相关论文: Neural Network Matrix Product Operator: A Multi-Di…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art \textit{ab initio} theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete…

Whilst the primary bottleneck to a number of computational workflows was not so long ago limited by processing power, the rise of machine learning technologies has resulted in a paradigm shift which places increasing value on issues related…

We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…

Accounting for nuclear quantum effects (NQEs) can significantly alter material properties at finite temperatures. Atomic modeling using the path-integral molecular dynamics (PIMD) method can fully account for such effects, but requires…

Accurate potential energy surface (PES) descriptions are essential for atomistic simulations of materials. Universal machine learning interatomic potentials (UMLIPs)$^{1-3}$ offer a computationally efficient alternative to density…

Full dimensional potential energy surfaces (PESs) based on machine learning (ML) techniques provide means for accurate and efficient molecular simulations in the gas- and condensed-phase for various experimental observables ranging from…

Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive…

We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…

Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems…

Magnetotelluric (MT) forward modeling is fundamental for improving the accuracy and efficiency of MT inversion. Neural operators (NOs) have been effectively used for rapid MT forward modeling, demonstrating their promising performance in…

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

Several pool-based active learning algorithms (AL) were employed to model potential energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be…

A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…

We present an efficient approach for generating highly accurate molecular potential energy surfaces (PESs) using self-correcting, kernel ridge regression (KRR) based machine learning (ML). We introduce structure-based sampling to…

We present design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM)…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…