Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie

Artificial Intelligence is rapidly transforming materials science and engineering, offering powerful tools to navigate complexity, accelerate discovery, and optimize material design in ways previously unattainable. Driven by the accelerating pace of algorithmic advancements and increasing data availability, AI is becoming an essential competency for materials researchers. This review provides a comprehensive and structured overview of the current landscape, synthesizing recent advancements and methodologies for materials scientists seeking to effectively leverage these data-driven techniques. We survey the spectrum of machine learning approaches, from traditional algorithms to advanced deep learning architectures, including CNNs, GNNs, and Transformers, alongside emerging generative AI and probabilistic models such as Gaussian Processes for uncertainty quantification. The review also examines the pivotal role of data in this field, emphasizing how effective representation and featurization strategies, spanning compositional, structural, image-based, and language-inspired approaches, combined with appropriate preprocessing, fundamentally underpin the performance of machine learning models in materials research. Persistent challenges related to data quality, quantity, and standardization, which critically impact model development and application in materials science and engineering, are also addressed.

A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parameters' components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such as classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring its feasibility.