相关论文: Solving high-dimensional nonlinear filtering probl…

Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

Precise representation of large-scale undirected network is the basis for understanding relations within a massive entity set. The undirected network representation task can be efficiently addressed by a symmetry non-negative latent factor…

In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of…

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…

We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…

We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

The state-of-the-art tensor network Kalman filter lifts the curse of dimensionality for high-dimensional recursive estimation problems. However, the required rounding operation can cause filter divergence due to the loss of positive…

We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…

Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…

We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system. Numerical solution of this…

Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

The Kalman Filter is a widely used approach for the linear estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks.…