Table 4

Summary of emerging machine learning and deep learning architectures, including their core concepts and key advantages

ArchitectureCore conceptKey advantages
Transformers / attentionUses self-attention mechanisms to capture long-range dependencies and global context within dataEffective for modeling complex sequential and spatial relationships; scalable and flexible across data modalities
Graph neural networks (GNNs)Processes data represented as graphs, where nodes and edges encode relationships among entitiesNaturally handles irregular and non-Euclidean data while capturing complex relational structures
Physics-Informed neural networks (PINNs)Incorporates governing physical laws and constraints into the learning process through the loss functionImproves physical consistency, interpretability and generalization, particularly when data are limited
Operator learning methods (DeepONet, FNO)Learns mappings between function spaces rather than discrete input-output pairsEnables rapid approximation of complex physical systems and efficient surrogate modeling
Explainable AI (XAI)Provides methods to interpret and explain model predictions and decision-making processesImproves transparency, trustworthiness and validation of machine learning models

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