How to predict and optimize molecular properties

Abstract

The present invention relates to a method for predicting physical and / or chemical property values ​​of a molecule by a computer, which method uses as input a molecular structure of the molecule as an atom-bond-graph comprising at least the atoms of the molecular structure and the bonds of the molecular structure as nodes, and provides as output predicted values ​​of the physical and / or chemical properties.

Description

[Technical field]

[0001] The present invention relates to the field of predicting physical and / or chemical properties of molecules, in particular emitter molecules for application in organic light-emitting diodes (OLEDs), and relates to a method for predicting physical and / or chemical property values ​​of molecules by a computer, a method for automatically designing molecules by a computer, a computer program having program code for carrying out one of said methods, a method for training a neural network for use in said methods, and a system configured to perform said method and / or training a neural network. [Background technology]

[0002] Organic electroluminescent devices, including one or more organic-based light-emitting layers, such as organic light-emitting diodes (OLEDs), light-emitting electrochemical cells (LECs) and light-emitting transistors, are becoming increasingly important. In particular, OLEDs are promising devices for electronic products, such as screens, displays and lighting devices. Unlike most electroluminescent devices, which are inorganic in nature, organic-based organic electroluminescent devices are often flexible and can be produced in particularly thin layers.

[0003] Many applications, including OLED emitter molecular design, require molecules with optimized physical and / or chemical properties for the application. However, due to the large number of theoretically feasible molecular structures, it generally takes a lot of time to synthesize a sufficient number of possible molecules, measure the desired physical and / or chemical properties, and / or simulate the molecules and their properties by known methods, and optimize the molecular structure based on such findings. Therefore, there is a need for an improved approach to predict the physical and / or chemical properties of molecules and to design molecules optimized in terms of their physical and / or chemical properties. Summary of the Invention [Problem to be solved by the invention]

[0004] The object of the present invention is to provide a method and a system for predicting the values ​​of physical and / or chemical properties of molecules, as well as a method and a system for designing molecules optimized with respect to said physical and / or chemical properties. In the present invention, the physical and / or chemical properties of a molecule should be understood as any physical and / or chemical properties of an individual molecule and / or of a (molecular) substance composed of a number of said molecules. In particular, the object of the present invention is to design and optimize molecules for use as materials for specific purposes. [Means for solving the problem]

[0005] One embodiment of the present invention is a method for predicting values ​​of physical and / or chemical properties of a molecule by a computer, said method using as input a molecular structure of the molecule as an atom-bond-graph that includes at least the atoms of the molecular structure and the bonds of the molecular structure as nodes, said method providing as output predicted values ​​of the physical and / or chemical properties. a) For all n in the atom-bond-graph nodes For each node of the nodes, d features extracting a dimensional feature vector; b) Extracted n nodes n feature vectors nodes ×d features generating a feature matrix of dimension; c) n based on and / or including the distance between the atom and the bond of the molecular structure nodes ×n nodes calculating a squared distance matrix D of dimension; d) applying a trained neural network comprising a transformer that uses the squared distance matrix D for self-attention decay on the feature matrix to make predictions on physical and / or chemical property values ​​of the molecules; The feature vector includes a node type, preferably one of atom, bond, and global, and the feature vector includes additional data related to the node if the node type is atom or bond; The neural network comprises: The above n nodes ×d features From the n-dimensional feature matrix nodes ×d model A trained input encoder that generates a dimensional input matrix, where d model is the dimension of the transformer model) and As the transformer, we use the squared distance matrix D for self-attention decay. layers > 1, and uses the input matrices of the input encoder as inputs, nodes ×d model A trained transformer-encoder stack that produces a dimensional matrix as output; Using the matrix generated by the training transformer-encoder stack as input, d model a trained projection layer including a self-attention layer configured to generate a x-dimensional vector as output; and a trained multi-layer perceptron configured to generate predictions of the physical and / or chemical property values ​​from the output vectors of the trained projection layer.

[0006] In the method, the n layers Each of the trained transformer-encoder layers contains a trained multi-head reduced self-attention network, a trained feedforward network, two trained layer normalizations, and two residual connections.

[0007] In the method, additional input parameters are used as additional inputs to the trained multi-layer perceptron.

[0008] In the method, the physical and / or chemical property is one of the highest occupied molecular orbital (HOMO) energy level, the lowest unoccupied molecular orbital (LUMO) energy level, the singlet energy level, the triplet energy level, the singlet-triplet energy gap, the oscillator strength, the dipole moment, the photoluminescence quantum yield, the delayed fluorescence lifetime, and / or the peak emission wavelength.

[0009] In the method, the squared distance matrix D is calculated using abstract distances derived from the atom-bond-graph.

[0010] In the method, a part of a trained neural network, for example the transformer of the trained neural network, is initialized by another transformer of another trained neural network suitable for performing the method described above.

[0011] One embodiment of the present invention is a method for automated computational design of molecules, preferably emitter molecules for use in OLEDs, particularly thermally activated delayed fluorescence (TADF) emitters, using a genetic algorithm that includes as input a set of starting molecular structures including at least one molecular structure, a set of mutation rules for specifying mutations allowed by the genetic algorithm, a score function for the molecular structures based on one or more predicted physical and / or chemical properties of the corresponding molecules, and a termination condition; The method provides as output a molecular structure of the designed molecule, the method comprising: a) providing a set of starting molecular structures to said genetic algorithm as a population of parent structures; b) using said genetic algorithm to generate a population of progeny molecular structures, partially or completely, from the population of parent structures by mutating at least one member of said population using said genetic algorithm; c) predicting values ​​of one or more physical and / or chemical properties of molecules corresponding to members of the population of progeny molecular structures using any of the methods described above, and calculating, based thereon, a value of a score function for each member of the population of progeny molecular structures; d) determining whether the termination condition is satisfied, and if not, generating a new population of parent molecular structures composed of at least one member of the population of progeny molecular structures having the best score function value among the progeny molecular structures; e) repeating steps b), c) and d) until a termination condition is satisfied; and and f) selecting as output a molecular structure generated by step b) or an iteration of step b). the values ​​of one or more of the physical and / or chemical properties are predicted using a neural network that employs a transformer with self-attention decay associated with molecular structure; The neural network uses the molecular structure as input and predicts the value of one or more physical and / or chemical properties of the member.

