AI-driven inverse design of materials: Past, present and future

The discovery of advanced materials is the cornerstone of human technological development and progress. The structures of materials and their corresponding properties are essentially the result of a complex interplay of multiple degrees of freedom such as lattice, charge, spin, symmetry, and topology. This poses significant challenges for the inverse design methods of materials. Humans have long explored new materials through a large number of experiments and proposed corresponding theoretical systems to predict new material properties and structures. With the improvement of computational power, researchers have gradually developed various electronic structure calculation methods, particularly such as the one based density functional theory, as well as high-throughput computational methods. Recently, the rapid development of artificial intelligence technology in the field of computer science has enabled the effective characterization of the implicit association between material properties and structures, thus opening up an efficient paradigm for the inverse design of functional materials. A significant progress has been made in inverse design of materials based on generative and discriminative models, attracting widespread attention from researchers. Considering this rapid technological progress, in this survey, we look back on the latest advancements in AI-driven inverse design of materials by introducing the background, key findings, and mainstream technological development routes. In addition, we summarize the remaining issues for future directions. This survey provides the latest overview of AI-driven inverse design of materials, which can serve as a useful resource for researchers.

AI-accelerated discovery of high critical temperature superconductors

The discovery of new superconducting materials, particularly those exhibiting high critical temperature ($T_c$), has been a vibrant area of study within the field of condensed matter physics. Conventional approaches primarily rely on physical intuition to search for potential superconductors within the existing databases. However, the known materials only scratch the surface of the extensive array of possibilities within the realm of materials. Here, we develop an AI search engine that integrates deep model pre-training and fine-tuning techniques, diffusion models, and physics-based approaches (e.g., first-principles electronic structure calculation) for discovery of high-$T_c$ superconductors. Utilizing this AI search engine, we have obtained 74 dynamically stable materials with critical temperatures predicted by the AI model to be $T_c \geq$ 15 K based on a very small set of samples. Notably, these materials are not contained in any existing dataset. Furthermore, we analyze trends in our dataset and individual materials including B$_4$CN$_3$ and B$_5$CN$_2$ whose $T_c$s are 24.08 K and 15.93 K, respectively. We demonstrate that AI technique can discover a set of new high-$T_c$ superconductors, outline its potential for accelerating discovery of the materials with targeted properties.

AI-accelerated Discovery of Altermagnetic Materials

Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the very limited availability of known altermagnetic materials (e.g., 14 confirmed materials) hinders the study of such properties. Hence, discovering more types of altermagnetic materials is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next-generation information technologies, e.g., storage devices and high-sensitivity sensors. Here, we report 25 new altermagnetic materials that cover metals, semiconductors, and insulators, discovered by an AI search engine unifying symmetry analysis, graph neural network pre-training, optimal transport theory, and first-principles electronic structure calculation. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 8 i-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeting properties.

Variational optimization of the amplitude of neural-network quantum many-body ground states

Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational methods. However, there are still some difficulties in the optimization of NQSs, such as local minima, slow convergence, and sign structure optimization. Here, we split a quantum many-body variational wave function into a multiplication of a real-valued amplitude neural network and a sign structure, and focus on the optimization of the amplitude network while keeping the sign structure fixed. The amplitude network is a convolutional neural network (CNN) with residual blocks, namely a ResNet. Our method is tested on three typical quantum many-body systems. The obtained ground state energies are lower than or comparable to those from traditional variational Monte Carlo (VMC) methods and density matrix renormalization group (DMRG). Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results are better than those of the complex-valued CNN in the literature, implying that the sign structure of the complex-valued NQS is difficult to be optimized. We will study the optimization of the sign structure of NQSs in the future.

