DESC:FORM 2

THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003

COMPLETE SPECIFICATION
(See Section 10 and Rule 13)

Title of invention:
METHOD AND SYSTEM FOR MATERIAL PROPERTY PREDICTION USING ELEMENT SPECIFIC NEURAL NETWORKS

Applicant:
Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th Floor,
Nariman Point, Mumbai 400021,
Maharashtra, India

The following specification particularly describes the invention and the manner in which it is to be performed.
CROSS-REFERENCE TO RELATED APPLICATIONS AND PRIORITY
The present application claims priority from Indian provisional patent application no. 202221028956, filed on May 19, 2022. The entire contents of the aforementioned application are incorporated herein by reference.

TECHNICAL FIELD
The present invention generally relates to the field of material informatics and, more particularly, to method and system for material property prediction using element specific neural networks.

BACKGROUND
Low-cost computational power and explosive growth in the fields of deep learning (DL) and machine learning (ML) has driven the physical sciences community to develop prediction models for property predictions to screen out potential new materials for a number of applications such as battery catalysts, solar cells and so on. Data availability from public repositories such as Novel Materials Discovery (NOMAD), Materials Project, Automatic Flow (AFLOW), Open Quantum Materials Database (OQMD), Joint Automated Repository for Various Integrated Simulations (JARVIS) and so on also played a big role in the advancement of the field of material informatics by catering the need of training data required to develop ML and DL models. Most of the existing methods use only gross elemental descriptors, such as atomic size, electronegativity, melting point, and the like, to build predictive models to predict material properties such band gap, catalytic activity, thermal conductivity, formation enthalpies, free energies, melting temperatures, mechanical properties, and the like. However, these methods often neglect the crucial aspect of local crystal structure. Thus, ML models derived using features dependent on the gross elemental descriptors alone are less reliable. For instance, these models are unable to predict the changes in properties across different polymorphs of a material of any given composition. This severely limits the ability of these models to screen suitable materials from vast chemical and configurational spaces.
Recent developments in graph neural networks (GNN) allow ML models to exploit high level features of crystal structures, thereby performing better than traditional ML algorithms. However, the GNNs suffer from problem of high data requirement and over-smoothing which makes training process difficult. Another work Compositionally Restricted Attention-Based network (CrabNet) (disclosed in Wang et. al. 2021) learns inter-element interactions within a compound and uses these interactions to generate property predictions. However, this method is limited to training of compounds with 4 different elements and is difficult to extend to general multicomponent systems.
Often ML and DL models are black box, and it is challenging to interpret how the model has arrived at a decision. This could be major challenge in cases where domain knowledge is necessary for testing reliability of results or in cases of problem with data scarcity and data-driven models could not be trusted. Work by Kumar et al. devise interpretation from traditional ML models using SHapley Additive exPlanations (SHAP) values. There are few works which talk about the Explainable AI (Chen et al., 2018 & Yuan et al., 2021) for DL models. However, these works drive their interpretability from complex algorithms. Thus, the state of the art methods have challenges in reliability, interpretability, and extension to multiple elements, defects etc., in the crystal structure of a material.

SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one embodiment, a method for material property prediction using element specific neural networks is provided. The method includes receiving training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio. Further the method includes extracting a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Furthermore, the method includes training one or more models based on each of the one or more properties and the extracted features. Each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials. Each of the one or more models are trained to predict a specific property among the one or more properties.
In another aspect, a system for material property prediction using element specific neural networks is provided. The system includes: a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to: receive training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio. Further the one or more hardware processors are configured to extract a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Furthermore, the one or more hardware processors are configured to train one or more models based on each of the one or more properties and the extracted features. Each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials. Each of the one or more models are trained to predict a specific property among the one or more properties.
In yet another aspect, there are provided one or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause a method for material property prediction using element specific neural networks. The method includes receiving training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio. Further the method includes extracting a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Furthermore, the method includes training one or more models based on each of the one or more properties and the extracted features. Each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials. Each of the one or more models are trained to predict a specific property among the one or more properties.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 illustrates an exemplary block diagram of a system for material property prediction using element specific neural networks, according to some embodiments of the present disclosure.
FIG. 2 is a flow diagram illustrating a method for material property prediction using element specific neural networks, according to some embodiments of the present disclosure.
FIG. 3 illustrates an example of material property prediction using element specific neural networks, according to some embodiments of the present disclosure.
FIG. 4 illustrates element counts in a training dataset for training of a model to predict band gap property, according to some embodiments of the present disclosure.
FIG. 5 illustrates train and test Mean Absolute Error (MAE) upon training the model against all materials with a finite bandgap, according to some embodiments of the present disclosure.
FIG. 6 illustrates train and test Mean Absolute Error (MAE) upon training the model against all materials having bandgap>=0.5eV, according to some embodiments of the present disclosure.
FIG. 7 illustrates train and test Binary Cross Entropy (BCE) as a function of number of training epochs, according to some embodiments of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments.
Predicting property of materials is important to identify the materials suitable for applications such as battery catalysts, solar cells and so on. Existing methods have challenges in reliability, interpretability, and extension to multiple elements. Thus, embodiments of present disclosure provide a method and system for material property prediction using element specific properties. Initially, a training dataset comprising a plurality of materials and their corresponding properties is received by the system. The plurality of materials are made up of one or more elements in a definite ratio. Further, a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials are extracted. The plurality of features comprise elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Once the features are extracted, one or more models are trained based on each of the one or more properties and the extracted features. Each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials and are trained to predict a specific property among the one or more properties. Thus, both compositional and structural features of the materials are inherently built into the neural networks.
In order to predict a property of a given material, firstly elements comprised in the material are identified, model trained to predict the property is identified and element specific neural networks corresponding to the identified elements are obtained. Further, a plurality of features of each atom among one or more atoms corresponding to one or more elements present in the material are extracted. The plurality of features comprise elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Once the features are extracted, contribution of each atom of the identified elements in the material is estimated using the element specific neural networks and the property of the material is predicted based on contribution from each atom. Due to this, the method of present disclosure can straightaway be applied to different polymorphs of a given material. Also, the disclosed method is able to predict the properties of the material even in the presence of defects such as dopants and vacancies in the materials. Thus, the method is highly reliable. Also, there is no restriction on the maximum number of atoms (elements) in a crystal structure of any given material for property prediction, i.e., method of present disclosure is independent of size of the material. Further, inputs to individual neural networks can be of different dimensions and therefore feature vector of the material need not be normalized to a fixed dimension unlike the existing methods. Such generality allows screening of materials from a vast chemical and configurational space, beyond what simple composition-based ML models are capable of. Thus, the method of present disclosure can be easily extended to materials having multiple elements. Further, since the property of a material is obtained as a sum of contributions from atoms comprising the material, variation in the property upon changing the element type, inclusion of dopants, creation of defects etc. can be directly quantified. Thus, the method of present disclosure provides interpretability.