[0012] In the method, a termination condition is met if the score function for at least one member of the population of progeny molecular structures is greater than, less than, or equal to a predefined value, and / or the number of iterations of steps b), c), and d) reaches a predefined value.

[0013] In the method, the mutation using the genetic algorithm is fragment-based mutation and / or string-based mutation.

[0014] In the method, the genetic algorithm uses tournament selection and / or elite selection.

[0015] One embodiment of the present invention is a method for training a neural network for use in the above method, using a system including at least one processor and a storage device, the neural network including a transformer configured to use a squared distance matrix D for attention decay, one or more projection layers including an attention layer configured to use the matrix generated by the transformer as an input and generate a vector as an output, and one or more multi-layer perceptrons using an output of one of the one or more projection layers as an input; The method comprises: a) providing a data set comprising a molecular structure of a molecule and physical and / or chemical property values ​​of the molecule assigned to one of the multilayer perceptrons; b) converting said molecular structure for each molecule into an atom-bond-graph that includes at least the atoms of the molecular structure and the bonds of the molecular structure as nodes; c) All n in the atom-bond-graph nodes For each node of the nodes, d features extracting a dimensional feature vector; d) Extracted n nodes n feature vectors nodes ×d features generating a feature matrix of dimension; e) n based on and / or including the distance between the atom and the bond of the molecular structure nodes ×n nodes calculating a squared distance matrix D of dimension; f) generating multi-layer perceptron output values ​​assigned to said physical and / or chemical properties; g) adjusting the neural network based on a comparison of the output values ​​of the multi-layer perceptron and the physical and / or chemical property values ​​assigned to the multi-layer perceptron. The feature vector includes a node type, preferably one of atom, bond, and global, and the feature vector includes additional data associated with the node if the node type is atom or bond.

[0016] In the method, the neural network includes at least two multilayer perceptrons, and steps a) through g) are repeated for different data sets comprising molecular structures and different physical and / or chemical property values ​​of the molecules, and the different physical and / or chemical properties are assigned to different multilayer perceptrons.

[0017] In the method, steps a) through g) are repeated for different data sets comprising molecular structures of different molecules and physical and / or chemical property values ​​of the different molecules.

[0018] Part of the neural network, for example the transformer, is initialized using another transformer of another trained neural network suitable for use in the method.

[0019] A system including a processor and a storage device, the system configured to execute the method according to the neural network training method.

[0020] A computer program comprising program code for causing said system to carry out said method. Effect of the Invention

[0021] The present invention provides a method and system for predicting physical and / or chemical property values ​​of molecules, as well as a method and system for designing molecules optimized in relation to such physical and / or chemical properties. Specific embodiments will now be described with reference to the drawings. [Brief description of the drawings]

[0022] [Figure 1] FIG. 2 illustrates, as a flow chart, a possible neural network for use in the method according to the first aspect of the invention. [Diagram 2] 4 is a flow chart illustrating a method according to a second aspect of the present invention. [Diagram 3] FIG. 1 is a schematic diagram of a system for carrying out the methods of predicting physical and / or chemical property values, designing molecules, and training neural networks according to the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] The present invention relates to a method for predicting values ​​of physical and / or chemical properties 180a, 180b of a molecule by a computer, the method taking as input an atom-bond-graph 100 including at least atoms of a molecular structure and bonds of the molecular structure as nodes, and providing as output predicted values ​​of the physical and / or chemical properties 180a, 180b. The method includes: nodes For each node of the nodes, dfeatures extracting (120) a 3-dimensional feature vector (the feature vector includes a node type, the node type being preferably one of atom, bond, and global, and if the node type is atom or bond, data related to the node is further extracted); nodes The feature vectors of the nodes are nodes ×d features generating a feature matrix of dimension n based on and / or including distances between atoms and bonds of the molecular structure; nodes ×n nodes and applying the trained neural network with a transformer that uses the squared distance matrix D for self-attention decay on the feature matrix (140) to generate predictions for values ​​of the molecule's physical and / or chemical properties 180a, 180b.

[0024] Here, the neural network has n nodes ×d features From the n-dimensional feature matrix nodes ×d model A trained input encoder 130 that generates an input matrix having dimensions d model is the dimension of the transformer model) and n, which uses the squared distance matrix D for self-attention decay as the transformer. layers >1, and uses the input matrix of the input encoder (130) as input, nodes ×d model A trained transformer-encoder stack that produces a dimensional matrix as output and a matrix produced by the trained transformer-encoder stack as input, modelThe trained projection layer 160a, 160b includes a self-attention layer configured to generate a x-dimensional vector as output, and a trained multi-layer perceptron 170a, 170b configured to generate predictions of physical and / or chemical property values ​​from the output vector of the trained projection layer.

[0025] This object is achieved by the subject matter of the independent claims. Advantageous embodiments are defined in the dependent claims and in the following description.

[0026] According to a first aspect of the present invention, there is provided a computer-implemented method for predicting physical and / or chemical properties of molecules, particularly emitter molecules and / or host molecules for use in organic light-emitting diodes (OLEDs), particularly thermally activated delayed fluorescence (TADF) emitters, as follows. The method inputs a molecular structure of the molecule as an atom-bond-graph, which is a graph including at least the atoms and bonds of the molecular structure as nodes. If no other node types are used, the graph may be divided into two separate and independent sets (atoms and bonds) connected by edges. In that case, the graph is a bipartite undirected graph. For example, the atom-bond-graph may be generated from a simplified molecular input line entry specification (SMILES) string that represents the examined molecular structure. In the context of the present invention, the molecular structure of a molecule should be understood as information relating to at least the arrangement of the atoms of the molecule, including the elements of each atom of the molecule, as well as the type of bonds between the atoms of the molecule.

[0027] Optionally, when generating the atom-bond-graph, so-called global nodes can be added, which are connected to all other nodes. The global nodes can act as global (graph-level) attributes that transmit information and / or context about the entire molecule to / from distant nodes (e.g., atoms and / or bonds as nodes) for the neural network used in the method. Thus, the global nodes act as a shortcut to exchange global information between nodes, bypassing the need for information to travel along edges at various levels. Adding such global nodes is generally very useful, as it often improves prediction performance.

[0028] The method provides as output predicted values ​​(preferably scalar values) of physical and / or chemical properties and comprises the steps of:

[0029] First, all n in the atomic connectivity graph nodes For each node of the nodes, d features A x-dimensional feature vector is extracted (one-hot encoding can be used for this purpose). The feature vector includes the node type, which can be, for example, "atomic", "bond", or "global", and the feature vector further includes data associated with each node, referred to as node feature data, at least if the node type is atomic or bond.

