Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Krämer, Nicholas"'
Autor:
Krämer, Nicholas
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow references to W
Externí odkaz:
http://arxiv.org/abs/2409.06752
Tuning scientific and probabilistic machine learning models -- for example, partial differential equations, Gaussian processes, or Bayesian neural networks -- often relies on evaluating functions of matrices whose size grows with the data set or the
Externí odkaz:
http://arxiv.org/abs/2405.17277
Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit uncertainty quantifi
Externí odkaz:
http://arxiv.org/abs/2208.01565
Autor:
Wenger, Jonathan, Krämer, Nicholas, Pförtner, Marvin, Schmidt, Jonathan, Bosch, Nathanael, Effenberger, Nina, Zenn, Johannes, Gessner, Alexandra, Karvonen, Toni, Briol, François-Xavier, Mahsereci, Maren, Hennig, Philipp
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential equation simulation. PNMs naturally incorporate prior information abo
Externí odkaz:
http://arxiv.org/abs/2112.02100
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately, serially, and
Externí odkaz:
http://arxiv.org/abs/2110.11847
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed implementati
Externí odkaz:
http://arxiv.org/abs/2110.11812
Autor:
Krämer, Nicholas, Hennig, Philipp
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and tailor it spe
Externí odkaz:
http://arxiv.org/abs/2106.07761
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential equation. The ma
Externí odkaz:
http://arxiv.org/abs/2103.10153
Autor:
Krämer, Nicholas, Hennig, Philipp
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of theoretical
Externí odkaz:
http://arxiv.org/abs/2012.10106
Autor:
Kersting, Hans, Krämer, Nicholas, Schiegg, Martin, Daniel, Christian, Tiemann, Michael, Hennig, Philipp
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by
Externí odkaz:
http://arxiv.org/abs/2002.09301