Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Bosch, Nathanael"'
Efficiently learning a sequence of related tasks, such as in continual learning, poses a significant challenge for neural nets due to the delicate trade-off between catastrophic forgetting and loss of plasticity. We address this challenge with a grou
Externí odkaz:
http://arxiv.org/abs/2410.06800
Autor:
Beck, Jonas, Bosch, Nathanael, Deistler, Michael, Kadhim, Kyra L., Macke, Jakob H., Hennig, Philipp, Berens, Philipp
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 allow for gra
Externí odkaz:
http://arxiv.org/abs/2402.12231
Autor:
Lahr, Amon, Tronarp, Filip, Bosch, Nathanael, Schmidt, Jonathan, Hennig, Philipp, Zeilinger, Melanie N.
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and s
Externí odkaz:
http://arxiv.org/abs/2401.17731
Autor:
Bosch, Nathanael, Corenflos, Adrien, Yaghoobi, Fatemeh, Tronarp, Filip, Hennig, Philipp, Särkkä, Simo
Publikováno v:
Journal of Machine Learning Research, 2024
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and thereby quant
Externí odkaz:
http://arxiv.org/abs/2310.01145
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems, where small
Externí odkaz:
http://arxiv.org/abs/2305.14978
We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary d
Externí odkaz:
http://arxiv.org/abs/2202.01287
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
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
Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include
Externí odkaz:
http://arxiv.org/abs/2110.10770
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate
Externí odkaz:
http://arxiv.org/abs/2012.08202