[0030] The node feature data may also include the atomic number associated with the atom (e.g., one-hot and / or integer), an aromatic flag, a flag for being part of a ring structure, and / or the number of implicit hydrogen atoms connected. In the case of bonds, the node feature data may also include the bond type (i.e., single, double, triple, aromatic). features A feature vector x with dimension x=(node type feat atom feat bond ) format, where node type is the encoding of the node type, featatom is the encoding of node feature data in atomic case (atomic feature, for other node types such as bonds and globals atomic features are preferably 0), feat bond is an encoding of the node feature data in the case of bonds (bond features; for other node types such as atoms and globals, the bond features are preferably 0). type is also a one-hot encoding of one of the node types: atom, bond or global. Using global nodes is a matter of choice. If the global nodes are used, i.e., if the atom-bond-graph contains global nodes, the feature vector x is expressed as x=(node type feat atom feat bond feat global ) format, where feat global is an encoding of the node feature data associated with the global node (global features are preferably 0 for other node types such as atoms and bonds), which may also indicate or include any parameters associated with all other nodes.

[0031] For a particular element of the feature vector, it is advantageous to provide the same information in different formats. For example, the atomic number can be added to the feature vector as an integer and one-hot. One-hot encoding is commonly used to make it easier for neural networks to process particular atomic numbers in a special way, but it removes metric information (i.e., atomic numbers are similar). Since more continuous properties can be derived from the atomic number, e.g., the total molecular weight, it is more natural to process the atomic number directly, i.e., as an integer.

[0032] Overall, n nodes The feature vectors are the n nodes From the feature vector, n nodes ×d featuresA feature matrix of dimension is constructed, which is (x 1 ,x 2 ,x 3 ,···,x nnodes ) form, x i is a feature vector. Also, n nodes ×n nodes The square distance matrix D of dimension 1 is calculated based on and / or including the distances between the atoms and bonds of the molecular structure. The square distance matrix is ​​such that the (i,j) element is 0 when i=j, and d ij 2 n nodes ×n nodes matrix, where each node is assigned an index, i,j, which indicates the node index. ij is the distance between node i and node j. Therefore, the squared distance matrix is ​​the distance d ij The squared distance matrix D may include information on the atomic coordinates of the nodes, and may be based on metric distances between nodes (derived from experimentally determined and / or simulated atomic coordinates) or abstract distances between nodes derived purely from the atom-bond-graph without information on the atomic coordinates. When global nodes are used, the squared distance matrix D also includes values ​​of distances between the global nodes and other nodes (e.g., of type atom or bond). The distances between the global nodes and other nodes are preferably the same value c for all other nodes. That is, if one of i and j indicates a global node, then d ij 2 = c. The value of c is preferably 0.

[0033] Finally, the feature matrix is ​​fed into a trained neural network containing a Transformer model (Transformer), a machine learning model first described in "Attention Is All You Need" (Vaswani et al., 2017), which uses the squared distance matrix D for self-attention decay to generate predictions for the values ​​of the molecule's physical and / or chemical properties.

[0034] Using the methods according to the invention, physical and / or chemical properties such as the highest occupied molecular orbital (HOMO) energy level, the lowest unoccupied molecular orbital (LUMO) energy level, the singlet energy level, the triplet energy level, the singlet-triplet energy gap, the oscillator strength, the dipole moment, the photo-luminescent quantum yield, the delayed fluorescence lifetime, and / or the peak emission wavelength may be predicted.

[0035] The method uses a squared distance matrix D for self-attention decay, n layers >1, preferably n layers A trained Transformer-Encoder stack with 6 Transformer-Encoder layers (as transformers), and nodes ×d features As input to a trained transformer-encoder stack generated from an n-dimensional feature matrix, nodes ×d model A neural network is utilized that includes a trained input encoder (including an input encoder layer) configured to generate an input matrix having a dimension, where d model is the dimension of the transformer model (e.g., d model = 128), where the trained transformer-encoder stack is trained on n nodes ×d model After the first layer, the Transformer Encoder layers (n layers ) are n nodes ×d modelThe output of the previous layer, which is also a matrix of dimension, is used as input. The squared distance matrix D has the advantage of reintroducing the distance information lost in the feature matrix generation stage.

[0036] The neural network is also trained on d (using the matrices generated by the trained transformer-encoder stack, i.e., its outputs, as input). model The trained projection layer may also include a self-attention layer configured to generate as output a x-dimensional vector, and finally a trained multi-layer perceptron (MLP) configured to generate predictions of physical and / or chemical property values ​​(as targets), e.g., in scalar form, from the output vector of the trained projection layer.

[0037] Preferably, the MLP has one or two hidden layers and / or utilizes ReLU (rectified linear unit) activation and / or dropout. It should be noted that with the MLP, different sets of projection layers can be used in parallel to target different goals, i.e., different physical and / or chemical properties. That is, in the last layer of the neural network, the information extracted from the network is combined with an additional self-attention layer (in the form of a projection layer) and a feedforward network (the MLP) for each goal to predict a set of scalar quantities per molecular structure.

[0038] Preferably, the trained transformer-encoder stack has n layers n transformer-encoder layers, each of which has trained multi-head decaying self-attention (i.e., a group of multiple, e.g., four, decaying self-attention layers running in parallel). layersIt is composed of two Transformer Encoder layers, a trained feedforward network (Transformer Feedforward Network (e.g., with a dimension of 512)), two trained normalization layers (applying the LayerNorm function, preferably layer normalization by “Layer Normalization” (Ba et al., 2016) (one for the output of the Transformer Encoder layers and one for the output of the Feedforward Network)), and two residual connections around the Transformer Encoder layers and the Feedforward Network (sublayer) that allow realizing LayerNorm(x+sublayer(x)), where x is the input of each sublayer, as described in Vaswani et al. (2017) and in section S7 (Solution 1) of “A community-powered search of machine learning strategy space to find NMR property prediction models” (Bratholm et al., 2020). It should be noted that the Transformer does not make any distinction between atoms and bonds. Therefore, to generate a representation for each atom-bond-graph with the same dimensions, we use a trained input encoder and convert the feature matrix composed of feature vectors into n nodes ×d model Convert it into a dimensional matrix.