Referring now to the drawings, and more particularly to FIGS. 1 to 7, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 illustrates an exemplary block diagram for material property prediction using element specific properties. In an embodiment, the system 100 includes one or more processors 104, communication interface device(s) 106 or Input/Output (I/O) interface(s) 106 or user interface 106, and one or more data storage devices or memory 102 operatively coupled to the one or more processors 104. The memory 102 comprises a database 108. The one or more processors 104 that are hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) is configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the system 100 can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices, workstations, mainframe computers, servers, a network cloud, and the like.
The I/O interface device(s) 106 can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the I/O interface device(s) 106 receives a material as input and gives property of the material as output.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. The database 108 may store information but not limited to information associated with at least one of: training dataset, one or more trained element specific neural networks and so on. Further, the database 108 stores information pertaining to inputs fed to the system 100 and/or outputs generated by the system (e.g., at each stage), specific to the methodology described herein. Functions of the components of system 100 are explained in conjunction with flow diagram depicted in FIG. 2 and example illustrated in FIG. 3 for material property prediction using element specific properties. The method illustrated in FIG. 2 is further explained using a use case example and results illustrated in FIGS. 4 to 7.
In an embodiment, the system 100 comprises one or more data storage devices or the memory 102 operatively coupled to the processor(s) 104 and is configured to store instructions for execution of steps of the method (200) depicted in FIG. 2 by the processor(s) or one or more hardware processors 104. The steps of the method of the present disclosure will now be explained with reference to the components or blocks of the system 100 as depicted in FIG. 1, the steps of flow diagram as depicted in FIG. 2 and an example illustrated in FIG. 3. Although process steps, method steps, techniques or the like may be described in a sequential order, such processes, methods, and techniques may be configured to work in alternate orders. In other words, any sequence or order of steps that may be described does not necessarily indicate a requirement that the steps to be performed in that order. The steps of processes described herein may be performed in any order practical. Further, some steps may be performed simultaneously.
FIG. 2 is a flow diagram illustrating a method 200 for material property prediction using element specific properties, according to some embodiments of the present disclosure. At step 202 of the method 200, the one or more hardware processors 104 are configured to receive training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio. Once the training data is received, at step 204 of the method 200, the one or more hardware processors 104 are configured to extract a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials. The plurality of features comprise elemental properties of the one or more elements present in each of the materials (for example, atomic size, electronegativity, melting point, boiling point etc.) and location specific properties describing local structure and chemistry around each atom of the one or more elements present in each of the materials (for example, bond-orientational order parameters, local property difference, coordination number etc.). As understood by a person skilled in the art, the features can be extracted using techniques known in the art, for example, using a python library called Matminer.
Once the features are extracted, at step 206 of the method 200, the one or more hardware processors 104 are configured to train one or more models based on each of the one or more properties and the extracted features. Each of the one or more models are trained to predict a specific property among the one or more properties and comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials. The training of each of the one or more models is carried out by a combination of forward propagation process and backward propagation process for a plurality of training epochs. The forward propagation process loops over all the materials in the training dataset to train the model by calculating the property using existing weights of the element specific neural networks of the model. The backward propagation process loops over all the elements in the training dataset to update the weights of element specific neural networks. In the forward propagation process, initially number of elements (n_elements) and number of atoms (n_sites) corresponding to the one or more elements in each of the plurality of materials are identified. Next, weights (W) of element specific neural networks corresponding to each of the one or more elements are obtained and feed forward process is performed through one or more hidden layers for each of the element specific neural networks based on the extracted features to compute the contribution of each of the element in the material. As understood by a person skilled in the art, each of the element specific neural networks comprise an input layer, one or more hidden layers and an output layer. Equations 1 to 5 correspond to the forward propagation for element specific neural network of an element ‘k’. Equations 1 and 2 correspond to first hidden layer. Similarly, equations 3 and 4 correspond to jth hidden layer and equation 5 governs the output layer. In the equations 1 to 4, X is the feature matrix comprising the extracted features for element k, W_k^1 is the weight of 1st layer of the element specific neural network of element ‘k’, Z_k^1 is unactivated output of 1st layer of the element specific neural network of element ‘k’, A_k^1 is activation values in the 1st layer of the element specific neural network of element ‘k’, ?Activation_1?_k () is activation function of the 1st layer of the element specific neural network of element ‘k’, W_k^j is the weight of jth layer of the element specific neural network of element ‘k’, Z_k^j is unactivated output of jth layer of the element specific neural network of element ‘k’, A_k^(j-1) is activation value in (j-1)th layer of the element specific neural network of element ‘k’, ?Activation_j?_k () is activation function of jth layer of the element specific neural network of element ‘k’, and A_k^j is activation values in layer j of the element specific neural network of element ‘k’. In equation 5, A_k^n is activation values in nth hidden layer of the element specific neural network of element ‘k’, W_k^(n+1) is weight of (n+1)th layer of the element specific neural network of element ‘k’, and Y_k is output of the element specific neural network of element ‘k’.
