Code and data to replicate our experiments can be found at https://github.com/ppope/rho-learn. 1.1 DFT Relaxations We use the PBE exchange-correlation functional for all relaxations. In particular a much smaller model was used than the state-of-the-art SCN results. An SCF run may be initialized with a custom density, e.g. one generated from a machine-learning

The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts.

In density functional theory, the charge density is the core attribute of atomic systems from which all chemical properties can be derived.

In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet existing approaches either lack accuracy or scalability. We propose a recipe that can achieve both. In particular, we identify three key ingredients: (1) representing the charge density with atomic and virtual orbitals (spherical fields centered at atom/virtual coordinates); (2) using expressive and learnable orbital basis sets (basis function for the spherical fields); and (3) using high-capacity equivariant neural network architecture. Our method achieves state-of-the-art accuracy while being more than an order of magnitude faster than existing methods. Furthermore, our method enables flexible efficiency-accuracy trade-offs by adjusting the model/basis sizes.

KEYWORDS Physics-informed neural network, Capacitive sensor, Simulation, Surrogate model, Maxwell's equations ABSTRACT Maxwell's equations are the fundamental equations for understanding electric and magnetic field interactions and play a crucial role in designing and optimizing sensor systems like capacitive touch sensors, which are widely prevalent in automotive switches and smartphones. This paper introduces a novel approach using a Physics-Informed Neural Network (PINN) based surrogate model to accelerate the design process. The PINN model solves the governing electrostatic equations describing the interaction between a finger and a capacitive sensor. Inputs include spatial coordinates from a 3D domain encompassing the finger, sensor, and PCB, along with finger distances. The learned model thus serves as a surrogate sensor model on which inference can be carried out in seconds for different experimental setups without the need to run simulations. Efficacy results evaluated on unseen test cases demonstrate the significant potential of PINNs in accelerating the development and design optimization of capacitive touch sensors.

In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet existing approaches either lack accuracy or scalability. We propose a recipe that can achieve both. In particular, we identify three key ingredients: (1) representing the charge density with atomic and virtual orbitals (spherical fields centered at atom/virtual coordinates); (2) using expressive and learnable orbital basis sets (basis function for the spherical fields); and (3) using high-capacity equivariant neural network architecture. Our method achieves state-of-the-art accuracy while being more than an order of magnitude faster than existing methods. Furthermore, our method enables flexible efficiency-accuracy trade-offs by adjusting the model/basis sizes.

The revolution in materials in the past century was built on a knowledge of the atomic arrangements and the structure-property relationship. The sine qua non for obtaining quantitative structural information is single crystal crystallography. However, increasingly we need to solve structures in cases where the information content in our input signal is significantly degraded, for example, due to orientational averaging of grains, finite size effects due to nanostructure, and mixed signals due to sample heterogeneity. Understanding the structure property relationships in such situations is, if anything, more important and insightful, yet we do not have robust approaches for accomplishing it. In principle, machine learning (ML) and deep learning (DL) are promising approaches since they augment information in the degraded input signal with prior knowledge learned from large databases of already known structures. Here we present a novel ML approach, a variational query-based multi-branch deep neural network that has the promise to be a robust but general tool to address this problem end-to-end. We demonstrate the approach on computed powder x-ray diffraction (PXRD), along with partial chemical composition information, as input. We choose as a structural representation a modified electron density we call the Cartesian mapped electron density (CMED), that straightforwardly allows our ML model to learn material structures across different chemistries, symmetries and crystal systems. When evaluated on theoretically simulated data for the cubic and trigonal crystal systems, the system achieves up to $93.4\%$ average similarity with the ground truth on unseen materials, both with known and partially-known chemical composition information, showing great promise for successful structure solution even from degraded and incomplete input data.

The calculation of electron density distribution using density functional theory (DFT) in materials and molecules is central to the study of their quantum and macro-scale properties, yet accurate and efficient calculation remains a long-standing challenge in the field of material science. This work introduces ChargE3Net, an E(3)-equivariant graph neural network for predicting electron density in atomic systems. ChargE3Net achieves equivariance through the use of higher-order tensor representations, and directly predicts the charge density at any arbitrary point in the system. We show that our method achieves greater performance than prior work on large and diverse sets of molecules and materials, and scales to larger systems than what is feasible to compute with DFT. Using predicted electron densities as an initialization, we show that fewer self-consistent iterations are required to converge DFT over the default initialization. In addition, we show that non-self-consistent calculations using the predicted electron densities can predict electronic and thermodynamic properties of materials at near-DFT accuracy.