Related papers: Committor functions via tensor networks
It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow…
This research introduces a new method for the transition from partial to ordinary differential equations that is based on the Kolmogorov superposition theorem. In this paper, we discuss the numerical implementation of the Kolmogorov theorem…
In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…
We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…
The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…
The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization…
In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the…
Computing spectral functions in large, non-periodic super-moir\'e systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing…
This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states.…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of…