Z_k^1=X×W_k^1 ..... (1)
A_k^1=??Activation_1?_k (Z?_k^1) .....(2)
Z_k^j=A_k^(j-1)×W_k^j .....(3)
A_k^j=??Activation_j?_k (Z?_k^j) .....(4)
Y_k=A_k^n×W_k^(n+1) .....(5)
Once the feed forward process is completed, contribution of element ‘k’ to the property is then obtained as the reduced sum of Y_k according to equation 6.
y_k= reduced_sum(Y_k) .....(6)
Once the contribution of each element is computed, the property is calculated as- (a) sum of contribution of each of the elements or (b) a function of sum of contribution of each of the elements. For example, the function can be linear or non-linear such as ReLU, sigmoid etc. In an embodiment, the property is computed according to equation 7 wherein the property is computed as a function of sum of contribution of each element in the material. In equation 7, Y ¯_i is the computed property of ith material in the training dataset, Activation_(n+1) is a function which can be linear or non-linear and the term within bracket of Activation_(n+1) function denotes contribution of all elements in the ith material. Once the property is computed, a cost of the model is calculated by one of- (a) a plurality of metrics comprising mean absolute error, root mean square error when the model is trained for a regression task or (b) a binary cross entropy loss when the model is trained for a classification task. Equations 8 and 9 provide an example cost calculation for regression task and classification task respectively, wherein m is number of materials in the training dataset, Y ¯_i is the computed property (property predicted by the model during training) of ith material in the training dataset and Y_i^true is the actual or true value of the property of ith material mentioned in the training dataset.
Y ¯_i= Activation_(n+1) ((?_k^(n_elements)¦y_k )/n_sites )= Activation_(n+1) (Z_i^(n+1)) .....(7)
Where Z_i^(n+1)=((?_k^(n_elements)¦y_k )/n_sites )
Cost= 1/2m* ?_(i=1)^m¦[Y ¯_i- Y_i^true ]^2 .....(8)
Cost= -1/m* ?_(i=1)^m¦? [ Y_i^true log?(Y ¯_i )+ (1-Y_i^true)log?(1-Y ¯_i ) ] ? .....(9)
Once the forward propagation process is completed, backward propagation is performed to update the weights of the element specific neural networks. In the backward propagation process, initially derivative of the calculated cost with respect to the weights of each of the element specific neural networks is computed using chain rule of differentiation and the weights of each of the element specific neural networks are updated based on the calculated derivative. The equations 10-27 govern backward propagation process for updating the weight of element specific neural network for a representative element ‘a’. After the training epoch ‘t’, update to the jth layer weight of element a’s element specific neural network is given by equation 10, wherein LR is learning rate.
W_(a(t+1))^j= W_(a(t))^j-LR* ?Cost/(?W_(a(t))^j ) .....(10)
For the last layer in the element specific neural network (i.e., (n+1)th weight), the partial derivative in the equation 10 (i.e., ?Cost/(??W?_a^(n+1) )) can be computed according to equation 11. Similarly for the last but one layer, (i.e. the nth weight), the partial derivative can be computed using chain rule according to equations 12 to 14.
?Cost/(??W?_a^(n+1) )=?Cost/(?y_a )×(?y_a)/(??W?_a^(n+1) ) = ?Cost/(?y_a )×A_a^n = D_a^(n+1)×A_a^n .....(11)
where (?y_a)/(??W?_a^(n+1) )=A_a^n is the vector of activation values in the nth layer of the element specific neural network and ?Cost/(?y_a )=D_a^(n+1).
?Cost/(??W?_a^n )=?Cost/(?y_a )×(?y_a)/(??A?_a^n )×(?A_a^n)/(?Z_a^n )×(?Z_a^n)/(??W?_a^n ) .....(12) where (?Y_a)/(??A?_a^n )=W_a^(n+1), (?A_a^n)/(?Z_a^n )=??A?_a^n, (?Z_a^n)/(??W?_a^n )=A_a^(n-1)
?Cost/(??W?_a^n )=D_a^(n+1)×W_a^(n+1)×??A?_a^n×A_a^(n-1) ......(13)
?Cost/(??W?_a^n )=D_a^n×A_a^(n-1) .....(14) where D_a^n=D_a^(n+1)×W_a^(n+1)×??A?_a^n
In general, for the jth layer weight, the partial derivative is given by equation 15. The derivative with respect to the first layer weight is given by equation 16. Thus, once D_a^(n+1)=?Cost/(?y_a ) is evaluated, the values of every other derivative can be computed using this value and the activation values for each layer obtained during the forward propagation step.
?Cost/(??W?_a^j )=D_a^j×A_a^(j-1) .....(15) where, D_a^j=D_a^(j+1)×W_a^(j+1)×??A?_a^j
?Cost/(??W?_a^1 )=D_a^1×A_a^0=D_a^1×X .....(16)
The partial derivative of cost function with respect to elemental contribution from an element ‘a’ for material ‘i’ can be written via chain rule as equation 17. The terms in the equation 17 can be further expanded according to equations 18 to 22.
?Cost/(?y_a^i )=?Cost/(?Y ¯_i )* (?Y ¯_i)/(?Z_i^(n+1) )* (?Z_i^(n+1))/(?y_a^i ) .....(17)
In an embodiment, the model is trained for regression task wherein the first term (i.e. ?Cost/(?Y ¯_i )) is expanded according to equations 18 and 19.
?Cost/(?Y ¯_i )= 1/2m*(??_(i=1)^m¦[Y ¯_i- Y_i^true ]^2 )/(?Y ¯_i ) .....(18)
?Cost/(?Y ¯_i )= 1/m*[Y ¯_i- Y_i^true ] .....(19)
In another embodiment, the model is trained for classification task wherein the first term is expanded according to equation 20.
?Cost/(?Y ¯_i )= -[(Y_i^true)/Y ¯_i - ((1-Y_i^true))/((1-Y ¯_i))] .....(20)
The second term (i.e. (?Y ¯_i)/(?Z_i^(n+1) )) is expanded according to equation 21 and the third term (i.e. (?Z_i^(n+1))/(?y_a^i )) is expanded according to equation 22.
(?Y ¯_i)/(?Z_i^(n+1) )= (?A_i^(n+1))/(?Z_i^(n+1) )= ?A_i^(n+1) .....(21)
(?Z_i^(n+1))/(?y_a^i )=?((?_(k=1)^(n_elements^i)¦y_k^i )/(n_sites^i ))/(?y_a^i ) .....(22)
If the derivative of the Z_i^(n+1) with respect to y_a^i is the same for all sites containing atom ‘a’ in material ‘i’ and total number of sites containing atom ‘a’ is n_a^i, then, equation 22 can be written as equation 23.
(?Z_i^(n+1))/(?y_a^i )=[¦(1/(n_sites^i )@¦(1/(n_sites^i )@?))]_((n_a^i,1))......(23)
Hence, the equation 17 is expanded according to equations 24 and 25 when the model is trained for regression task in an embodiment and equation 26 when the model is trained for classification task in another embodiment.
?Cost/(?y_a^i )= 1/m*[Y ¯_i- Y_i^true ]*?A_i^(n+1)*[¦(1/(n_sites^i )@¦(1/(n_sites^i )@?))]_((n_a^i,1)) .....(24)
?Cost/(?y_a^i )= [¦(1/(n_sites^i*m)*[Y ¯_i- Y_i^true ]*?A_i^(n+1)@¦(1/(n_sites^i*m)*[Y ¯_i- Y_i^true ]*?A_i^(n+1)@?))]_((n_a^i,1)) .....(25)
?Cost/(?y_a^i )= [¦((-1)/(n_sites^i*m)*[(Y_i^true)/Y ¯_i - ((1-Y_i^true))/((1-Y ¯_i))]*?A_i^(n+1)@¦((-1)/(n_sites^i*m)*[(Y_i^true)/Y ¯_i - ((1-Y_i^true))/((1-Y ¯_i))]*?A_i^(n+1)@?))]_((n_a^i,1)) ......(26)
The derivative of the cost with respect to element ‘a’ from all materials can then be stacked as a vector as represented by equation 27. This value is then used to compute the derivatives of the cost function with respect to the weights for all layers using the equations 11-16. The training of the one or more models is carried out over a plurality of training epochs till a convergence is reached.
