method allows to optimize the elaboration and storage resources by identifying selective communities to be processed.

[0107] Furthermore, the method 100 innovatively adopts algorithms processing emergent properties of the materials permitting to actuate a new and inventive approach to the materials comprehension, analysis and prediction.

[0108] From a macroscopic perspective, the method 100 comprises several modules synergistically collaborating among them. More precisely, the method begins with an inception module (comprising steps 101-103) aimed at initializing the material dataset. It is interesting to note that according to the invention in issue, the initial dimension of the material dataset could be even zero and / or randomly populated by a priori uncorrelated materials.

[0109] Then the method proceeds with a clustering module (comprising steps 104-106) aimed at building a structured and intra-related materials matrix where the elements are mutually ranked in order to define an eligible compounds community closest to a target t.

[0110] Then the method proceeds with a prediction module (comprising steps 107-108) aimed at training a train predictor in order to formulate a possible new candidate compound. Then the method proceeds with a growth module (comprising step 109) and characterization module (comprising step 110).

[0111] At this point, the method 100 proceed in comparing the emergent properties of the new candidate compound with the target (see steps 11 and 112) and if the result is deemed satisfactory the method ends at step 113.

[0112] In case that the predicted new candidate compound is not deemed satisfactory the method proceeds actuating an active learning loop (comprising steps 114-116) to formulate better and more satisfying new candidate compounds.

[0113] It is interesting to notice that two different embodiments are considered for the active learning loop: a “short route” that does not perform a further training of a predictor algorithm (see steps 114, 115 and 116 and “true” branch), and a “long route” that requires performing a further training of a predictor algorithm (see steps 114, 115 and “false” branch).

[0114] Moving now to a more detailed analysis, the method 100 starts at step 101.

[0115] At step 102 it requires defining a material dataset MDS comprising N compounds, wherein each compound is represented by

[0116] - a composition vector, which is a (d| -n| ) - dimensional vector resulting from the concatenation of UE hot-vector of all the elements in the compound,

[0117] - a property vector, which is a p-dimensional vector whose real-valued entries measure a predetermined plurality of emergent properties for each compound of the N compounds.

[0118] For immediate reference an example is disclosed in the followings.

[0119] The organic compound C2iH24C13FeN2 could be preferably represented by the composition vector [24,0,0,0,0,21,2,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], where elements are ordered according to the atomic number Z, i.e. [H, He, Li, . . . ], which could be stopped at an arbitrary value (Z = 34, i.e. at selenium (Se) for the example above). For this compound, the property vector would be, e.g. [0.98, 1.40, 2, 5.19, 2.28, 0.01], where the elements of the vector are [indirect bandgap (eV), crystal density (g / cm3), space group, effective electron mass (electronic mass units), effective light hole mass (electronic mass units), magnetization (pi; / A') | . A possible list of the desired emergent properties could comprise bandgap value, space group, magnetization, crystal density, etc.

[0120] At step 103 proceeds defining a target t compound having predefined emergent properties 103 and being expressed by a p-dimensional property vector.

[0121] Then the method 100 proceeds with step 104 defining a N x N dimensional first correlation matrix Cy correlated to the N compounds of the material dataset MDS as indices and whose edges Cy measure a correlation value between compound i and j .

[0122] In the embodiment considered the correlation value is preferably a function of a cosine similarity Sc computed on the p-dimensions of the property vectors of the N compounds of the material dataset MDS according to the formula

[0123] The method comprises defining a complete graph C-MDS of the N compounds by filling the entries of the first correlation matrix Cy preferably calculating the Euclidean distance Dc(i,j) of the p-dimensions of the property vectors between compound i and j and defined by:

[0124] Furthermore, the method proceeds with storing the material dataset MDS, the target t and the complete graph C-MDS in a storage medium Ml operatively connected to an elaboration unit EU1.

[0125] Such a storage medium Ml is an inner hard disk medium, an external hard disk medium, a server or the like.

[0126] The elaboration unit EU1 is a CPU (Central Processin Unit), a RAM, a router or the like.

[0127] At step 105 the method applies a clustering algorithm Ca configured to cluster 105 the complete graph C-MDS identifying one or more communities Co, each having a sub-correlation matrix sub-Cy having a dimension Nk x Nk smaller than the N x N dimension of the first correlation matrix Cy and being close, preferably according to the Euclidean distance Dc(i,j), to the target compound t. In preferred embodiments the clustering algorithm Ca is a Minimum Spanning Tree (MST) or a Minimum Spanning Forest (MSF) algorithm. For instance, when the Minimum Spanning Forest (MSF) algorithm is applied to the material dataset MDS the matrix obtained can be labeled as MSF-MDS.

