Probabilistic sampling for physics: finding needles in a field of high-dimensional haystacks

Abstracts

45. Welcome address

04/09/2023 09:30

General address

2. Flashtalks - Amphitheatre

04/09/2023 10:30

17. Finding saddle points of energy landscapes: why and how?

Tony LELIEVRE (Ecole des Ponts ParisTech)

04/09/2023 11:30

Challenge and Perspective

One way to bridge the scale between full atomistic models and more coarse-grained descriptions is to use Markov State models parameterized by the Eyring Kramers formulas. These formulas give the hopping rates between local minima of the potential energy function. They require to identify the local minima and saddle points of the potential energy function. This approach is for example used in...

9. Exploration with saddle point search

Pierre Monmarche

04/09/2023 14:00

Challenge and Perspective

According to Large Deviation Principles, in a metastable regime, a local explorer is likely to exit from local modes through energy saddle points. Looking alternatively for minimizers or saddle points thus appears as a reasonable direction in order to find unknown modes in a high-dimensional non-convex landscape. The goal of this talk is to introduce the useful tools for that purpose, in...

18. Predicting the atomic kinetics of materials with uncertainty

Thomas Swinburne (Centre Interdisciplinaire de Nanoscience de Marseille, CNRS, Aix-Marseille Université)

04/09/2023 15:30

Challenge and Perspective

I will discuss two methods to coarse-grain and predict atomic kinetics generated by molecular dynamics, with application to diffusion and plasticity in metals. When the energy landscape is metastable, atomic kinetics can be mapped to a discrete Markov chain with robust Bayesian bounds on unseen transitions. These bounds are used to allocate resources in massively parallel computation and...

33. Metastability

Thomas Swinburne (Centre Interdisciplinaire de Nanoscience de Marseille, CNRS, Aix-Marseille Université)

04/09/2023 16:30

Brainstorming

3. Population Monte Carlo as a meta-algorithm

Martin Weigel (Chemnitz University of Technology, Chemnitz, Germany)

05/09/2023 10:00

Challenge and Perspective

As a meta-algorithm, population annealing can be combined with a wide range of simulation methods, including Monte Carlo and molecular dynamics. In the past, we have analyzed the approach regarding the scaling of statistical and systematic errors, proposed improvements and implemented the method on highly-efficient graphics processing units. In the present talk I will discuss recent...

5. Sampling glassy disordered systems

Misaki Ozawa (CNRS, Univ. Grenoble Alpes, France)

05/09/2023 11:30

Challenge and Perspective

In this talk, I will introduce sampling issues in glassy disordered systems, particularly glass-forming liquids, which consist of a long-standing problem in condensed matter physics. I will explain why this is important and difficult, and I will review various previous attempts.

15. Upgrading MCMC dynamics by necessary symmetries and non-reversibility

Manon MICHEL (LMBP)

05/09/2023 14:00

Challenge and Perspective

In this talk, I will review the older and most recent developments regarding reversibility breaking in Markov-chain Monte Carlo (MCMC), from lifting to piecewise deterministic Markov processes. This will offer the opportunity to discuss the differences between necessary and sufficient symmetries for correctness in MCMC and how removing restrictive conditions can lead to more efficient...

34. Beyond random-walk behavior

Manon MICHEL (LMBP)

05/09/2023 15:30

Brainstorming

42. Multiscale Interaction Models of Physical Energies and Deep Networks - Stéphane Mallat (ENS Paris)

06/09/2023 10:00

Colloquium

Building probabilistic models and sampling complex physical fields is an outstanding issue, despite remarkable numerical results of deep networks. Relying on the renormalization group approach, we show that the curse of dimensionality can be avoided by separating variabilites at multiple scales in wavelet bases. The main difficulty is to model interactions across scales. We show that these...

4. Sampling with generative models

Grant Rotskoff (Stanford University)

06/09/2023 11:30

Challenge and Perspective

In probability theory, the notion of "weak convergence" is often used to describe two equivalent probability distributions. This metric requires equivalence of the average value of well-behaved functions under the two probability distributions being compared. In coarse-grained modeling, Noid and Voth developed a thermodynamic equivalence principle that has a similar requirement. Nevertheless,...

12. The effect of Monte Carlo Sampling in the training of Energy Based Models

Beatriz Seoane Bartolomé (LISN)

06/09/2023 14:00

Challenge and Perspective

Energy-based models (EBMs) are powerful generative machine learning models that are able to encode the complex distribution of a dataset in the Gibbs-Boltzmann distribution of a model energy function. This means that, if properly trained, they can be used to synthesize new patterns that resemble those of the data set as closely as possible, but also that this energy function can be used to...

8. Opportunities and challenges in enhancing sampling with generative models

Marylou Gabrié (École Polytechnique)

06/09/2023 15:30

Challenge and Perspective

Deep generative models parametrize very flexible families of distributions able to fit complicated datasets of images or text. These models provide independent samples from complex high-distributions at negligible costs. On the other hand, sampling exactly a target distribution, such a Bayesian posterior, is typically challenging: either because of dimensionality, multi-modality,...

