Organizing committee

(CNRS & Université Paris-Dauphine),

📩 iacob(at)ceremade(dot)dauphine(dot)fr

(CERMICS & MATHERIALS project, Inria Paris),

📩 gabriel(dot)stoltz(at)enpc(dot)fr

This summer school is cofunded by CECAM-MOSER, the ERC Synergy projet EMC2, the Groupe Calcul (CNRS) and Inria.

## Aims and Scope

Sampling high dimensional probability measures is a key issue in various scientific fields, including molecular dynamics and computational statistical physics (with applications in physics, chemistry, materials science and computational biology), as well as statistics (in particular Bayesian statistics) and more recently machine learning. Current challenges include

the sampling of trajectories connecting local modes of probability measures – the so- called reactive paths in molecular dynamics –, which is useful for both physical (e.g. computing reaction rates) and numerical reasons (efficiently sampling probability measures by reducing the metastability of dynamics);

the sampling of the invariant probability measure of nonequilibrium systems, for which it is not possible to resort to Metropolis-like methods and variance reduction strategies such as importance sampling since the invariant probability measure has no analytical expression.

the sampling of complex energy landscapes with many local minima, as those encountered in computational biology and machine learning (when sampling Bayesian neural networks for instance).

Interactions between molecular dynamics and computational statistics have a fruitful and successful history. We believe that a school at the intersection of these two fields will be beneficial to both communities, as the best methods can be transferred to both fields, which would then be able to exchange and share their respective knowledge and expertise. Young researchers are a particularly receptive audience to this end, as we strongly believe that being simultaneously exposed to both fields at an earlier stage of the career will have a long lasting impact on their scientific production.

The school is intended primarily for PhD students and postdocs working in the following fields:

applied mathematics, in particular numerical methods for molecular dynamics;

statistics and machine learning using sampling methods;

numerical methods for physics, chemistry, materials science and computational biology.

The program is divided in 2 moduli: (Advanced) MCMC methods (3 days); Molecular Dynamics with Julia (2 days). The first modulus is devoted to general lectures and hands-on sessions for both statisticians and applied mathematicians, and researchers from physics, chemistry, materials science and computational biology. The second modulus is dedicated to a training on the molecular dynamics package Molly, written in the Julia language, which allows an easy implementation of new numerical methods, while being quite computationally efficient. It is possible to attend only the first or the second part of the school.

## Program

### Monday, September 25th: Markov Chain Monte Carlo methods

09:00 - 09:30 Welcome coffee and registration

09:30 - 10:30 An introduction to high dimensional sampling, Gabriel Stoltz (Ecole des Ponts) 💬

10:30 - 10:45 Short break

10:45 - 11:45 Molecular dynamics simulations in biophysics, Paraskevi Gkeka (Sanofi) 💬

11:45 - 12:00 Short break

12:00 - 13:00 Applications and motivations in statistics and machine learning, Arnak Dalayan (ENSAE) 💬

13:00 - 14:00 Lunch

14:00 - 15:30 Numerical analysis of sampling errors, Benjamin Jourdain (Ecole des Ponts) 💬

15:30 - 16:00 Break

16:00 - 17:30 Hands-on Session: Discretization of Langevin dynamics and its Metropolization, Régis Santet (École des Ponts and Inria), 🗒️

17:30 - 18:00 Flash presentations by the participants (1’ each)

18:30 - 20:00 Poster session and cocktail

### Tuesday, September 26th: Advanced sampling methods

9:30 - 11:00 Coupling methods, Pierre Jacob (ESSEC) 💬

11:00 - 11:30 Break

11:30 - 13:00 Introduction to Sequential Monte Carlo strategies, Mathias Rousset (Inria Rennes) 💬

13:00 - 14:00 Lunch

14:00 - 15:30 Nonequilibrium systems and computation of transport coefficients, Urbain Vaes (Inria Paris) 💬

15:30 - 16:00 Break

16:00 - 18:00 Hands-on session: Nonequilibrium systems and coupling methods, Shiva Darshan (École des Ponts and Inria), 🗒️