[0039] Additionally, the transformer encoder layer preferably utilizes an attention function for self-attention decay given by Equation 1 below:

number

[0040] where Q is a query matrix constructed by query vectors, K is a key matrix constructed by key vectors, V is a value matrix constructed by value vectors, and d kis the dimension of the key vector, D is the squared distance matrix, γ is a learnable parameter, and softmax is the softmax function (normalized exponential function) described in Vaswani et al. (2017) and Bratholm et al. (2020), section S7 (Solution 1). The matrices Q, K, and V can be computed using learned matrices from the input matrices of each group of self-attention layers in the transformer-encoder stack. That is, Q, K, and V are computed from the input matrices of the current self-attention layer via a learnable linear transformation, which is the output of the input encoder for the first group of self-attention layers, and the output of the previous self-attention layer otherwise. Using the squared distance matrix D to modify the matrix in the argument of the softmax function reduces the interaction strength between pairs of nodes that are far apart in the atom-bond-graph. The learnable reduction parameter γ is used to scale the influence of the squared distance matrix D and can be initialized to 1. A value of 0 for the parameter γ allows attention to the entire graph, while γ=∞ restricts attention to direct neighbors in the graph, thus achieving distance-scaled self-attention.

[0041] In another advantageous embodiment, the method may use one or more additional input parameters as additional inputs to the trained multi-layer perceptron. The additional input parameters may be physical and / or chemical parameters predicted by the method according to the invention and / or predicted using other methods and / or measured physical and / or chemical parameters and / or parameters describing the properties of the molecular environment under consideration. Such an approach increases flexibility and is particularly useful when training a neural network because generally available experimental or simulation data were generated in different conditions (e.g., in the case of OLED emitters, different emitter concentrations and / or host materials). Thus, the specific conditions of an experiment may be used as additional input features (i.e. additional input parameters) to the multi-layer perceptron so that all data available in different experiments can be used for training. After training, the additional input parameters may be set to the desired target conditions.

[0042] In a preferred embodiment of the method, the squared distance matrix D is calculated using distances derived from the atom-bond-graph, i.e., not using physical atom positions. The distance between two nodes of the atom-bond-graph is an abstract distance. Preferably, the distance is calculated by dividing the edge distance (the number of edges on the shortest path between two nodes) on the atom-bond-graph by 2 and truncating. For example, in the case of a "C1-s4-C2-d5-O3" structure (s4 indicates a single bond, d5 indicates a double bond, C1, C2 indicate carbon atoms, O3 indicates an oxygen atom, and the number indicates a node index), the distance d between C1 and d5 is d(C1,d5)=floor(3 / 2)=1. According to the above definition, when a global node is used, the distance between the global node and any other node can be defined as 0.

[0043] It has been found that the square distance matrix based on the abstract distances (not physical distances) is sufficient for most applications, especially when simulating the properties of emitter molecules for use in OLEDs. Advantageously, the approach requires less computational effort than using actual atomic coordinates, and less computer memory, since integers can be used. Thus, even without available three-dimensional information, it is possible to simulate physical / chemical properties based on abstract distances extracted from atom-bond-graphs. The method also significantly simplifies the presented method, since no additional simulation is required to estimate the atomic positions.

[0044] In a particularly advantageous embodiment of the method, a part of the trained neural network, for example the transformer of the trained neural network, is initialized using transfer learning. For initialization, it has been found that parts of trained neural networks suitable for carrying out one of the methods presented above or other can be used when training said or other neural networks with suitable data that can be easily accessed. In particular, it is possible to pre-train the transformer and the input encoder using physical and / or chemical property values ​​as targets, which can be simulated separately, for example using density functional theory (DFT). Through this, a large amount of training data can be generated for training the transformer and the input encoder. Preferably, to train the final model, the head of the newly initialized neural network, i.e. the projection and MLP layers, is first trained using the input encoder frozen for a defined number of epochs with a constant learning rate and the pre-trained transformer. Afterwards, the transformer encoder can be unfrozen and fine-tuned together with the head by a cosine learning rate schedule.

[0045] According to a second aspect of the invention, the method for computational prediction of molecular physical and / or chemical properties may desirably be used in automated molecular design.

[0046] In particular, a method for automatically designing molecules, preferably emitter molecules and / or host molecules for use in OLEDs, in particular TADF (thermally activated delayed fluorescence) emitters, using a genetic algorithm has as input a set of starting molecular structures including at least one molecular structure, a set of mutation rules for specifying allowed mutations for the genetic algorithm, a scoring function for the molecular structures based on one or more predicted physical and / or chemical property values ​​of the molecule, and a termination condition. The method also provides as output a molecular structure of the designed molecule. It includes the steps of providing the set of starting molecular structures to the genetic algorithm as a population of parent structures, using the genetic algorithm to generate a population of progeny molecular structures partially or completely from the population of parent molecular structures by mutating at least one member of the population, using the method according to the first aspect of the invention to predict one or more physical and / or chemical property values ​​of molecules corresponding to the members of the population of progeny molecular structures and calculating a value of the scoring function for each member of the population of progeny molecular structures based thereon.

[0047] Here, the one or more physical and / or chemical property values ​​may be predicted by a neural network using a Transformer model with self-attention decay on the molecular structure, which uses the molecular structure as an input and predicts the one or more physical and / or chemical property values ​​of the members. Here, the machine learning model is preferably designed by one of the models additionally described above. Then, a termination condition is checked, and if not satisfied, a new population of parent molecular structures is generated, which is composed of at least one member of the population of progeny molecular structures having the best (also the highest or lowest) score function value among the progeny molecular structures.

[0048] The final steps (generating a population of offspring molecular structures, predicting the physical and / or chemical properties of the molecules and calculating the value associated with the score function, generating a new population of parent molecular structures) are repeated until a termination condition is met. One of the generated molecular structures is then selected as output. The termination condition may vary depending on the score function value associated with the best molecular structure in the current generation, but also additionally depending on the number of iterations (i.e., only a certain number of iterations are performed). In particular, the termination condition may be defined as being satisfied if the value of the score function associated with at least one member of the population of offspring structures is greater than, less than, or equal to a predefined value and / or if a predefined number of iterations is reached.

[0049] That is, the method optimizes a set of molecules (population) over a set of genetic optimization iterations (generations). In each generation, the value of a score function (score) is maximized or minimized and a set of parent molecules is selected based on the score function. The score function considers a set of physical and / or chemical properties estimated with the aid of a machine learning model. The selected molecules are then modified (mutated) by performing any set of possible elementary modifications. Finally, for the next generation, the process is repeated until a termination condition is met, e.g. a specific value of the score function.

