Related papers: Integrating Neural Networks and Tensor Networks fo…

Estimating free energy is a fundamental problem in statistical mechanics. Recently, machine-learning-based methods, particularly the variational autoregressive networks (VANs) have been proposed to minimize variational free energy and to…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and…

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense…

We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…

A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in…

Sampling complex free energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a…

The design and application of regression-free tensor network representations for integration is presented. Tensor network methods are demonstrated to outperform Monte Carlo for test problems, and exponential convergence is shown to be…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…