19:30 Social dinner

### Wednesday, September 27th: Sampling trajectories

9:30 - 11:00 Accelerated molecular dynamics methods, Tony Lelièvre (Ecole des Ponts) 💬

11:00 - 11:30 Break

11:30 - 13:00 Hands-on session: Accelerated molecular dynamics methods, Noé Blassel (École des Ponts and Inria), 🗒️

13:00 - 14:30 Lunch

14:30 - 16:00 Adaptive multilevel splitting methods, Arnaud Guyader (Sorbonne- Université) 💬

16:00 - 16:30 Break

16:30 - 18:00 Hands-on session: Adaptive multilevel splitting methods, Arnaud Guyader (Sorbonne- Université)) 🗒️

### Thursday, September 28th: Molly (day 1)

9:30 - 11:00 Introduction to Julia, Antoine Levitt (Orsay University)

11:00 - 11:30 Break

11:30 - 13:00 Introduction to Molly, Joe Greener (MRC Laboratory of Molecular Biology) 💬

13:00 - 14:00 Lunch

14:00 - 17:00 Hands-on session: Computing average properties in molecular dynamics with Molly, Joe Greener (MRC Laboratory of Molecular Biology) 🗒️

### Friday, September 29th: Molly (day 2)

9:00 - 10:30 Coding and implementing with Molly, Joe Greener (MRC Laboratory of Molecular Biology) 💬

10:30 - 11:00 Break

11:00 - 11:30 Computation of transport coefficients with Molly, Noé Blassel (Ecole des Ponts) 💬

11:30 - 13:00 Hands-on session: Computation of transport coefficients with Molly, Renato Spacek (Ecole des Ponts) 🗒️

13:00 - 14:00 Lunch

## Speakers & Abstracts

Noé Blassel (Ecole des Ponts)

Title: Computation of transport coefficients with Molly

This lecture will present how to use the Julia package Molly to compute non-equilibrium properties of molecular systems. We will discuss in a first part how to use integrators in Molly to simulate Langevin dynamics, as well as how to implement the NEMD and Green-Kubo methods to compute transport coefficients.

Frédéric Cérou and Mathias Rousset (Inria Rennes)

Title: Introduction to Sequential Monte Carlo strategies

We will give a general audience introduction to the Feynman-Kac approach to Sequential Monte Carlo methods, with motivation from two generic problems that are ubiquitous in computational statistical physics. First problem: i) sampling a (''low-temperature'') target distribution known up to a normalization and computing the latter. Second problem: ii) estimating the large deviations of trajectory averages of Markov processes. A special focus on re-sampling schemes for weighted empirical averages will be given in the end.

Arnak Dalayan (ENSAE),

Title: Applications and motivations in statistics and machine learning

Paraskevi Gkeka (Sanofi)

Title: Molecular dynamics simulations in biophysics

Molecular dynamics (MD) is a key tool for studying biophysical phenomena. In this lecture, I will first introduce some basic notions and technical implications around MD: how to build a molecular model, how to describe the underlying physics and chemistry of the molecules and finally how to follow the evolution of the system of interest over time. In the second part of the lecture, I will try to highlight some of the key developments of MD applied in the pharmaceutical industry and propose some future directions of emerging methodologies.

Joe Greener (MRC Laboratory of Molecular Biology)

Title (session #1): Introduction to Molly

This lecture will introduce Molly.jl, an open-source pure Julia package for molecular dynamics. Molly allows flexible simulations including of biomolecules. Various common simulators and interactions are available, and users can define their own in a performant way.

Title (session #2): Coding and implementing with Molly

This lecture will describe more advanced use cases of Molly.jl, including implementing custom features and differentiable simulations. Design and performance considerations will be discussed, along with future plans for development.

Arnaud Guyader (Sorbonne- Université)

Title: Adaptive Multilevel Splitting methods

In this lecture, I will present a family of Monte Carlo techniques, called Adaptive Multilevel Splitting or Subset Simulation, to simulate and estimate rare events in a static context (rare event for a random vector) as well as in a dynamic one (rare event for a random process).

