Overview of services that model the properties and structure of materials using GNNs to design new materials and predict their properties.
OBJECTIVE:
The service for designing new materials and predicting their properties using Graph Neural Networks (GNNs) will be aimed at increasing research and development efficiency, reducing costs and rapidly discovering new high-performance materials in the field of materials science. It functions by modelling the properties and structure of materials using GNNs to assist in the design of new materials and the prediction of their properties.
Role of GNNs:
GNNs model the atomic structure of a material as a graph, representing each atom as a node and the bonds between atoms as edges, and learn this graph structure to predict material properties (e.g. mechanical, thermal and electrical properties).
Main features of the service:
1. material data collection and pre-processing
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- Data collection: collection of atomic structure and property data of materials from public databases (e.g. Materials Project, OQMD, AFLOW) and in-house company databases.
- Data pre-processing: convert the collected data into a graph structure and calculate node features (e.g. atomic type, electronegativity, atomic radius) and edge features (e.g. bond length, bond strength).
2. construction and training of GNN models:
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- Model building: models are built using GNN architectures such as Graph Convolutional Network (GCN), Graph Attention Network (GAT) and Message Passing Neural Network (MPNN), which are described below.
- Model training: train GNN models using collected data to learn material properties.
3. designing new materials and predicting their properties:
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- Material design: design new material candidates using GNN models and generate their structures.
- Property prediction: predict the properties of designed materials using GNN models and select high performance materials.
4. optimisation and simulation:
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- Optimisation algorithms: optimise the structure and properties of new materials using reinforcement learning and Bayesian optimisation.
- Simulation: validation of predicted results using molecular dynamics simulation and first-principles calculations.
Added value of services:
- Accelerated research and development: automated prediction of material properties and design significantly shortens the research and development cycle.
- Reduced costs: reduce the number of experiments and simulations, thereby reducing costs.
- Discover new materials: rapidly discover new, high-performance materials and increase market competitiveness.
Example implementations:
The following is a simple Python code example for predicting material properties using GNN.
Data preparation: material data is prepared as a graph structure.
import torch
from torch_geometric.data import Data
# Characteristics of the node (e.g. properties of each atom)
node_features = torch.tensor([
[1.0, 2.0], # Features of Atom 1
[2.0, 3.0], # Features of Atom 2
[3.0, 4.0], # Features of Atom 3
], dtype=torch.float)
# Edge lists (e.g. bonds between atoms)
edge_index = torch.tensor([
[0, 1, 2, 0],
[1, 0, 0, 2]
], dtype=torch.long)
# Creation of graphical data
data = Data(x=node_features, edge_index=edge_index)Model definition: define a model using a Graph Convolutional Network (GCN).
import torch.nn.functional as F
from torch_geometric.nn import GCNConv
class GCN(torch.nn.Module):
def __init__(self):
super(GCN, self).__init__()
self.conv1 = GCNConv(in_channels=2, out_channels=16)
self.conv2 = GCNConv(in_channels=16, out_channels=8)
self.fc = torch.nn.Linear(8, 1) # Linear layer for property prediction.
def forward(self, data):
x, edge_index = data.x, data.edge_index
x = self.conv1(x, edge_index)
x = F.relu(x)
x = self.conv2(x, edge_index)
x = F.relu(x)
x = torch.mean(x, dim=0) # Aggregate features across the graph.
x = self.fc(x)
return x
model = GCN()Training loop: train the model.
import torch.optim as optim
# Dummy target value (e.g. characteristic value)
targets = torch.tensor([5.0], dtype=torch.float)
# Loss functions and optimisation
criterion = torch.nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)
# training loop
model.train()
for epoch in range(200):
optimizer.zero_grad()
out = model(data)
loss = criterion(out, targets)
loss.backward()
optimizer.step()
if epoch % 10 == 0:
print(f'Epoch {epoch}, Loss: {loss.item()}')Prediction and optimisation: after training, the model is used to predict the properties of the new material.
model.eval()
with torch.no_grad():
predicted_value = model(data)
print(f'Predicted Property Value: {predicted_value.item()}')Service implementation process:
- Needs analysis: analyse the client’s specific needs in material design.
- Data collection and preparation: collect the required material data and transform them into a graphical structure.
- Model building and training: GNN models are built and trained on the collected data.
- Prediction and optimisation: design new materials, predict their properties and optimise them.
- Validation and implementation: validate the predicted results by simulation and experiment and put them into practical use.
Expected results:
- Rapid discovery of new materials: rapid design and property prediction of high-performance materials, reducing time to market.
- Reduced R&D costs: reduce R&D costs through efficient material design and property prediction.
