2021-03-18-bosch21a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Calibrated Adaptive Probabilistic ODE Solvers	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 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. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bosch21a	0	Calibrated Adaptive Probabilistic ODE Solvers	3466	3474	3466-3474	3466	false	Bosch, Nathanael and Hennig, Philipp and Tronarp, Filip	given family Nathanael Bosch given family Philipp Hennig given family Filip Tronarp	2021-03-18		Proceedings of The 24th International Conference on Artificial Intelligence and Statistics	130	inproceedings	date-parts 2021 3 18	http://proceedings.mlr.press/v130/bosch21a/bosch21a.pdf	label link Supplementary PDF http://proceedings.mlr.press/v130/bosch21a/bosch21a-supp.pdf