Pierre Jacob (ESSEC)

Title: Coupling methods

Since their introduction by Wolfgang Doeblin in the 1930s, couplings have been helpful in the study of the convergence of Markov chains to their stationary measure. In this lecture we review the basic coupling technique and its use in both theoretical and methodological developments of Markov chain Monte Carlo. Specifically we'll see how couplings can be used to obtain unbiased estimators of expectations with respect to the stationary measure, to obtain upper bounds on the mixing time, and to estimate the asymptotic variance in the central limit theorem for MCMC estimators

Benjamin Jourdain (Ecole des Ponts)

Title: Numerical analysis of sampling errors

In this lecture I will address the strong and weak errors introduced when discretizing by the Euler scheme a Stochastic Differential Equation with additive Brownian noise. I will present the multilevel Monte Carlo method, which, in this context, permits to recover the complexity of an unbiased Monte Carlo estimation. Finally, I will discuss the bias and statistical errors for the approximation of an integral with respect to the invariant measure of the SDE.

Tony Lelièvre (Ecole des Ponts)

Title: Accelerated molecular dynamics methods

Accelerated molecular dynamics are numerical methods which have been developed in Los Alamos National Laboratories over the past 30 years in order to efficiently sample metastable dynamics. We will present the mathematical foundations of accelerated molecular dynamics, using the quasi-stationary distribution approach to metastability. The analysis requires to make a rigorous link between two families of models to simulate the evolution of thermostated molecular systems: Langevin dynamics and kinetic Monte Carlo (or Markov State Models). The lectures will in particular present a natural way to justify the Harmonic Transition State Theory, namely the parametrization of transitions in kinetic Monte Carlo models by Eyring-Kramers formulas.

Antoine Levitt (Orsay University)

Title: Introduction to Julia

Julia has become in the last few years an alternative to the traditional model of both Fortran/C++ wrapped in python scripts (for application scientists) and Matlab/python (for applied mathematicians). I will explain what distinguishes it from the languages that came before, and introduce the main features of the language.

Gabriel Stoltz (Ecole des Ponts)

Title: An introduction to high dimensional sampling

The aim of this introductory lecture is to give some common basis for the talks to come. I will present some popular dynamics to sample probability measures, namely stochastic differential equations such as (overdamped) Langevin dynamics and their discretizations, and Metropolis-type algorithms.

Urbain Vaes (Inria Paris)

Title: Nonequilibrium systems and computation of transport coefficients

The calculation of transport coefficients from microscopic models constitutes an important application of computational statistical physics, because it enables bridging the microscopic and macroscopic properties of matter. These coefficients can be estimated at the microscopic level from the response of the system to small external forcings. More precisely, a transport coefficient can be defined as the expectation of an appropriate observable with respect to the probability distribution describing the steady state of the perturbed dynamics. Since there is generally no explicit expression for this probability distribution, standard Metropolis—Hastings approaches and methods for variance reduction are not directly applicable for the calculation of transport coefficients, and so other approaches need to be employed. In this lecture, we will present the main approaches for calculating transport coefficients, including estimators based on linear response and on the Green—Kubo formalism.

## Flash Presentations & Poster Session

➡️ Daniel Adams (Heriot-Watt university) [flash presentation]

Poster title: Wasserstein Gradient Flows

➡️ Charly Andral (Université Paris-Dauphine) [flash presentation]

Poster title: The Importance Markov Chain

➡️ Ainara Claveras Cabezudo (Max Planck Institute of Biophysics) [flash presentation]

Poster title: Theoretical Investigation of Cellular Transporters

➡️ Shiva Darshan (École des Ponts and Inria) [flash presentation]

Poster title: Sticky Coupling as a Control Variate for Computing Transport Coefficients

➡️ Leonardo Galliano (University of Trieste) [flash presentation]

Poster title: Policy Guided Monte Carlo for Glassy Liquids

➡️ Nicolaï Gouraud (Sorbonne Université) [flash presentation]