[0128] At step 106 the method proceeds further identifying within each of such communities Co an eligible group PROXY A(t) consisting of the eligible compounds c that are the closest according to the Euclidean distance Dc(i,j), to the target t i.e. compounds c that have a Euclidean distance Dc(i,j) smaller than a predetermined eligibility threshold value A.

[0129] Figure 2 shows an example of a possible sub-correlation matrix sub-Cij that is a matrix of dimensions 30 X 40 which is much smaller than the correlation matrix of all materials that has a dimension of IO80. In some embodiments a series of sub-correlation matrix can be performed and the last sub-correlation matrix can have a dimension which is between the 10% and the 60% of the first correlation matrix Cij. As shown in figure 2, in order to identify more easily and efficiently the identified communities Co a color scale is adopted.

[0130] Figure 3 shows a plurality of communities Co corresponding to some sub-correlation matrix sub-Cij wherein, thanks to Minimal Spanning Tree it is possible to identify clearly the relative branches which are correlated to specific sub-correlation matrix sub-Cij .

[0131] Still, also in the case shown in figure 3, the relative branches are identified with specific colors in order to better distinguish them from other sub-correlation matrix sub-Cij .

[0132] Now with regard to figure 4, the color scale portraited represents the normalized value of one of the chosen properties (e.g. the space group), with the compounds forming a complex structure where communities of similar compounds are found in proximity to each other. The chosen property is evenly distributed across the map of materials, but the sub-branches or even entire areas tend to have similar colors.

[0133] In further embodiments of the present invention different material properties could be added to the above database or to completely different databases in order to perform different more tuned searches. Preferably, different similarity measures on top of the cosine similarity, such as bipartite networks, Jaccard index or Pearson correlation coefficient can be perform in order to create the original correlation matrix and or to specifically tune the desired submatrix to be selectively saved and processed on the second storage medium.

[0134] Preferably, different filters, e.g., a simple plot of the M strongest correlations amongst the N22 - N possible ones, planar maximally filtered graph, minimal spanning forest, community detection by means of the so called “Louvain algorithm” can be further adopted in order to satisfy specific elaboration requirements.

[0135] More specifically, when applying the Louvain algorithm it is possible to perform the following steps:

[0136] - Starting from the correlation matrix or sub-correlation matrix defined above,

[0137] - Deleting all the links with a weight smaller than the average value of weights,

[0138] - Applying Louvain algorithm for community detection to the resulting new sub-correlation matrix,

[0139] - Proceeding with method coherently with the new communities Co.

[0140] At step 107 the method 100 proceeds with initializing to zero a counter b measuring the size of the next batch of eligible compounds and then executing a prediction module 108 comprising actuating a train predictor, preferably an autoencoder AE comprising a pair of deep neural networks, an encoder and a decoder, configured to be trained on at least one of the eligible compounds c of at least one of the one or more communities Co.

[0141] Once the train predictor, preferably AE, is trained the method proceeds using the decoder to predict a new candidate compound nc. More specifically, the AE is structured as Variational Autoencoder (VAE). Alternative possible embodiments could be based on other deep-learning networks (e.g. Generative Adversarial Networks - GAN), or perturbation theory or genetic algorithms or else on materials-science informed combinatorics.

[0142] It is interesting to notice that training the VAE can require significant resources of time and in order to reduce this drawback the Applicant has developed the active learning sub-loop 115 described in the followings. Thanks to this technical solution it is possible to run the predictor in order to obtain different new candidate compounds c without necessarily performing the VAE training again. Clearly all the method processes parameters herein described and adopted can be advantageously modified by the user in order to efficiently tune the search of the desired new candidate compound balancing the required computational resources.

[0143] At step 109 the method comprises executing the growth module comprising synthesizing the new candidate compound nc.

[0144] Preferred ways of synthesizing the new candidate compound nc can be addressed to coating materials on substrates as physical vapor deposition (such as RF magnetron sputtering), chemical vapor deposition (such as Plasma enhanced CVD), Atomic Layer Deposition or similar technologies or to bulk materials such as casting or similar methodologies.

[0145] At step 110 and 111, the method comprises executing a characterization module 110 assessing the predefined emergent properties of the new candidate compound nc comprising computing the new candidate compound nc p-dimensional property vector. More preferably, at step 111 the new candidate compound nc is stored in the medium Ml .