?Cost/(?y_a )=[¦(?Cost/(?y_a^1 )@?Cost/(?y_a^2 )@?)]_((m,1)) ......(27)
Once the training of the one or more models is completed, they can be used for predicting property of a material. First, one or more elements comprised in the material are identified, model trained to predict the property is identified from among the one or more trained models and element specific neural networks corresponding to the identified elements are selected from the identified model. Further, a plurality of features of each atom among one or more atoms corresponding to the one or more elements present in the material are extracted using techniques known in the art (for example, using Matminer library). The plurality of features comprise elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements. Once the features are extracted, contribution of each atom among the one or more atoms corresponding to the one or more elements present in the material are calculated using the selected element specific neural networks of the model. Further, the property of the material is predicted based on contribution from each atom. In an embodiment, the property can be predicted as sum of contribution of each atoms. In another embodiments, the property can be predicted as a function of sum of contribution of each atoms.
FIG. 3 illustrates an example of material property prediction using element specific neural networks for Fe2O3 material, according to some embodiments of the present disclosure. FIG. 3 considers element specific neural networks with 1 hidden layer and a feature vector of size 3 for each atom in the material. Since there are 2 Fe (Iron) and 3 O (Oxygen) sites in the material, contribution of Fe atoms (yFe¬) to the property is obtained as a sum of a 2 dimensional vector while contribution of O atoms (yO) to the property is obtained as a sum of a three dimensional vector. The property of Fe2O3 material is calculated as sum of contribution of Fe and O atoms normalized by the number of atoms in the material (i.e. 5). It is evident from this example that there is no need to provide a fixed dimensional input for the model trained by method 200 to predict material property unlike most of the state of the art methods. Thus, the trained models can be used to predict property any material irrespective of number of elements in the material or number of atoms in the material.
USE CASE EXAMPLE:
As a use case example, the method 200 is used to train the models for inorganic oxides (materials). The trained models are further used to screen materials for photocatalytic water splitting. At the step 202, the training dataset was obtained from Materials Project (MP), an open materials database. The training data consisted of crystal structures of various oxides, their band gaps (Egap) and energy above hull (e_above_hull) values. For a material to qualify as a photocatalyst, it must possess a finite bandgap and be thermodynamically stable. Feature matrix for each material was then constructed at step 204 by computing a feature vector for each atomic site in the material using the Matminer open-source python package. These features included 30 Bond-Orientational order parameters, 10 Generalized radial distribution functions, 17 local property difference values and a coordination number for each site. Thus, each atomic site was represented by a total of 58 features. The feature matrix for each material had a dimension of [nsites, 58], where nsites is the number of atom sites in the material and it varies for different materials. Once the features are extracted and feature matrix is constructed, two models were trained at step 206 of the method 200. One model was trained to predict the Egap value and the other one was trained to predict the e_above_hull value.
For a material to be a potentially good photocatalyst for water splitting, it must be stable (e_above_hull <= 0.15eV) and have a bandgap in the range of 1.6 eV to 3 eV to absorb maximum amount of solar radiation. Apart from band gap and stability, the energies of the conduction band edges (CB), and valence band edges (VB) should also be in appropriate ranges. Equations 28-30 were used to compute band edge positions.
E_CB^0=?(X) - E_e-?1/2 E?_gap .....(28)
E_VB^0=?(X) - E_e+1/2 E_gap .....(29)
?(X) = v(N&X_1^a X_2^b X_3^c....X_n^q ) .....(30)
where ECB0 and EVB0 are the conduction and valence band edge energies, Egap and Ee are the band gap of material and absolute electrode potential of the standard hydrogen electrode, X and ?(X) are the electronegativity of the constituent elements in the material and geometric mean of the electronegativities of the elements in the material. Specifically, the VB should lie above 1.23 eV and CB should lie below 0 eV on the standard hydrogen electrode scale.
RESULTS:
Analysis of the oxide materials data obtained from the MP database revealed that 15726 materials had a non-zero bandgap, formed from 53 different elements. Since the model relies on the development of element specific neural networks, it is essential that each element is represented in a sufficient number of materials to minimize any bias in the model that may be introduced due to lack of data. Accordingly, only materials containing those elements that were represented in at least 500 different materials was considered for training. This reduced the total number of datapoints to 10,409 oxides formed from 30 different elements. A distribution of the number of different materials in which each of these 30 elements were present is shown in FIG. 4.
The training dataset was divided into train and test data in 80:20 ratio. The model hyperparameters considered are shown in table 1 for all training tasks. The element specific neural networks consisted of 3 hidden layers. The training was performed for 500 training epochs. FIG 5 illustrates the plot of train mean absolute error (MAE) and test mean absolute error with the number of epochs. The minimum test MAE was found to be 0.52 eV. Since the criteria for selection of new material for photocatalytic application is between 1.6 to 3 eV, another model was trained on materials that had a band gap >= 0.5. This dataset consisted of 7,261 materials formed from 26 different elements. FIG 6 shows the plot of train MAE and test MAE with number of epochs. For this task, minimum test MAE was 0.44 eV.
Table 1: Hyperparameters for training
Hyperparameter Value
Number of training epochs 500
Number of hidden layers 3
n_hidden_layer1 64
n_hidden_layer2 32
n_hidden_layer3 16
n_output_layer 1
Learning rate 0.001
beta2 0.9
epsilon 1e-8
Activation for hidden layers tanH
Optimizer RMSProp