- Enhanced competitiveness: to be the first to bring innovative materials to market and enhance competitiveness.
Algorithms related to services that model the properties and structure of materials using GNNs to design new materials and predict their properties.
The following section describes the main algorithms associated with services that use GNNs to model the properties and structure of materials and to design new materials and predict their properties. These algorithms are used to represent the atomic structure data of materials as graphs for property prediction and new material design.
1. graph convolutional network (GCN: Graph Convolutional Network):
Abstract: GCNs learn the features of each node in a graph by combining the features of neighbouring nodes. In materials science, each atom is modelled as a node and the bonds between atoms as edges; for more information on GCNs, see Graph Convolutional Neural Networks (GCN): overview, algorithms and implementation examples.
Applications: prediction of material properties (e.g. mechanical, thermal, electrical, etc.).
2 Message Passing Neural Networks (MPNN):
Abstract: MPNNs are a method of receiving messages from neighbouring nodes in order to update the features of a node. Messages are conveyed and aggregated through edges. For more information on message passing, see also “Message passing in machine learning: overview, algorithms and implementation examples“.
Applications: energy prediction of molecular structures, prediction of chemical reactions, stability assessment of materials, etc.
3. graph attention network (GAT):
Abstract: GAT introduces an attention mechanism at each node to its neighbours, highlighting information at important nodes. In materials science, this can be useful to highlight the influence of specific atomic bonds on properties; for more information on GAT, see GAT (Graph Attention Network): Overview, Algorithm and Example Implementation.
Application: prediction of mechanical properties of materials, identification of critical bonds.
4 Graph Autoencoder:
Abstract: Graph autoencoders learn about the latent space by compressing and reconstructing node features. It captures hidden patterns in the latent structure and properties of materials. For more information on graph autoencoders, see “Overview of encoder/decoder models, algorithms and implementation examples in GNNs“.
Application: anomaly detection in materials, search for latent structures.
5 Graph Generation Models
Abstract: Graph generation models are models that generate new graph structures, applying VAE (Variational Autoencoder) described in “Variational Autoencoder (VAE) Overview, Algorithm and Example Implementation and GAN (Generative Adversarial Network) to generate the atomic structure of a new material.” See also “Overview of Variational Graph Auto-Encoders (VGAE) and examples of algorithms and implementations“.
Application: design of new materials, search for unknown material structures.
6. dynamic graph neural networks (Dynamic GNN):
Abstract: Dynamic GNNs model graph structures that change over time and are useful when material processes and reaction pathways change over time; for more information on D-GNNs, see Dynamic Graph Neural Networks (D-GNN) Overview, Algorithms and Examples. About D-GNNs.
Applications: modelling of material reaction processes, prediction of time-dependent properties.
Specific examples of algorithm application:
1. message passing neural networks (MPNNs): the following is an example of using MPNNs to predict material properties.
import torch
import torch.nn.functional as F
from torch_geometric.nn import MessagePassing
from torch_geometric.utils import degree
class MPNN(MessagePassing):
def __init__(self, in_channels, out_channels):
super(MPNN, self).__init__(aggr='add') # "Add" aggregation.
self.lin = torch.nn.Linear(in_channels, out_channels)
def forward(self, x, edge_index):
# x: node feature matrix
# edge_index: edge index
return self.propagate(edge_index, x=x)
def message(self, x_j):
# message passing step
return self.lin(x_j)
def update(self, aggr_out):
# Update Steps
return F.relu(aggr_out)
# Preparation of input data
node_features = torch.tensor([
[1.0, 2.0], # Features of Atom 1
[2.0, 3.0], # Features of Atom 2
[3.0, 4.0], # Features of Atom 3
], dtype=torch.float)
edge_index = torch.tensor([
[0, 1, 2, 0],
[1, 0, 0, 2]
], dtype=torch.long)
# Defining and running the model
model = MPNN(in_channels=2, out_channels=2)
out = model(node_features, edge_index)
print(out)2. graphical attention network (GAT): the following is an example of using GAT to highlight important interatomic bonds and predict material properties.
from torch_geometric.nn import GATConv
class GAT(torch.nn.Module):
def __init__(self):
super(GAT, self).__init__()
self.conv1 = GATConv(in_channels=2, out_channels=8, heads=4, concat=True)
self.conv2 = GATConv(in_channels=8*4, out_channels=8, heads=1, concat=True)
def forward(self, data):
x, edge_index = data.x, data.edge_index
x = self.conv1(x, edge_index)
x = F.elu(x)
x = self.conv2(x, edge_index)
return x
# Preparation of input data
data = Data(x=node_features, edge_index=edge_index)
# Defining and running the model
model = GAT()
out = model(data)
print(out)Areas of application of the algorithm:
- Design of new materials: use generation models to design the atomic structure of new materials and predict their properties.
