Zobrazeno 1 - 10
of 369
pro vyhledávání: '"P. Eigel"'
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) format. It is based on the annealing path commonly used in MCMC literature,
Externí odkaz:
http://arxiv.org/abs/2412.07637
Autor:
Aksenov, Vitalii, Eigel, Martin
The possibility of using the Eulerian discretization for the problem of modelling high-dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to the Wasse
Externí odkaz:
http://arxiv.org/abs/2411.12430
Autor:
Schütte, Janina Enrica, Eigel, Martin
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling best-in-class metho
Externí odkaz:
http://arxiv.org/abs/2408.10838
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric variables of solut
Externí odkaz:
http://arxiv.org/abs/2403.13770
Autor:
Schütte, Janina E., Eigel, Martin
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve training eff
Externí odkaz:
http://arxiv.org/abs/2403.12650
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-time diffusion processes depending on the log-densities of Ornstein-Uhl
Externí odkaz:
http://arxiv.org/abs/2402.15285
Autor:
Eigel, Martin, Miranda, Charles
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of Deep Operator Networks (DeepONets), which is based on operator learni
Externí odkaz:
http://arxiv.org/abs/2402.03028
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 target. To that end, we propose using a neural network architecture ins
Externí odkaz:
http://arxiv.org/abs/2311.03242
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse approximations i
Externí odkaz:
http://arxiv.org/abs/2310.08942
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An in-depth theoreti
Externí odkaz:
http://arxiv.org/abs/2304.00388