35. Learning and Sampling

Grant Rotskoff (Stanford University)

06/09/2023 16:30

Brainstorming

11. Dimensionality Reduction and Metastability Analysis using the Koopman Operator

Feliks Nüske (Max Planck Institute DCTS Magdeburg)

07/09/2023 10:00

Challenge and Perspective

The Koopman Operator presents a powerful framework for dimensionality reduction of (stochastic) dynamical systems. In addition, metastable sets and their rates of transition can be obtained by analysing its spectrum. In this talk, we first recap the basics of Koopman methods, and then move on to discuss recent advances and current challenges.

28. Stochastic models form enhanced sampling in Chemistry

Léon Huet (IMPMC - Sorbonne Université)

07/09/2023 11:30

Result Communication

The study of chemical reactions involving covalent links and breaks inherently presents stochastic complexities. To overcome the challenges posed by large energy barriers, researchers commonly use enhanced sampling techniques like transition path sampling and umbrella sampling to collect relevant data at the DFT level. However, the data acquired through these processes requires careful...

19. Sparse approximation of the Lieb functional in DFT with moment constraints

Virginie EHRLACHER (Ecole des Ponts ParisTech & INRIA)

07/09/2023 14:00

Challenge and Perspective

(joint work with Luca Nenna)
In this talk, we will present recent mathematical results about the Lieb functional in Density Functional Theory. More precisely, the Lieb functional, for a given electronic density, can be viewed as a generalized form of optimal transport problem for which the electronic density plays the role of a marginal. A numerical discretization of this problem can be...

6. Barrier Hamiltonian Monte Carlo

Alain Durmus (Ecole Polytechnique)

07/09/2023 15:30

Challenge and Perspective

This talk introduces Barrier Hamiltonian Monte Carlo (BHMC), a version of HMC which aims at sampling from a Gibbs distribution π on a manifold M, endowed with a Hessian metric g derived from a self-concordant barrier. Like Riemannian Manifold HMC, our method relies on Hamiltonian dynamics which comprise g. It incorporates the constraints defining M and is therefore able to exploit its...

36. Preserving physics in dynamics

Pierre Monmarche

07/09/2023 16:30

Brainstorming

23. Discover committor-consistent path by neural networks

Haochuan Chen (University of Lorraine)

08/09/2023 10:00

Result Communication

A significant challenge faced by atomistic simulations is the difficulty, and often impossibility, to sample the transitions between metastable states of the free-energy landscape associated to slow molecular processes. Importance-sampling schemes represent an appealing option to accelerate the underlying dynamics by smoothing out the relevant free-energy barriers, but require the definition...

27. Stochastic Interpolants: A unifying framework for flows and diffusions

Michael Albergo (New York University)

08/09/2023 10:30

Result Communication

I will discuss recent work on unifying flow-based and diffusion based methods through a
generative modeling paradigm we call stochastic interpolants. These models enable the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining...

30. Beyond translational flows in non-reversible sampling

Tristan Guyon (Laboratoire de Mathématiques Blaise Pascal, Université Clermont-Auvergne)

08/09/2023 11:30

Result Communication

Breaking reversibility in Monte Carlo algorithms often leads to substantial accelerations in sampling complex systems. Event-Chain Monte Carlo (ECMC) has allowed to investigate the bidimensional hard-sphere phase transition, building on non-reversible continuous translational moves. However, more general systems require rotations of some sort to thermalize.
In this work, we build on the...

25. Sampling efficiency of transverse forces in dense liquids

Federico Ghimenti (Université Paris Cité)

08/09/2023 12:00

Result Communication

Sampling the Boltzmann distribution using forces that violate detailed balance can be faster than with the equilibrium evolution, but the acceleration depends on the nature of the nonequilibrium drive and the physical situation. Here, we study the efficiency of forces transverse to energy gradients in dense liquids through a combination of techniques: Brownian dynamics simulations, exact...

26. Parallel Replica algorithm for Langevin dynamics and Adaptative Metadynamics

Mouad Ramil

08/09/2023 12:30

Result Communication

This talk will be divided into two independent parts. The first part shall focus on the extension of the formalization of an algorithm (Parallel Replica) to the case of the Langevin dynamics. Parallel Replica is used in material science to sample rare-events and consists in a parallelization in time of the sampling. It can be formalized using the notion of quasi-stationary distributions which...

20. Optimizing the diffusion for sampling with overdamped Langevin dynamics Gabriel Stoltz (CERMICS ,Ecole des Ponts and Matherials, Inria Paris)

Gabriel STOLTZ (Ecole des Ponts & Inria Paris)

11/09/2023 10:00

Challenge and Perspective

Overdamped Langevin dynamics are stochastic differential equations, where gradient dynamics are perturbed by noise in order to sample high dimensional probability measures such as the ones appearing in computational statistical physics and Bayesian inference. By varying the diffusion coefficient, there are in fact infinitely many overdamped Langevin dynamics which preserve the target...