- Property prediction: using GCN and GAT to predict the properties of existing materials with high accuracy.
- Process modelling: use dynamic GNNs to modelling the formation processes and reaction pathways of materials and to predict their time-dependent properties.
- Anomaly detection: use graphical autoencoders to detect anomalies that occur during the material production process.
The application of these algorithms is expected to significantly streamline the research and development process in materials science and accelerate the discovery of new materials.
Challenges and Solution for services that use GNNs to model the properties and structure of materials and to design new materials and predict their properties.
The challenges associated with services that use GNNs to model the properties and structure of materials, design new materials and predict their properties are summarised below.
1. data quality and quantity:
Challenges:
Lack of data: it is difficult to collect sufficient high-quality data in materials science.
Data imbalance: abundance of data on some materials and properties, while data is scarce in other areas.
Solution:
Data Augmentation: make use of data augmentation techniques (Data Augmentation) and simulation data. For example, use computational chemistry and molecular dynamics simulations to generate data.
Data balancing: use sampling techniques (oversampling and undersampling) to balance data sets. Also integrate data from different sources.
2. model interpretability:
Challenges:
Black box problem: while GNN models have high predictive performance, their inner workings are prone to black boxing.
Solution:
Introduce explainable AI (XAI) techniques: use methods such as GNNExplainer and Grad-CAM to visualise the determinants of the model and make them interpretable.
Use with simple models: complement GNN results by using them with more easily interpretable models such as linear models and decision trees.
3. computational cost and scalability:
Challenges:
Computational resource consumption: GNNs are computationally expensive and consume large amounts of computational resources when dealing with large datasets and complex graph structures.
Scalability issues: handling large graphs is difficult and there are challenges in scaling up.
Solution:
Use efficient algorithms: use computationally efficient algorithms such as GraphSAGE and Mini-Batch Training.
Use of cloud resources: use cloud services such as AWS, GCP and Azure to scale up computational resources.
4. ensuring real-time:
Challenges:
Lack of real-time: it is sometimes difficult to predict material properties in real-time.
Solution
Introduce stream processing: introduce stream processing technologies such as Apache Kafka and Apache Flink to achieve real-time data processing.
Incremental learning: introduce incremental learning, where models are updated each time new data is available.
5. model evaluation and validation:
Challenges:
Difficulties in evaluating models: the diversity of material properties can make it difficult to evaluate the performance of models.
Solution:
Use appropriate metrics: use appropriate metrics for the prediction task (e.g. RMSE, MAE, R² score, etc.).
Conduct cross-validation: split the dataset and cross-validate to assess the generalisation performance of the model.
6. privacy and security:
Challenge:
Data privacy issues: material data may contain sensitive information and privacy protection is important.
Solution:
Data anonymisation: anonymise personal and sensitive information to protect privacy.
Secure data processing: data encryption and security protocols should be implemented to ensure data safety.
7. anomaly detection and response:
Challenges:
Anomaly detection difficulties: material data may contain outliers, which are difficult to detect.
Solution:
Introduction of anomaly detection algorithm: introduce a GNN-based anomaly detection algorithm for early detection of anomalous patterns.
Develop an anomaly response protocol: develop a response procedure after anomaly detection to enable rapid response.
8. implementation and operational costs:
Challenges:
High implementation costs: the initial cost of implementing new technologies is high.
Operational complexity: the operation and maintenance of the model is complex and requires specialist knowledge.
Solution:
Phased implementation: to reduce initial investment, implement in phases and scale up as the benefits are verified.
Use of operational support services: use expert operational support services to reduce operational costs and ensure effective operation.
9. technology standardisation and compatibility:
Challenges:
Lack of standardisation of technology: new technology, lack of standardisation and compatibility issues.
Countermeasures:
Use open source technology: utilise open source libraries such as PyTorch Geometric and use standardised implementations.
Community involvement: join standards bodies and communities and contribute to the standardisation of technologies.
参考情報と参考図書
グラフデータの詳細に関しては”グラフデータ処理アルゴリズムと機械学習/人工知能タスクへの応用“を参照のこと。また、ナレッジグラフに特化した詳細に関しては”知識情報処理技術“も参照のこと。さらに、深層学習全般に関しては”深層学習について“も参照のこと。
参考図書としては”グラフニューラルネットワーク ―PyTorchによる実装―“
“Graph Neural Networks: Foundations, Frontiers, and Applications“等がある。
“Materials Informatics: Methods, Tools, and Applications”
“Computational Materials Science: An Introduction”
“Graph Representation Learning”
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