A simple framework for contrastive learning phases of matter

A main task in condensed-matter physics is to recognize, classify, and characterize phases of matter and the corresponding phase transitions, for which machine learning provides a new class of research tools due to the remarkable development in computing power and algorithms. Despite much exploration in this new field, usually different methods and techniques are needed for different scenarios. Here, we present SimCLP: a simple framework for contrastive learning phases of matter, which is inspired by the recent development in contrastive learning of visual representations. We demonstrate the success of this framework on several representative systems, including classical and quantum, single-particle and many-body, conventional and topological. SimCLP is flexible and free of usual burdens such as manual feature engineering and prior knowledge. The only prerequisite is to prepare enough state configurations. Furthermore, it can generate representation vectors and labels and hence help tackle other problems. SimCLP therefore paves an alternative way to the development of a generic tool for identifying unexplored phase transitions.

Parameter-Efficient Mixture-of-Experts Architecture for Pre-trained Language Models

The state-of-the-art Mixture-of-Experts (short as MoE) architecture has achieved several remarkable successes in terms of increasing model capacity. However, MoE has been hindered widespread adoption due to complexity, communication costs, and training instability. Here we present a novel MoE architecture based on matrix product operators (MPO) from quantum many-body physics. It can decompose an original matrix into central tensors (containing the core information) and auxiliary tensors (with only a small proportion of parameters). With the decomposed MPO structure, we can reduce the parameters of the original MoE architecture by sharing a global central tensor across experts and keeping expert-specific auxiliary tensors. We also design the gradient mask strategy for the tensor structure of MPO to alleviate the overfitting problem. Experiments on the three well-known downstream natural language datasets based on GPT2 show improved performance and efficiency in increasing model capacity (7.26x fewer parameters with the same amount of experts). We additionally demonstrate an improvement in the positive transfer effects of our approach for multi-task learning.

Enabling Lightweight Fine-tuning for Pre-trained Language Model Compression based on Matrix Product Operators

This paper presents a novel pre-trained language models (PLM) compression approach based on the matrix product operator (short as MPO) from quantum many-body physics. It can decompose an original matrix into central tensors (containing the core information) and auxiliary tensors (with only a small proportion of parameters). With the decomposed MPO structure, we propose a novel fine-tuning strategy by only updating the parameters from the auxiliary tensors, and design an optimization algorithm for MPO-based approximation over stacked network architectures. Our approach can be applied to the original or the compressed PLMs in a general way, which derives a lighter network and significantly reduces the parameters to be fine-tuned. Extensive experiments have demonstrated the effectiveness of the proposed approach in model compression, especially the reduction in finetuning parameters (91% reduction on average).

A Model Compression Method with Matrix Product Operators for Speech Enhancement

The deep neural network (DNN) based speech enhancement approaches have achieved promising performance. However, the number of parameters involved in these methods is usually enormous for the real applications of speech enhancement on the device with the limited resources. This seriously restricts the applications. To deal with this issue, model compression techniques are being widely studied. In this paper, we propose a model compression method based on matrix product operators (MPO) to substantially reduce the number of parameters in DNN models for speech enhancement. In this method, the weight matrices in the linear transformations of neural network model are replaced by the MPO decomposition format before training. In experiment, this process is applied to the causal neural network models, such as the feedforward multilayer perceptron (MLP) and long short-term memory (LSTM) models. Both MLP and LSTM models with/without compression are then utilized to estimate the ideal ratio mask for monaural speech enhancement. The experimental results show that our proposed MPO-based method outperforms the widely-used pruning method for speech enhancement under various compression rates, and further improvement can be achieved with respect to low compression rates. Our proposal provides an effective model compression method for speech enhancement, especially in cloud-free application.

Compressing deep neural networks by matrix product operators

A deep neural network is a parameterization of a multi-layer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully-connected as well as convolutional layers, contain most of the variational parameters that are trained and stored. Compressing a deep neural network to reduce its number of variational parameters but not its prediction power is an important but challenging problem towards the establishment of an optimized scheme in training efficiently these parameters and in lowering the risk of overfitting. Here we show that this problem can be effectively solved by representing linear transformations with matrix product operators (MPO). We have tested this approach in five main neural networks, including FC2, LeNet-5, VGG, ResNet, and DenseNet on two widely used datasets, namely MNIST and CIFAR-10, and found that this MPO representation indeed sets up a faithful and efficient mapping between input and output signals, which can keep or even improve the prediction accuracy with dramatically reduced number of parameters.