Author Correction: Physics guided deep learning for generative design of crystal materials with symmetry constraints

Correction to:npj Computational Materials https://doi.org/10.1038/s41524-023-00987-9,published online 18 March 2023 The original version of this Article contained typos in both the PDF and the HTML versions.In the fourth and fifth sentences of the first paragraph of the‘Case study of three example stable materials’section of the Results,the incorrect expression“β=β”has been replaced by“α=β”.

Physics guided deep learning for generative design of crystal materials with symmetry constraints

Discovering new materials is a challenging task in materials science crucial to the progress of human society. Conventionalapproaches based on experiments and simulations are labor-intensive or costly with success heavily depending on experts’heuristic knowledge. Here, we propose a deep learning based Physics Guided Crystal Generative Model (PGCGM) for efficient crystalmaterial design with high structural diversity and symmetry. Our model increases the generation validity by more than 700%compared to FTCP, one of the latest structure generators and by more than 45% compared to our previous CubicGAN model.Density Functional Theory (DFT) calculations are used to validate the generated structures with 1869 materials out of 2000 aresuccessfully optimized and deposited into the Carolina Materials Database www.carolinamatdb.org, of which 39.6% have negativeformation energy and 5.3% have energy-above-hull less than 0.25 eV/atom, indicating their thermodynamic stability and potentialsynthesizability.

Million-scale data integrated deep neural network for phonon properties of heuslers spanning the periodic table

Existing machine learning potentials for predicting phonon properties of crystals are typically limited on a material-to-materialbasis, primarily due to the exponential scaling of model complexity with the number of atomic species. We address this bottleneckwith the developed Elemental Spatial Density Neural Network Force Field, namely Elemental-SDNNFF. The effectiveness andprecision of our Elemental-SDNNFF approach are demonstrated on 11,866 full, half, and quaternary Heusler structures spanning 55elements in the periodic table by prediction of complete phonon properties. Self-improvement schemes including active learningand data augmentation techniques provide an abundant 9.4 million atomic data for training. Deep insight into predicted ultralowlattice thermal conductivity (<1 Wm^(−1) K^(−1)) of 774 Heusler structures is gained by p–d orbital hybridization analysis. Additionally, aclass of two-band charge-2 Weyl points, referred to as “double Weyl points”, are found in 68% and 87% of 1662 half and 1550quaternary Heuslers, respectively.

Efficiently searching extreme mechanical properties via boundless objective-free exploration and minimal first-principles calculations

Despite the machine learning(ML)methods have been largely used recently,the predicted materials properties usually cannot exceed the range of original training data.We deployed a boundless objective-free exploration approach to combine traditional ML and density functional theory(DFT)in searching extreme material properties.This combination not only improves the efficiency for screening large-scale materials with minimal DFT inquiry,but also yields properties beyond original training range.We use Stein novelty to recommend outliers and then verify using DFT.Validated data are then added into the training dataset for next round iteration.We test the loop of training-recommendation-validation in mechanical property space.By screening 85,707 crystal structures,we identify 21 ultrahigh hardness structures and 11 negative Poisson’s ratio structures.The algorithm is very promising for future materials discovery that can push materials properties to the limit with minimal DFT calculations on only~1%of the structures in the screening pool.