[0146] It is apparent that the choice of the characterizing techniques are coherent with the predetermined emergent properties selected. Preferred techniques can be FT-IR, Secondary Ion Mass Spectroscopy, Atomic Force Microscopy, Dynamometer and similar apparatuses.

[0147] At step 112 the method comprises calculating the normalized distance Dc(nc,t) between the new candidate compound nc and the target t.

[0148] In this phase the algorithm adopted is prompted to evaluate if

[0149] Dc(nc,t) < 6 where 5 is a predetermined final threshold value, smaller than the predetermined eligibility threshold value A, employed to assess the adequacy between the new candidate compounds nc and the target t.

[0150] In positive outcome, at step 112 the new candidate compound nc is identified as the desired solution, save it in the storage medium Ml and the method 100 ends at step 113.

[0151] Otherwise, at step 114 the method proceeds with increasing the counter b by 1 and modifying the first correlation matrix Cy extending it by adding the new candidate compound nc as a vertex increasing its dimension to N+l x N+l. At this point, and still with reference to figure 1, the method proceeds with the evaluation at step 115 if the counter b < p, where is a maximum value correlated to batches of new candidate compound nc.

[0152] If the outcome is positive, then the active learning sub-loop 116 “short route” is performed and the method returns to step 108.

[0153] On the contrary, the active learning loop takes the “long route” and the method returns to step 105.

[0154] Figure 5 shows the number of communities versus the size of the dataset according to an embodiment of the present invention. The plot shows a first fit of the data according to a logarithmic fit (solid line) and a secondo fit of the data according to a sigmoidal behaviour (dashed line).

[0155] As can be clearly seen from Figure 5, thanks to the solution of the invention in issue, the number of communities Co tends to stabilize around a value of approximately 100, when the total number of compounds in the database reaches values around 35000.

[0156] It is thus immediately apparent that such a technical condition defines a huge and significant advantage in computing and energy resources, as the search for compounds can conducted within one of the communities instead of the entire database.

[0157] In another embodiment of the present invention, the claimed method 100 is applied for the efficient computational advantage processing desirable substituting materials of the rare-earth elements achieving steps from a. to t. by adopting the following features as specific m properties for each i-th compound of the N compounds:

[0158] - Bandgap,

[0159] - Space group,

[0160] - Magnetization,

[0161] - Crystal density,

[0162] - Heat capacity,

[0163] - Thermal conductivity,

[0164] - Electron-phonon coupling.

[0165] For the person skilled in the art by careful exploration of communities in the space of compounds he shall be able to detect materials with still unknown properties or unknown technical connections that are similar to the known ones owned by the other members of the same community adopting an efficient and computationally advantageous method.

[0166] The Applicant considers the claimed method preferably promising to detect substances with properties similar to the “rare-earths elements”. These materials are necessary for a technology with a smaller carbon footprint, but they come at the expense of pollution during extraction, as well as of geopolitical consequences.

[0167] Moreover, the Applicant considers the claimed method preferably promising to detect alloys with specific macroscopic properties as superconductivity or permanent large magnetization or, more generally speaking, any technological requirement of new materials. In other words, further benefits, among those previously discussed, of the claimed method is the extremely reduced computational and hence energy cost in the exploration of the space of compounds, compared to methods based on artificial intelligence algorithms.

[0168] In this sense the invention in re is an effective approach to a scalable mapping of the space of compounds, bringing order through network metrics to an almost infinite unstructured set of substances allowing at the same time a meaningful saving of computational resources (e.g. energy consumption) and process overall time.

[0169] Finally, the Applicant considers as a bonus benefit the fact that the adoption of such a method could push forward the scientific understanding of materials and their properties.