[0050] Each time a new molecular structure is generated, it is assigned a score, a scalar value also called fitness, based on a scoring function. The score describes how well a molecular structure matches a desired target criterion and is optimized by the algorithm by allowing molecular structures with higher scores to survive and produce more offspring with a higher probability. To calculate the score, one or more physical and / or chemical property values ​​(provided as scalar values) are predicted using a neural network with a transformer with self-attention decay on the molecular structure, which may be provided, for example, as a SMILES string. A user can define a scoring function (e.g., a linear ramp, a Gaussian-shaped curve, or the like) by selecting a set of physical and / or chemical properties (features) of interest to the user. Each of the features is then calculated and mapped to a feature score in a defined range (e.g., [0,1]) with a user-configurable scoring function, where the defined range specifies how well the feature value matches the desired target value. Finally, the individual feature scores may be combined, possibly via a user-configurable aggregation function, into a final score for each molecular structure.

[0051] Preferably, the mutation using the genetic algorithm is a fragment-based mutation and / or a string-based mutation. In the case of fragment-based mutation, the molecular structure of the molecule must be represented as a graph of interconnected molecular fragments, which are added, removed or replaced for the mutation. In contrast, the string-based mutation is based on a string representing the molecular structure, and applies a (predefined) elementary transformation to the string representing the molecular structure at a specific position. For example, the string-based mutation may utilize SMILES arbitrary target specification (SMARTS). In that case, the string is a simplified molecular input line entry specification (SMILES) string, and SMARTS pattern matching may be used to find suitable positions for the transformation.

[0052] More specifically, in the case of fragment-based mutations, the molecular structure of a molecule is represented by a graph of interconnected molecular fragments, where the molecular fragments (also called fragments) are representations of the molecular structure with a number of placeholder atoms (symbols used in the graph that mark positions to which other fragments may be attached when mutating the fragments). A number of the placeholder atoms may be attached precisely to one other atom of the fragment and may be attached to placeholder atoms of other fragments. Instead of purely abstract symbols, the placeholder atoms may also be atoms of differently unused elements, for example atoms of the actinide series (e.g. Am, Bk).

[0053] In general, a graph showing a molecular structure can be constructed by merging fragments along the linked placeholder atoms by adding a single bond between the two atoms connected to the placeholder atoms of the link and removing the placeholder atoms. A graph constructed by fragments is called a fragment graph. Thus, a single fragment is also a fragment graph. The fragment graph is generated, for example, by connecting the following three fragments with two Am-Bk links, indicated by double arrows:

[0054] [ka] (F1)

[0055] After removing the remaining Am atoms, the molecule displayed is:

[0056] [ka] (F2)

[0057] Fragment-based mutations can be constructed using the above-mentioned placeholder atoms, specifying a set of fragments in the form of a SMILES string, and defining for each fragment an integer weight that specifies the relative probability of selecting it in the mutation. Furthermore, a set of linking rules can be specified for each placeholder atom type. That is, the list of rules specified for each placeholder atom type is the list of placeholder atom types to which the placeholder atom type can be linked. For example, in the case of Am, Bk, and U atoms interacting with placeholder atoms in a set of fragments, the linking rules state that Am atoms can only be linked to Am or Bk atoms, Bk atoms can only be linked to Am or Bk atoms (which can be denoted as "(Am,Bk)"), but U atoms can only be linked to other U atoms. The use of placeholder atoms makes it possible to allow only specific linking between specific fragments and / or sets of specific fragments.

[0058] Using fragment-based mutations, various actions are possible to mutate the molecular structure. Possible mutations are:

[0059] Leaf fragment addition: Any fragment with any free linking position is selected, and any fragment that can be linked to the linking position according to the linking rules is added and linked to the fragment graph. The added fragment is called a leaf fragment because it is linked to only one other fragment. For example, M1 is mutated to M2.

[0060] [ka] (M1)

[0061] [ka] (M2)

[0062] Leaf fragment removal: Any fragment connected to only a single fragment (e.g., a leaf of the fragment graph) is removed from the fragment graph. For example, M3 is mutated to M4.

[0063] [ka] (M3)

[0064] [ka] (M4)

[0065] Internal fragment addition: Any link (connected to a fragment) is selected and any fragment that can be connected to that placeholder atom is inserted at the link position. For example, M5 is mutated to M6.

[0066] [ka] (M5)

[0067] [ka] (M6)

[0068] Intra-fragment removal: Any fragment connected to two fragments that can be connected by a linking rule is removed from the fragment graph. For example, M7 is mutated to M8.

[0069] [ka] (M7)

[0070] [ka] (M8)

[0071] Fragment replacement: Any fragment is replaced with any fragment that has at least the placeholder atom amount of each type that replaces the currently attached fragment (e.g., if the fragment to be replaced is attached to two Am placeholder atoms and one Bk placeholder atom, then a fragment with at least two Am placeholder atoms and one Bk placeholder atom is selected). A new fragment is attached to the fragment graph at any compatible position, and the current fragment is removed from the fragment graph. For example, M9 is mutated to M10.

[0072] [ka] (M9)

[0073] [ka] (M10)

[0074] Cross-over: With a defined probability, instead of normal mutation, it is also possible to perform so-called "cross-over mutation". The cross-over mutation uses two fragments, i.e., a second individual is sampled from the pool of current parent structures. Then, two parent molecules (first parent and second parent) are combined by first splitting each parent molecule from any links of the same type (e.g., between the same placeholder atom type), and then further linking interchangeable molecular parts from each parent. For example (child molecule is generated by the circled molecular parts of the first and second parents):

[0075] [ka] (M11; first parent) (M12; second parent) JPEG2025507276000016.jpg31170(M13;child)

[0076] In all the above actions, where random selection is performed, instead of random selection being evenly distributed, random selection with weighting is also possible. In general, when mutating a molecular structure, one of the above actions is selected randomly or with weighting.

[0077] Then, possible fragments are shown as examples, with Am, Bk and U atoms acting as placeholder atoms (linker atoms).

