We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector, and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level. TOC graphic3 Accurate and efficient interaction potential energy surfaces (PESs) are crucial for spectroscopic, molecular dynamics, and thermodynamics simulations 1 . Traditional empirical or semi-empirical force field models such as the embedded atom method (EAM) 2-3 , while physically meaningful and highly efficient, are severely limited by their accuracy. More recently, tremendous efforts have been devoted to developing machine learning (ML) based PESs 4 , which are capable of representing a large set of ab initio data more accurately on chemical properties 5 , molecules 6-13 , gas phase and surface reactions 14-18 , and materialsError! Bookmark not defined. 10,[19][20][21][22] .Since known ML techniques in computer science themselves do not recognize the intrinsic symmetry of a chemical system, it is essential to design a ML representation for a PES that preserves rotational, translational, and permutational symmetry in an accurate and efficient way 23 . In this regard, permutation invariant polynomials (PIPs) in terms of internuclear distances 24 were used as the input of neural networks (NNs) 14 and Gaussian process regression (GPR) 25 in low-dimensional systems. For highdimensional problems, Behler and Parrinello 26 first handcrafted a set of atom centered symmetry functions (ACSFs) 23 as the input of atomistic neural networks (AtNN), which were later improved in various ways 9, 27 . More recently, the deep learning molecular dynamics (DPMD) model 10 and its symmetrized edition (DeepPot-SE) 28 map the coordinate matrix to a multi-output NN making descriptors themselves self-adapted in training. Deep tensor NN (DTNN) model 11 utilizes a vector of nuclear charges and an inter-atomic distance matrix as descriptors and its variant SchNet model 12 further introduces a continuous-filter convolutional layer to extract features from these

Machine learning has revolutionized the highdimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant. Here, we propose tensorial neural network (NN) models to learn both tensorial response and transition properties in which atomic coordinate vectors are multiplied with scalar NN outputs or their derivatives to preserve the rotationally covariant symmetry. This strategy keeps structural descriptors symmetry invariant so that the resulting tensorial NN models are as efficient as their scalar counterparts. We validate the performance and universality of this approach by learning response properties of water oligomers and liquid water and transition dipole moment of a model structural unit of proteins. Machine-learned tensorial models have enabled efficient simulations of vibrational spectra of liquid water and ultraviolet spectra of realistic proteins, promising feasible and accurate spectroscopic simulations for biomolecules and materials.

The van der Waals (vdW) materials offer an opportunity to build all-two-dimensional (all-2D) spintronic devices with high-quality interfaces regardless of the lattice mismatch. Here, we report on an all-2D vertical spin valve that combines a typical layered semiconductor MoS 2 with vdW ferromagnetic metal Fe 3 GeTe 2 (FGT) flakes. The linear current−voltage curves illustrate that Ohmic contacts are formed in FGT/MoS 2 interfaces, while the temperature dependence of the junction resistance further demonstrates that the MoS 2 interlayer acts as a conducting layer instead of a tunneling layer. In addition, the magnitude of the magnetoresistance (MR) of 3.1% at 10 K is observed, which is around 8 times larger than that of the reported spin valves based on MoS 2 sandwiched by conventional ferromagnetic electrodes. The MR decreasing monotonically with increasing temperature follows the Bloch's law. As the bias current decreases exponentially, the MR increases linearly up to a maximum value of 4.1%. Our results reveal the potential opportunities of vdW heterostructures for developing novel spintronic devices.