Miguel A. L. Marques

Jonathan Schmidt, Noah Hoffmann, Hai-Chen Wang et al.

Crystal-graph attention networks have emerged recently as remarkable tools for the prediction of thermodynamic stability and materials properties from unrelaxed crystal structures. Previous networks trained on two million materials exhibited, however, strong biases originating from underrepresented chemical elements and structural prototypes in the available data. We tackled this issue computing additional data to provide better balance across both chemical and crystal-symmetry space. Crystal-graph networks trained with this new data show unprecedented generalization accuracy, and allow for reliable, accelerated exploration of the whole space of inorganic compounds. We applied this universal network to perform machine-learning assisted high-throughput materials searches including 2500 binary and ternary structure prototypes and spanning about 1 billion compounds. After validation using density-functional theory, we uncover in total 19512 additional materials on the convex hull of thermodynamic stability and ~150000 compounds with a distance of less than 50 meV/atom from the hull. Combining again machine learning and ab-initio methods, we finally evaluate the discovered materials for applications as superconductors, superhard materials, and we look for candidates with large gap deformation potentials, finding several compounds with extreme values of these properties.

Jonathan Schmidt, Haichen Wang, Georg Schmidt et al.

Garnets, known since the early stages of human civilization, have found important applications in modern technologies including magnetorestriction, spintronics, lithium batteries, etc. The overwhelming majority of experimentally known garnets are oxides, while explorations (experimental or theoretical) for the rest of the chemical space have been limited in scope. A key issue is that the garnet structure has a large primitive unit cell, requiring an enormous amount of computational resources. To perform a comprehensive search of the complete chemical space for new garnets,we combine recent progress in graph neural networks with high-throughput calculations. We apply the machine learning model to identify the potential (meta-)stable garnet systems before systematic density-functional calculations to validate the predictions. In this way, we discover more than 600 ternary garnets with distances to the convex hull below 100~meV/atom with a variety of physical and chemical properties. This includes sulfide, nitride and halide garnets. For these, we analyze the electronic structure and discuss the connection between the value of the electronic band gap and charge balance.

Arthur Bizzi, Leonardo M. Moreira, Márcio Marques et al.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.