[0078] Eight donor fragments containing the Am linker atom:

[0079] [ka] (F3)

[0080] Four acceptor fragments containing the Bk linker atom:

[0081] [ka] (F4)

[0082] Two spacer fragments containing U linker atoms:

[0083] [ka] (F5)

[0084] Said fragments are particularly advantageous for use in the automated design method of molecules according to the invention using fragment-based mutagenesis, in which the linking rules are, for example, (Am,Bk), (Am,U), (Bk,U), (U,U), etc., i.e., the donor can be linked to an acceptor or spacer, the acceptor can be linked to the donor or the spacer, and the spacer can be linked to itself.

[0085] An alternative to fragment-based mutagenesis is string-based mutagenesis, e.g., SMARTS-based mutagenesis. Instead of tracking a graph of fragments, string-based mutagenesis strategies represent the molecular structure by a single string, e.g., a SMILES string. However, as in fragment-based mutagenesis, the string also contains additional markers, e.g., in the form of isotope tags and / or placeholder atoms (also called linker atoms), that are removed for output and scoring, e.g., from the actinide series.

[0086] The tags can also be used to search for specific positions introduced by previous mutations, and fragment-based mutations can be defined with the string-based approach. Compared to the fragment-based approach, the string-based mutation approach allows the definition of more detailed basic molecular operations, such as adding / removing bonds, changing atom types / bond types, exchanging atom types between adjacent atoms, adding / removing substructures at molecular edges or between existing bonds, shifting a substructure connected to one atom to an adjacent atom, and replacing a set of atoms with yet another set of atoms. Overall, string-based mutation can be viewed as a more general variant of fragment-based mutation.

[0087] Also, in most applications it is advantageous to use tournament selection and / or elite selection in relation to the genetic algorithm. Using tournament selection, a certain number of "tournaments" are run by selecting a defined number of molecular structures in the current population of offspring molecular structures and / or by selecting a starting molecular structure for each tournament (from the first iteration) arbitrarily to generate a new generation of parent molecular structures (parent selection). For each tournament, a certain number of molecular structures with the highest scores in each tournament are selected to form the set of parent molecular structures for the next generation, i.e., the molecular structures used for mutation. Elite selection can additionally be used, where a defined number of the best-scoring molecular structures in the current population of offspring molecular structures or the starting molecular structures (in the first iteration) are kept without mutation. Instead, they are directly copied to the next generation, i.e., automatically included in the next population of offspring molecular structures.

[0088] Collectively, the top scoring molecular structures (from elite selection) and the generated molecular structures (eg, by mutation using tournament selection) form a secondary population of parent molecular structures.

[0089] According to a further aspect of the invention, a system comprising at least one processor and a storage device is configured to perform a computer-based method according to one of the methods of the invention. Said computer-based method may be realized by a computer program executed by said system.

[0090] According to yet another aspect of the invention, a neural network for use in any of the aforementioned computer-based methods includes a transformer configured to use a squared distance matrix D for self-attention decay, one or more projection layers including a self-attention layer configured to use the matrix produced by the transformer as input and to produce a vector as output, and one or more multi-layer perceptrons using an output of one of the one or more projection layers as input, and may be trained by a method comprising the steps of:

[0091] First, a dataset is provided that contains the molecular structures of molecules and the physical and / or chemical property values ​​of the molecules (ground truth), where the physical and / or chemical properties are assigned to one of the multi-layer perceptrons. The molecular structure of each molecule is converted into an atom-bond-graph that contains at least the atoms of the molecular structure and the bonds of the molecular structure as nodes. All n nodes For each of the nodes, d features A n-dimensional feature vector is extracted, the feature vector including a node type, preferably one of atomic, bond, and global, and if the node type is atomic or bond, the feature vector including additional data associated with the node (node ​​feature data). nodes n feature vectors nodes ×d features A feature matrix of dimension n is generated based on and / or including the distances between atoms and bonds of the molecular structure. nodes ×n nodes A squared distance matrix D of dimension is computed.

[0092] Finally, output values ​​of the multi-layer perceptron assigned to the physical and / or chemical properties are generated. The neural network is trained based on a comparison of the output values ​​of the multi-layer perceptron to the physical and / or chemical property values ​​assigned to the multi-layer perceptron. A loss function is typically used to compare the output to actual measurements. The above steps may be repeated for a certain number of epochs using different data sets including molecular structures and physical and / or chemical property values ​​of molecules until the neural network is sufficiently trained.

[0093] In an advantageous embodiment of the method, the neural network comprises at least two multi-layer perceptrons and the above steps are repeated for different data sets comprising values ​​relating to the molecular structure of the molecule and to different physical and / or chemical properties, the different physical and / or chemical properties being assigned to different multi-layer perceptrons. This embodiment is based on the surprising discovery that the training of the neural network used in the method according to the first and second aspects of the invention, in particular the main part of the transformer, can be performed using empirical data for the different physical and / or chemical properties as separate outputs of the neural network when using multiple multi-layer perceptrons, i.e. all physical and / or chemical properties have to be assigned to a perceptron.

[0094] Similarly, a part of a neural network, for example a transformer, may be initialized using a corresponding part of another trained neural network suitable for use in the methods according to the first and second aspects of the invention. As already mentioned, it has been revealed that a part of another trained neural network may be used when training the other neural network with suitable data that may be more easily accessible and / or more easily generated for initialization. Through this, a large amount of training data may be generated. To train a model after initialization, preferably using a pre-trained part of another trained neural network, a newly initialized head of the neural network, including a multi-layer perceptron, is first trained with the pre-trained part at a constant learning rate for a defined number of epochs. After that, the remaining part of the neural network may be unfrozen and fine-tuned together with the head by a cosine learning rate schedule. For said training method, a system is used that includes at least one processor and a storage device. That is, at least some, preferably all steps of the training method described above are performed and / or supported by said system. In particular, the learning method is also a computer-implemented method.

[0095] 1 illustrates in a schematic manner a possible structure of a software program including a neural network that can be used in the method according to the invention. Furthermore, said figure also illustrates the following method according to a first aspect of the invention:

[0096] An atom-bond-graph 100 describing a molecular structure (e.g. generated from a SMILES string) is provided as input to the software program (e.g. generated from a SMILES string) for which physical and / or chemical property values ​​have to be predicted. The atom-bond-graph 100 is used by a graph feature extractor 120, which is a unit of the program that extracts a feature vector for each node (atom, bond, global) in the atom-bond-graph 100. The feature vector includes the node type of the node and, in the case of an atom or bond, additional data associated with the node. The graph feature extractor 120 extracts features has dimension n nodes n feature vectors nodes ×d features Through the input encoder layer 130, the feature matrix is ​​generated as layers n Transformer Encoder Layers 150 are used by the Transformer Encoder stack nodes ×d model Each of the layers 150 includes a trained multi-head damped self-attention 152, a trained transformer feedforward neural network 156, two layer normalizations 154, 158, and two residual connections 142, 144 that connect the inputs of the transformer encoder layer to the first layer normalization 154 and the inputs of the feedforward neural network 156 to the second layer normalization 158.