The models were trained against all materials that contained one or more of the 30 elements identified in FIG 4, irrespective of their Egap values. Thus, the total dataset contained 19,397 different materials. Train to test split was 80:20. For classificastion, e_above_hull <=0.15 eV was chosen as criteria for stability. FIG 7 shows the train and test binary cross entropy (bce) as a function of the number of training epochs. The best value of test binary cross entropy (test_bce) obtained was 0.27. The test accuracy obtained was 90%, with precision, recall and f1-score values 90%, 98% and 94% respectively.
The trained models were used to screen materials for photocatalytic water splitting from a large chemical and configurational space which was in silico constructed by systematically replacing cations in the materials from MP dataset to ensure that newly constructed material was charge neutral. For example, consider CaTiO3 material in the MP dataset, the cation Ca2+ is replaced by Ba2+ to construct BaTiO3 material. Similarly, CaSnO3 is constructed from CaTiO3 by replacing Ti4+ with Sn4+. A dictionary of commonly known oxidation states for all the cations was prepared apriori so that permissible cationic substitutions can be identified. Then the classification model trained with e_above_hull values was used to predict the probability of e_above_hull <=0.15 of the newly generated materials. Materials having 90% probability of e_above_hull <=0.15 eV were shortlisted. Further, the Egap value of the shortlisted materials was predicted using the model trained to predict the Egap and the materials having Egap >=0.5 were selected. Further, a more accurate Egap was predicted for the selected materials using a model trained (by method 200) against those materials with Egap >= 0.5eV and the materials having predcited Egap value in the range of 1.6eV to 3.0eV were shortlisted. CB and VB edge positions of the shortlisted materials were computed using the equations 28-30 and materials with CB <= 0eV and VB >= 1.23 eV were selected as final list of materials. The top 10 materials from the final list of materials that has the highest probabitlty of being stable were selected for photocatalytic water splitting. Table 2 lists the top 10 shortlisted ternary oxides that are potentially good photocatalysts for water splitting.
Table 2
formula space_group Ehull Gapall
(eV) pgap05
(eV) X
(eV) VBE
(eV) CBE
(eV) ref
SrZnO2 121 1.0 3.5 2.9 4.7 1.8 -1.1 mp-752844
Ba2VO3 36 1.0 3.1 2.3 4.6 1.3 -1.0 mp-4533
Sr2MoO4 70 1.0 2.8 2.0 4.7 1.3 -0.7 mp-18800
Na3MoO4 7 1.0 3.0 2.9 4.8 1.9 -1.0 mp-6391
SrCrO3 21 1.0 3.2 2.1 5.0 1.7 -0.4 mp-1222469
Na3VO4 7 1.0 3.1 2.8 4.8 1.8 -1.0 mp-6391
BaV2O4 159 1.0 3.3 2.8 5.2 2.2 -0.6 mp-9480
Na3MnO4 31 1.0 0.8 1.9 4.8 1.3 -0.5 mp-755436
Na3TaO4 121 1.0 2.6 2.1 4.9 1.5 -0.6 mp-752844
SrZn2O3 4 1.0 2.1 3.0 5.1 2.2 -0.8 mp-5012

