7 citations · 22 across the 7 of their papers we have counts for
7 papers
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs
Emilia Magnani, Nicholas Krämer, Runa Eschenhagen +2
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 t…
ProbNum: Probabilistic Numerics in Python
Jonathan Wenger, Nicholas Krämer, Marvin Pförtner +9
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential…
Probabilistic ODE Solutions in Millions of Dimensions
Nicholas Krämer, Nathanael Bosch, Jonathan Schmidt +1
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this w…
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations
Nicholas Krämer, Jonathan Schmidt, Philipp Hennig
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 s…
Linear-Time Probabilistic Solutions of Boundary Value Problems
Nicholas Krämer, Philipp Hennig
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…
A Probabilistic State Space Model for Joint Inference from Differential Equations and Data
Jonathan Schmidt, Nicholas Krämer, Philipp Hennig
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, be…
Stable Implementation of Probabilistic ODE Solvers
Nicholas Krämer, Philipp Hennig
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their co…