# Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging.

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# Parallel-in-Time Probabilistic Numerical ODE Solvers

Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation.

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# Probabilistic Exponential Integrators

However, like standard solvers, they suffer performance penalties for certain stiff systems, where small steps are required not for reasons of numerical accuracy but for the sake of stability.

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# Fenrir: Physics-Enhanced Regression for Initial Value Problems

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.

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# ProbNum: Probabilistic Numerics in Python

Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.

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# Probabilistic ODE Solutions in Millions of Dimensions

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

# Pick-and-Mix Information Operators for Probabilistic ODE Solvers

Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference.

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# Calibrated Adaptive Probabilistic ODE Solvers

The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error.

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# Planning from Images with Deep Latent Gaussian Process Dynamics

We propose to learn a deep latent Gaussian process dynamics (DLGPD) model that learns low-dimensional system dynamics from environment interactions with visual observations.

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