The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g., any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g., hardware means like e.g., an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g., an ASIC and an FPGA, or at least one microprocessor and at least one memory with software processing components located therein. Thus, the means can include both hardware means, and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g., using a plurality of CPUs.
The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various components described herein may be implemented in other components or combinations of other components. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
It is intended that the disclosure and examples be considered as exemplary only, with a true scope of disclosed embodiments being indicated by the following claims.

,CLAIMS:1. A processor implemented method (200) for material property prediction, the method comprising:
receiving (202), via one or more hardware processors, training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio;
extracting (204), via the one or more hardware processors, a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements; and
training (206), via the one or more hardware processors, one or more models based on each of the one or more properties and the extracted features, wherein each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials, and wherein each of the one or more models are trained to predict a specific property among the one or more properties.

2. The method as claimed in claim 1, comprising predicting a property of a material using a model, from among the one or more models, trained to predict the property by:
extracting, via the one or more hardware processors, a plurality of features of each atom among one or more atoms corresponding to one or more elements present in the material, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements;
estimating, via the one or more hardware processors, contribution of each atom among the one or more atoms corresponding to one or more elements present in the material using an element specific neural network of element corresponding to the atom from among the plurality of element specific neural networks of the model; and
predicting, via the one or more hardware processors, the property of the material based on contribution from each atom.

