7 papers
Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling
Robert Gruhlke, Julius Berner, David Sommer +1
Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process. A common approach involves solving for the tim…
Approximation and learning with compositional tensor trains
Martin Eigel, Charles Miranda, Anthony Nouy +1
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train form…
Sampling from Boltzmann densities with physics informed low-rank formats
Paul Hagemann, Janina Schütte, David Sommer +2
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) forma…
Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations
David Sommer, Robert Gruhlke, Max Kirstein +2
Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-t…
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures
Charles Miranda, Janina Schütte, David Sommer +1
We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e.g. the standard normal distribution, to samples from the t…
Less interaction with forward models in Langevin dynamics
Martin Eigel, Robert Gruhlke, David Sommer
Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invari…
Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation
Martin Eigel, Reinhold Schneider, David Sommer
We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-…