Search Results for author: Nicholas Krämer

Found 10 papers, 4 papers with code

Gradients of Functions of Large Matrices

1 code implementation27 May 2024 Nicholas Krämer, Pablo Moreno-Muñoz, Hrittik Roy, Søren Hauberg

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 number of parameters.

Gaussian Processes

Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs

no code implementations2 Aug 2022 Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, Philipp Hennig

Neural operators are a type of deep architecture that learns to solve (i. e. learns the nonlinear solution operator of) partial differential equations (PDEs).

Gaussian Processes Uncertainty Quantification

Linear-Time Probabilistic Solution of Boundary Value Problems

no code implementations NeurIPS 2021 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.

Uncertainty Quantification

Probabilistic ODE Solutions in Millions of Dimensions

no code implementations22 Oct 2021 Nicholas Krämer, Nathanael Bosch, Jonathan Schmidt, Philipp Hennig

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems.

Uncertainty Quantification

Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations

2 code implementations22 Oct 2021 Nicholas Krämer, Jonathan Schmidt, Philipp Hennig

Thereby, we extend the toolbox of probabilistic programs for differential equation simulation to PDEs.

Bayesian Inference

Linear-Time Probabilistic Solutions of Boundary Value Problems

no code implementations14 Jun 2021 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.

Uncertainty Quantification

Stable Implementation of Probabilistic ODE Solvers

no code implementations18 Dec 2020 Nicholas Krämer, Philipp Hennig

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems.

Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems

no code implementations ICML 2020 Hans Kersting, Nicholas Krämer, Martin Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig

To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood.

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