7 accepted papers
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been the opposite, with unstable training, poor predictive power…
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. While the state-of-the-art for…
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 with black-box algorithms, which obscures the inte…
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 implementation schemes behind solving high-dimensional ODEs wi…
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 main problem here is that the numerical solver is har…
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 specifically to BVPs, which allows computing a poster…
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 an ODE solver. This, however, is not a fundamenta…