Poster title: Velocity jump processes: an alternative route for faster molecular dynamics simulations

➡️ Louis Grenioux (École polytechnique) [flash presentation]

Poster title: On Sampling with Approximate Transport Maps and Balanced Training of Energy-Based Models with Adaptive Flow Sampling

➡️ David Greten (Fritz Haber Institute of the Max Planck Society) [flash presentation]

Poster title: Exploring Enhanced Sampling Using Boltzmann Generators

➡️ Lei Guo (Max Planck Institute for Dynamics of Complex Technical Systems) [flash presentation]

Poster title: Bi-linear Control Based On gEDMD for Metastable Systems

➡️ Stefan Oberdörster (University of Bonn) [flash presentation]

Poster title: Mixing of accept/reject Markov chains

➡️ Francesco Paolo Panei (Institut Pasteur and Sanofi) [flash presentation]

Poster title: Identifying small molecules binding sites in RNA conformational ensemble with SHAMAN

➡️ Dominic Phillips (University of Edinburgh) [flash presentation]

Poster title: Numerics with Coordinate Transforms for More Efficient Brownian Dynamics Simulations

➡️ Julia Stebani (Technical University of Munich) [flash presentation]

Poster title: Machine Learning-Assisted Selection of Collective Variables for Metadynamics - Application on Drug/Target Interactions

➡️ Alexander Sikorski (Zuse Institute Berlin) [flash presentation]

Poster title: ISOKANN - Learning the slowest dynamics from burst simulations

➡️ Xinyi Wu (University of Birmingham) [flash presentation]

Poster title: Computation of Transport Coefficients in Dissipative Particle Dynamics (DPD)

➡️ Lionel Zoubritzky (Chimie ParisTech - PSL and Air Liquide) [flash presentation]

Poster title: Crossed Methodologies for the Simulation and Prediction of Small Gas Adsorption in Zeolites

## Hands-on Sessions

Python and Julia notebooks for the hands-on sessions can be found al the following links:

Monday, Sept. 25: Discretization of Langevin dynamics and its Metropolization

Tuesday, Sept. 26: Nonequilibrium systems and coupling methods

Wednesday, Sept. 27 (morning): Accelerated molecular dynamics methods

Wednesday, Sept. 27 (afternoon): Adaptive multilevel splitting methods

Thursday, Sept. 28: Computing average properties in molecular dynamics with Molly.jl

Friday, Sept. 29: Computation of transport coefficients with Molly.jl [in preparation]

The repository containing all these notebooks can be found here.

## Getting to CERMICS

If you are arriving from outside the campus, please make a stop at RER A Noisy-Champs and locate the 'Cité Descartes' exit. To enter Ecole des Ponts, proceed through the security checkpoint on Boulevard Copernic, following the recommended route shown on the Google Maps image below.

Upon arrival, campus security may inquire about the purpose of your visit. Rest assured that we will provide them with a list of attendees the week before the event.

The Coriolis building is situated towards the rear of the campus and is easily recognizable due to its distinctive wooden architecture (see the picture alongside).

The conference room is located in the left wing of the building on the second floor, specifically in room B211.

Many thanks to Anne-Laure Chagnon for the school poster and to Stéphanie Bonnel for the picture and her precious help!

Many thanks also to Isabelle Simunic for the administrative support.

## Applications (closed)

Interested candidates should fill in this application form (a CV and a recommendation letter are required) before the deadline on May 28, 2023.

There are no registration fees. The following expenses are covered for everyone:

coffee breaks and lunches,

reception during the poster session on Monday evening,

social dinner on Tuesday evening

Accommodation in a nearby hotel can be provided to participants requiring it via the application form (from Sunday evening to Wednesday for those participating to the first part of the school only, from Wednesday evening to Friday for those participating to the second part only, and from Sunday evening to Friday for those participating to both parts).

Other expenses (extra nights of accommodation, travel expenses, dinners) are not covered.

We explicitly encourage female researchers to apply.