[0097] The multi-head decaying self-attention 152 is composed of multiple (eg, four) parallel decaying self-attention layers. The decaying self-attention can be realized using a function of the form described in Equation 1.

[0098] The essential matrix D (arrow 140) used is n nodes ×n nodesIt is a two-dimensional squared distance matrix, which may be calculated and provided, for example, by feature extraction unit 120 of the software.

[0099] The transformer-encoder stack is nodes ×d model Generate a matrix of dimension n nodes ×d model The dimensional matrix is ​​projected by one or more learned projection layers 160a, 160b, one for each target, d model The projection layers 160a, 160b include a self-attention layer that is associated with a 2-dimensional vector. In the figure, two projection layers 160a, 160b are shown, but more projection layers 190 are possible depending on the number of targets 180a, 180b. The vectors are used by MLPs 170a, 170b to finally calculate targets 180a, 180b, i.e., physical and / or chemical property values, as scalar values ​​based on the vectors and, optionally, one or more additional input parameters 110 (e.g., host molecule properties, concentrations, solvents). As with the projection layers, the number of MLPs 170a, 170b also depends on the number of targets 180a, 180b and may be greater than the two shown in the figure (190).

[0100] FIG. 2 is a flow chart for use in the method according to the second aspect of the invention.

[0101] The initialization 200 of the genetic algorithm comprises a step of providing at least one molecular structure as a starting molecular structure and other required parameters (mutation rules, score function, termination conditions), for example in the form of a configuration file. After the initialization 200 of the genetic algorithm, in a parent selection step (220), the starting molecular structure is defined as a parent molecular structure.

[0102] Then, in step 240, fragment-based or string-based mutation is applied to generate a population of progeny molecular structures. In step 260, for at least said molecular structures, the value of at least one physical and / or chemical property is predicted as a scalar value using the method according to the first aspect of the invention, and a value associated with a scoring function is calculated using the predicted values ​​of said physical and / or chemical properties. Then, in step 270, a termination condition is checked, which may depend on the calculated value of the scoring function.

[0103] If the termination condition is not met (arrow 210), then in step 220 a new set of parent molecular structures is generated. For this purpose, for example, a tournament selection can be used. The steps of generating a new parent generation (parent molecular structures) (220), generating a population of offspring molecular structures (using mutations) (240), predicting and scoring the physical and / or chemical properties of the molecules (260), and checking the termination condition (270) (said steps form one iteration 290 of the process) are repeated until the termination condition is met. If the termination condition is met, then in step 280 one or more generated molecular structures are provided, typically the generated molecular structure with the highest score.

[0104] FIG. 3 illustrates a system 300 for performing methods for predicting physical and / or chemical property values ​​and / or designing molecules and / or training neural networks in accordance with the present invention.

[0105] System 300 includes at least one processor 340 coupled to at least one storage device 350 and may include or be a computing device, such as a personal computer or a mobile device. System 300, or portions of the system, may also be a distributed computing system, such as a cloud computing system.

[0106] The processor 340 of the system 300 may be, for example, a microprocessor, a central processing unit (CPU), an application specific integrated circuit (ASIC), a graphics processing unit (GPU), a tensor processing unit (TPU) or a field programmable gate array (FPGA). The storage device 350 used may be, for example, a random access memory (RAM), a hard drive (HD), a solid state drive (SSD), a flash memory, a compact disk (CD) or a digital versatile disc (DVD). The system may also include one or more display devices and one or more controllers, for example a keyboard, a computer mouse and / or a touch screen.

[0107] The system 300 is adapted to carry out the method for predicting physical and / or chemical property values ​​according to the invention, in which as input 310 there is provided, for example, by a human operator or by a databank 380, a molecular structure of a molecule in a computer readable form, for example a SMILES string. The input 310 is provided by the system 300 to organize the atoms of the molecular structure of the atom-bond-graph 100 and the bonds of the molecular structure into n nodes The system 300 may also be configured to directly receive (330) the atom-bond-graph 100 as an input 310. The system 300 may also be configured to provide predicted values ​​of the physical and / or chemical properties as output 320, preferably after performing a method for predicting physical and / or chemical property values ​​according to the present invention.

[0108] Alternatively, or in addition, the system 300 may also be configured to perform a method for automated design of molecules according to the invention, in which it may receive as input 300 a set of starting molecular structures comprising at least one molecular structure, e.g. as a SMILES string, provided, e.g., by a human operator or by a databank 380, a set of mutation rules for specifying allowed mutations for the genetic algorithm, a score function for the molecular structures based on one or more predicted values ​​of physical and / or chemical properties of the corresponding molecule, and a termination condition. The system 300 may also be configured to provide as output 320 molecular structures of molecules designed by the method.

[0109] Alternatively, or in addition, the system 300 may be configured to execute a method for training a neural network for use in the method according to the invention, in which case the system 300 is designed to receive as input 310 input training data comprising molecular structures of different molecules and physical and / or chemical property values ​​of said molecules, for example provided by a human operator or by a data bank 380.

[0110] As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items and may also be abbreviated as " / ".

[0111] Although some aspects have been described in the context of an apparatus, it will be apparent that such aspects also refer to a description of the corresponding method, where a block or apparatus corresponds to a method step or feature of a method step. Analogously, aspects described in the context of a method step also refer to a description of the corresponding block or item or feature of the apparatus.

