# Working meeting "Uncertainty quantification in materials science" - May, 14th 2018

## Seminar co-organized by the GdR MASCOT-NUM and the GdR ModMat

**Organizers: ** Jean Baccou, Virginie Ehrlacher, Guillaume Perrin, Julien Reygner

May 14, 2018, at Amphithéâtre Hermite, Institut Henri Poincaré, Paris.

**Agenda**

9h00 - Welcome - Introduction

9h15 - Tony Lelièvre (Ecole des Ponts Paristech & INRIA): Introduction to numerical methods in molecular dynamics

10h15 - Break

10h30 - Fabien Cailliez (Université Paris-Sud): Parametric Uncertainties in Molecular simulations

11h15 - Céline Varvenne (Centre Interdisciplinaire de Nanoscience de Marseille): Uncertainty quantification for ab initio computation of point defects properties in alloys

12h - Lunch break (on your own)

14h30 - Pascal Pernot (Université Paris-Sud): Prediction Uncertainty of Computational Chemistry Methods

15h30 - Break

15h45 - Tom Swinburne (Los Alamos National Laboratory): Uncertainty-driven construction of Markov models from accelerated molecular dynamics

16h30 - Fabienne Ribeiro (IRSN, Cadarache): Uncertainty quantification in material multiscale modeling: what are the challenges?

17h15 - End

** Abstracts **

**Introduction to numerical methods in molecular dynamics**

I will present some algorithms which are used in molecular dynamics, and I will discuss the main sources of errors, and the interest of using statistical techniques in this context.

* Pascal Pernot: ** Prediction Uncertainty of Computational Chemistry Methods**

Computational Chemistry (CC) is the first stage in multiscale modeling of materials. Approximations and numerical schemes used in

performing CC methods are sources of errors that have to be carefully evaluated to derive a prediction uncertainty. Using the concept of Virtual Measurement (VM) I will introduce the standardized framework required to estimate VM uncertainty. This will be illustrated through various approaches used in the literature to estimate prediction uncertainty of CC methods, from simple a posteriori corrections to embedded stochastic models.

* Fabien Cailliez: ** Parametric Uncertainties in Molecular simulations**

Molecular simulations rely on the use of parametric expressions of the energy, called forcefields. These expressions contain the information about molecular interactions in the system and thus condition the values of the computed thermodynamic properties. I will describe recent efforts in monitoring the uncertainties and errors of molecular simulation outputs due to uncertainties in forcefield parameters. Strategies of statistical calibrations of forcefields and uncertainty propagation through molecular simulations will be described.

* Céline Varvenne: ** Uncertainty quantification for ab initio computation of point defects properties in alloys**

Point defects play an important role for the mechanical properties and the kinetic evolution of

metallic alloys. Their characteristics must then be computed accurately, preferentially using ab

initio atomistic simulations. However, due to the different possible chemical and structural

environments in non-dilute alloys, those characteristics are statistically distributed, making a precise

determination challenging for such methods. The quantification of the error associated with both the

finite size of the ab initio calculations and the incomplete sampling of the atomic configurations

will be discussed.

* Tom Swinburne: ** Uncertainty-driven construction of Markov models from accelerated molecular dynamics**

A common way of representing the long-time dynamics of materials is in terms of a Markov chain that specifies the transition rates for transitions between metastable states. This chain can either be used to generate trajectories using kinetic Monte Carlo, or analyzed directly, e.g., in terms of first passage times between distant states. While a number of approaches have been proposed to infer such a representation from direct molecular dynamics (MD) simulations, challenges remain. For example, as chains inferred from a finite amount of MD will in general be incomplete, quantifying their completeness is extremely desirable. Second, making the construction of the chain as computationally affordable as possible is paramount. In this work, we simultaneously address these two questions. We first quantify the local completeness of the chain in terms of Bayesian estimators of the yet-unobserved rate, and its global completeness in terms of the residence time of trajectories within the explored subspace. We then systematically reduce the cost of creating the chain by maximizing the increase in residence time against the distribution of states in which additional MD is carried out and the temperature at which these are respectively carried out. Using as example the behavior of vacancy and interstitial clusters in materials, we demonstrate that this is an efficient, fully automated, and massively-parallel scheme to efficiently explore the long-time behavior of materials.

* Fabienne Ribeiro: ** Uncertainty quantification in material multiscale modeling: what are the challenges?**

Multiscale and Multiphysics approaches became more and more popular during the last decades, due to their ability to access to a better understanding of complex materials by linking their microstructural description to their macroscopical behavior. This talk will first summarize the main modeling approaches at the various relevant spatial and time scales. Then, it will present the main interrogations and difficulties related to the necessary coupling between these different scales. This will be illustrated in the peculiar case of nuclear material simulation that definitely require to account for uncertainty quantification, which will allow to detail what remain the pending questions.