Related papers: Tensor approximation of the self-diffusion matrix …
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
A version of the projection method for solving the scattering problem for acoustic and electromagnetic waves is proposed and shown to be more efficient numerically than the earlier ones because the corresponding matrix is not…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic…
Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
Neural diffusion processes provide a scalable, non-Gaussian approach to modelling distributions over functions, but existing formulations are limited to single-task inference and do not capture dependencies across related tasks. In many…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear…
Estimation of Distribution Algorithms (EDAs) and Innovation Method are recognized methods for solving global optimization problems and for the estimation of parameters in diffusion processes, respectively. Well known is also that the…
In this paper we present new ideas to accelerate the computation of the eigenvector of the transition matrix associated to the PageRank algorithm. New ideas are based on the decomposition of the matrix-vector product that can be seen as a…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in…
Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific instance in novel contexts, i.e.,…
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…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…