Claims

1. A method for predicting the physical and / or chemical properties of a molecule using a computer, The above method uses the molecular structure of a molecule as input, as an atom-bond-graph that includes at least the atoms of the molecular structure and the bonds of the molecular structure as nodes. The method provides predicted values ​​of physical and / or chemical properties as output. a) A step of extracting a feature vector of dfeatures dimension for each of the nnodes nodes in the atom-bond-graph, b) A step of generating an nnodes × dfeatures dimension feature matrix composed of the extracted nnodes feature vectors, c) A step of calculating a squared distance matrix D of nnodes × nnodes dimensions based on and / or the distance between atoms and bonds in the molecular structure, d) The step of applying a trained neural network, which includes a transformer that uses the squared distance matrix D for self-attention decay of the feature matrix, to make predictions for the physical and / or chemical properties of the molecule, The feature vector includes a node type, the node type being one of atom, bond, and global, and if the node type is atom or bond, the feature vector includes additional data relating to the node. The aforementioned neural network is A trained input encoder that generates an input matrix of nnodes × dmodel dimensions from the nnodes × dfeatures dimension (where dmodel is the dimension of the transformer model), The transformer includes a trained transformer encoder stack having nlayers>1 which uses the squared distance matrix D for self-attention decay, and which uses the input matrix of the input encoder as input and generates a matrix of nnodes × dmodel dimensions as output. A trained projection layer including a self-attention layer configured to use a matrix generated by the aforementioned trained transformer-encoder stack as input and to generate a dmodel-dimensional vector as output, A method comprising: a trained multilayer perceptron configured to generate predictions of the physical and / or chemical characteristic values ​​from the output vectors of the trained projection layer.

2. The method according to claim 1, wherein each of the nlayers trained transformer-encoder layers includes a trained multihead reduction self-attention, a trained feedforward network, two trained layer normalizations, and two residual concatenations.

3. The method according to claim 1, wherein an additional input parameter is used as an additional input to the trained multilayer perceptron.

4. The method according to claim 1, wherein the physical and / or chemical properties are one of the following: HOMO (highest occupied molecular orbital) energy level, LUMO (lowest unoccupied molecular orbital) energy level, single-term energy level, triplet energy level, single-term-triplet energy gap, oscillator intensity, dipole moment, photoluminescence quantum yield, delayed fluorescence lifetime, and / or peak emission wavelength.

5. The method according to claim 1, wherein the squared distance matrix D is calculated using abstract distances derived from the atom-bond-graph.

6. The computer implementation method according to claim 1, wherein a portion of a trained neural network, for example, the transformer of the trained neural network, is initialized by other transformers of another trained neural network suitable for performing the method.

7. A method for automatically designing molecules, preferably organic light-emitting diodes (OLEDs), and especially emitter molecules for use in TADF (thermally activated delayed fluorescence) emitters, using a computer. The above method uses a genetic algorithm and takes as input, A set of initiation molecular structures containing at least one molecular structure, A set of mutation rules for specifying the mutations allowed in the aforementioned gene algorithm, A score function relating to molecular structure based on one or more predicted values ​​of the physical and / or chemical properties of the corresponding molecule, Termination conditions and, The above method provides the molecular structure of the designed molecule as output. The aforementioned method, a) A step of providing a set of starting molecular structures to the gene algorithm as the population of parent structures, b) Using the gene algorithm to mutate at least one member of the population, thereby generating a population of offspring molecular structures partially or completely from a population of parent structures; c) Using the method of claim 1, predict one or more values ​​of the physical and / or chemical properties of molecules corresponding to members of the population of progeny molecular structures, and based on these, calculate the value of a score function relating to each member of the population of progeny molecular structures; d) Check whether the termination condition is met, and if not, generate a new population of parent molecular structures composed of at least one member of the population of descendant molecular structures that has the optimal score function value among the descendant molecular structures, e) A step in which steps b), c), and d) are repeated until the termination condition is met, f) a step of selecting a molecular structure produced by step b) or a repetition of step b) as the output, One or more of the aforementioned physical and / or chemical properties are predicted using a neural network that employs transformers having self-attention decay related to molecular structure. A method for a neural network that uses the molecular structure as input to predict one or more values ​​of the physical and / or chemical properties of the members.

8. The termination condition is met if the score function relating to at least one member of the population of the descendant molecular structures is greater than, less than, or equal to a predefined value, and / or if the number of iterations of steps b), c), and d) reaches a predefined value. The method according to claim 7, which is added.

9. The method according to claim 7, wherein the mutations using the gene algorithm are fragment-based mutations and / or string-based mutations.

10. The method according to claim 7, wherein the gene algorithm uses tournament selection and / or elite selection.

11. A method for training a neural network used in the method described in claim 1, The above method uses a system including at least one processor and a storage device. The neural network includes a transformer configured to use a squared distance matrix D for attention decay, one or more projection layers including an attention layer configured to use the matrix generated by the transformer as input and generate a vector as output, and one or more multilayer perceptrons that use one of the outputs of the one or more projection layers as input. The aforementioned method, a) Providing a dataset including the molecular structure of the molecule and the physical and / or chemical property values ​​of the molecule assigned to one of the multilayer perceptrons; b) A step of converting the molecular structure of each molecule into an atom-bond-graph that includes at least the atoms of the molecular structure and the bonds of the molecular structure as nodes, c) A step of extracting a feature vector of dfeatures dimension for each of the nnodes nodes in the atom-bond-graph, d) A step of generating an nnodes × dfeatures-dimensional feature matrix composed of the extracted nnodes feature vectors, e) A step of calculating a squared distance matrix D of nnodes × nnodes dimensions based on and / or the distances between atoms and bonds in the molecular structure, f) A step of generating output values ​​for a multilayer perceptron assigned to the physical and / or chemical properties, g) A step of adjusting the neural network based on a comparison of the output value of the multilayer perceptron with the physical and / or chemical characteristic values ​​assigned to the multilayer perceptron, Includes, A learning method wherein the feature vector includes a node type, which is preferably one of atom, bond, and global, and the feature vector includes additional data relating to the node when the node type is atom or bond.

12. The neural network includes at least two multilayer perceptrons, Steps a) through g) are repeated for different datasets, including the molecular structure of the molecule and different physical and / or chemical properties. The learning method according to claim 11, wherein the different physical and / or chemical properties are assigned to different multilayer perceptrons.

13. The learning method according to claim 11, wherein steps a) through g) are repeated for different datasets, each containing molecular structures of different molecules and physical and / or chemical property values ​​of different molecules.

14. The learning method according to claim 11, wherein a portion of the neural network, for example, the transformer, is initialized using other transformers of another trained neural network suitable for use in the method of claim 1.

15. A system including a processor and a storage device, The system is configured to perform the method according to any one of claims 1 to 10 and / or the learning method according to any one of claims 11 to 14.

16. A computer program comprising program code that causes a system including a processor and a storage device to perform the method described in any one of claims 1 to 10.

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