# Probabilistic Gradients for Fast Calibration of Differential Equation Models

@article{Cockayne2021ProbabilisticGF, title={Probabilistic Gradients for Fast Calibration of Differential Equation Models}, author={Jon Cockayne and Andrew B. Duncan}, journal={ArXiv}, year={2021}, volume={abs/2009.04239} }

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a…

## 2 Citations

Bayesian Numerical Methods for Nonlinear Partial Differential Equations

- MathematicsStat. Comput.
- 2021

Proof-of-concept experimental results demonstrate that meaningful probabilistic uncertainty quantification for the unknown solution of the PDE can be performed, while controlling the number of times the right-handside, initial and boundary conditions are evaluated.

Theoretical Guarantees for the Statistical Finite Element Method

- Computer Science, PhysicsArXiv
- 2021

A bound is constituted on the Wasserstein-2 distance between the ideal prior and posterior and the StatFEM approximation thereof, and it is shown that this distance converges at the same mesh-dependent rate as finite element solutions converge to the true solution.

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