Claims

CLAIMS1. Computer implemented processing method (100) optimized for dynamically computing, discovering and generating new materials, comprising: a. Starting the method (101) defining a material dataset (MDS) comprising N compounds (102), wherein each compound is represented by a composition vector, which is a (di ni ) - dimensional vector resulting from the concatenation of UE hot-vector of all the elements in the compound, a property vector, which is a p-dimensional vector whose real-valued entries measure a predetermined plurality of emergent properties for each compound of the N compounds, b. Defining a target (t) compound having predefined emergent properties (103) and being expressed by a p-dimensional property vector, c. Defining a N x N dimensional first correlation matrix (Cy) correlated to the N compounds of the material dataset (MDS) as indices and whose edges (Cy) measure a correlation value between compound i and j (104), the correlation value being preferably a function of a cosine similarity (Sc) computed on the p-dimensions of the property vectors of the N compounds of the material dataset (MDS) according to the formulad. Defining a complete graph (C-MDS) of the N compounds by filling the entries of the first correlation matrix (Cy) preferably calculating the Euclidean distance Dc(i,j) of the p-dimensions of the property vectors between compound i and j and defined by:e. Storing the material dataset (MDS), the target (t) and the complete graph (C-MDS) in a storage medium (Ml) operatively connected to an elaboration unit (EU1), f. Apply a clustering algorithm (Ca) configured to cluster (105) the complete graph (C- MDS) identifying one or more communities (Co), each having a sub-correlation matrix (sub-Cij) having a dimension Nk x Nk smaller than the N x N dimension of the first correlation matrix (Cy) and being close, preferably according to the Euclidean distance Dc(i,j), to the target compound (t), g. Further identifying within each of such community (Co) an eligible group (PROXY A(t)) (106) consisting of the eligible compounds (c) that are the closest, according to the Euclidean distance Dc(i,j), to the target (t) having a Euclidean distance Dc(i,j) smaller than a predetermined eligibility threshold value (A), h. Saving the resulting eligible group (PROXY A(t)) in the storage medium (Ml), i. Initializing to zero a counter (b) measuring the size of the next batch of eligible compounds (107), j . Executing a prediction module (108) comprisingActuating a train predictor, preferably an autoencoder (AE) comprising a pair of deep neural networks, an encoder and a decoder, configured to be trained on at least one of the eligible compounds (c) of at least one of the one or more communities (Co),Once the train predictor, preferably AE, is trained using the decoder to predict a new candidate compound (nc), k. Executing a growth module (109) comprising synthesizing the new candidate compound (nc), l. Executing a characterization module (110) assessing the predefined emergent properties of the new candidate compound (nc) comprising computing the new candidate compound (nc) p-dimensional property vector (111),m. Calculating the normalized distance Dc(nc,t) between the new candidate compound (nc) and the target (t) (112), ifDc(nc, t) < 5 where 5 is a predetermined final threshold value, smaller than the predetermined eligibility threshold value (A), employed to assess the adequacy between the new candidate compounds (nc) and the target (t), then identify the new candidate compound (nc) as the desired solution, save it in the storage medium (Ml) and end (113) the computer implemented processing method (100), otherwise. n. Increase the counter (b) by 1 and modify the first correlation matrix (Cy) extending it by adding the new candidate compound (nc) as a vertex increasing its dimension to N+l x N+1 (114), evaluate if b < p, where is a maximum value correlated to batches of new candidate compound (nc), then perform an active learning sub-loop (115) returning to point j (108), else return to point f ( 105).

2. Computer implemented processing method (100) according to claim 1, wherein the action of point f (105) is achieved adopting a Minimal Spanning Tree or Forest algorithm.

3. Computer implemented processing method (100) according to any of the previous claims, wherein the clustering algorithm (Ca) is updated before actuating point f (105) to achieve a linear complexity (i.e. O(N), with N number of vertices on the graph / ) for the update of the MSF.

4. Computer implemented processing method (100) according to any of the previous claims, wherein the autoencoder (AE) is a variational autoencoder (VAE).

5. Computer implemented processing method (100) according to the previous claim, wherein the variational autoencoder (VAE) is trained adopting a loss function for the learning process which is the sum of a reconstruction loss improving the quality of the resulting components evaluatedbased on their composition vectors and the Kullback-Leibler divergence acting as a regularizer of the latent space evaluated on the composition vectors.

6. Computer implemented processing method (100) according to any of the previous claims, wherein the predetermined plurality of emergent properties for each compound of the N compounds of the property vector are electrical conductivity, bandgap, density, heat capacity, thermal conductivity, magnetization, electron-phonon coupling.

7. Computer implemented processing method (100) according to any of the previous claims, wherein the predetermined final threshold value (5) is about a tenth of the predetermined eligibility threshold value (A) as reported in the following formula5 - 0.1A8. Computer implemented processing method (100) according to any of the previous claims, wherein at least a sub-correlation matrix (subCij) is a matrix of dimensions 30 X 40 or has a dimension which is between the 10% and the 60% of the first correlation matrix (Cij).

9. Computer implemented processing method (100) according to any of the previous claims, wherein the method (100) is applied for the efficient computational advantage processing desirable substituting materials of the rare-earth elements achieving steps from a. to t. by adopting the following features as specific m properties for each i-th compound of the N compounds: a. Bandgap, b. Space group, c. Magnetization, d. Crystal density, e. Heat capacity, f. Thermal conductivity, g. Electron-phonon coupling.

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