3. The method as claimed in claim 1, wherein the training of each of the one or more models is carried out by a combination of forward propagation process and backward propagation process for a plurality of training epochs.

4. The method as claimed in claim 3, wherein the forward propagation process of training a model among the one or more models comprises:
identifying number of elements and number of atoms corresponding to the one or more elements in each of the plurality of materials;
obtaining weights of element specific neural networks corresponding to each of the one or more elements;
performing feed forward process through one or more hidden layers of each of the element specific neural networks based on the extracted features to compute the contribution of each of the element in the material;
computing the property as (a) sum of contribution of each of the elements or (b) a function of sum of contribution of each of the elements; and
calculating a cost of the model.

5. The method as claimed in claim 4, wherein the backward propagation process comprises:
computing derivative of the calculated cost with respect to the weights of each of the element specific neural networks; and
updating the weights of each of the element specific neural networks based on the calculated derivative.

6. The method as claimed in claim 4, wherein the cost of the model is calculated by one of (a) a plurality of metrics comprising mean absolute error, root mean square error when the model is trained for regression task, and (b) a binary cross entropy loss when the model is trained for classification task.

7. A system (100) for material property prediction, the system comprising:
a memory (102) storing instructions;
one or more communication interfaces (106); and
one or more hardware processors (104) coupled to the memory (102) via the one or more communication interfaces (106), wherein the one or more hardware processors (104) are configured by the instructions to:
receive training data comprising a plurality of materials and one or more properties of each of the plurality of materials, wherein each of the plurality of materials comprise one or more elements in a definite ratio;
extract a plurality of features of one or more atoms corresponding to the one or more elements of each of the plurality of materials, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements; and
train one or more models based on each of the one or more properties and the extracted features, wherein each of the one or more models comprise a plurality of element specific neural networks corresponding to each element among the one or more elements of each of the plurality of materials, and wherein each of the one or more models are trained to predict a specific property among the one or more properties.

8. The system of claim 7, wherein the one or more hardware processors are configured to predict a property of a material using a model, from among the one or more models, trained to predict the property by:
extracting a plurality of features of each atom among one or more atoms corresponding to one or more elements present in the material, the plurality of features comprising elemental properties of the one or more elements and location specific properties describing local structure and chemistry around each atom of the one or more elements;
estimating contribution of each atom among the one or more atoms corresponding to one or more elements present in the material using an element specific neural network of element corresponding to the atom from among the plurality of element specific neural networks of the model; and
predicting the property of the material based on contribution from each atom.

9. The system of claim 7, wherein the training of each of the one or more models is carried out by a combination of forward propagation process and backward propagation process for a plurality of training epochs.

10. The system of claim 9, wherein the forward propagation process of training a model among the one or more models comprises:
identifying number of elements and number of atoms corresponding to the one or more elements in each of the plurality of materials;
obtaining weights of element specific neural networks corresponding to each of the one or more elements;
performing feed forward process through one or more hidden layers of each of the element specific neural networks based on the extracted features to compute the contribution of each of the element in the material;
computing the property as (a) sum of contribution of each of the elements or (b) a function of sum of contribution of each of the elements; and
calculating a cost of the model.

11. The system of claim 10, wherein the backward propagation process comprises:
computing derivative of the calculated cost with respect to the weights of each of the element specific neural networks; and
updating the weights of each of the element specific neural networks based on the calculated derivative.

12. The system of claim 10, wherein the cost of the model is calculated by one of-(a) a plurality of metrics comprising mean absolute error, root mean square error when the model is trained for regression task and (b) a binary cross entropy loss when the model is trained for classification task.