10. Dynamically-accurate biasing using Accelerated Molecular Dynamics

Dr Danny Perez (Los Alamos National Laboratory)

11/09/2023 11:30

Challenge and Perspective

Modifying or biasing the dynamics of atomistic systems can result in faster mixing and convergence of thermodynamic observables, but it generally yields non-physical kinetics. I will introduce a family of so called "Accelerated Molecular Dynamics" methods that are specifically designed to produce statistically accurate "state-to-state" dynamics for metastable systems at a much reduced...

40. Sampling Complex Energy Landscapes in Material Science Using Data-Driven Force Fields - Mihai Cosmin Marinica

11/09/2023 14:00

Challenge and Perspective

A. Zhong (1), C. Lapointe (1), A.M. Goryaeva (1), J. Wrobel (3), T. D. Swinburne (2),
A. Allera (1), M. Athènes (1), M.-C. Marinica (1)

(1)DES - Service de Recherches de Métallurgie Physique, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
(2)CNRS, Centre Interdisciplinaire de Nanoscience de Marseille (CINaM), Université Aix-Marseille, France
(3) Faculty of Materials...

37. Enhanced sampling

Gabriel STOLTZ (Ecole des Ponts & Inria Paris)

11/09/2023 15:00

Brainstorming

7. Limiting distributions of Glauber coupling times

Tim Garoni (Monash University)

12/09/2023 10:00

Challenge and Perspective

Coupling from the past is a method for obtaining perfect samples from Markov chain Monte Carlo algorithms. The price paid is that the running time becomes random. We will present some recent results concerning the limit behaviour of this random time, and discuss a number of open conjectures.

21. Coupling methods to de-bias and assess MCMC algorithms

Pierre JACOB (ESSEC Business School)

12/09/2023 11:30

Challenge and Perspective

How to parallelize computation and how to diagnose convergence remain largely open questions regarding MCMC. Since Glynn & Rhee (Journal of Applied Probability, Vol. 51A, 2014), various advances based on couplings of MCMC algorithms have been proposed. The key is the design of coupled chains that, if properly constructed, can be employed to construct estimators that do not suffer from the...

47. Sampling protein structure

Frederic Cazals (Inria)

12/09/2023 14:00

Challenge and Perspective

Setting aside the problem of designing force fields, sampling protein conformations to estimate their thermodynamic and kinetic properties remains a challenge. In this talk, I will review recent work on two connected problems in this realm.

The first one is the calculation of high dimensional volumes of polytopes, using random walks (hit-and-run, HMC, PDMP).

The second one is the...

39. Mixing and convergence

Tim Garoni (Monash University)

12/09/2023 15:30

Brainstorming

13. Anomalous thermal relaxations of physical systems

Marija Vucelja (University of Virginia)

13/09/2023 10:00

Result Communication

Rapid cooling or heating of a physical system can lead to unusual thermal relaxation phenomena. A prime example of anomalous thermal relaxation is the Mpemba effect. The phenomenon occurs when a system prepared at a hot temperature overtakes an identical system prepared at a warm temperature and equilibrates faster to the cold environment. A similar effect exists in heating. Comparing two...

29. Approximate sampling and estimation of partition functions using neural networks

Eiji Kawasaki (CEA)

14/09/2023 14:00

Faraday discussion

Discussion about the arXiv preprint 2209.10423

"We consider the closely related problems of sampling from a distribution known
up to a normalizing constant, and estimating said normalizing constant. We show
how variational autoencoders (VAEs) can be applied to this task. In their standard
applications, VAEs are trained to fit data drawn from an unknown and intractable
distribution. We...

32. Probabilistic forecast of extreme heat waves and climate tipping points using neural networks and rare event simulations

Freddy BOUCHET (ENS, LMD, IPSL)

14/09/2023 15:30

Colloquium

Rare events are of primarily importance for understanding the impact of climate change. The first class are extreme events which have devastating impacts; the second are rare trajectories which lead to bifurcations and drastic changes of the climate system configurations and tipping points. However, because those events are too rare and realistic models are too complex, they cannot be computed...

43. Cooperative learning: improving inference through sampling with coupled systems

Giovanni CATANIA (Universidad Complutense Madrid)

15/09/2023 10:00

Result Communication

Constraint Satisfaction problems (CSPs) deal with finding a solution to a set of variables that satisfy a set of constraints. In the last decade, it has been found that many CSPs can have different levels of computational hardness when the number of constraints is changed. The same issue arises in inference problems in the so-called planted setting, where a planted configuration always exists...

44. Anharmonic thermo-elasticity of tungsten from accelerated Bayesian adaptive biasing force calculations with data-driven force fields

Anruo Zhong (Université Paris-Saclay, CEA, Service de Recherche en Corrosion et Comportement des Matériaux, SRMP, 91191 Gif-sur-Yvette, France)

15/09/2023 10:30

Result Communication

The elastic properties of tungsten, a ubiquitous material in future energy systems, are investigated up to its melting temperature by means of a data-driven approach. The proposed workflow combines machine learning of the force field and enhanced sampling of the crystalline structure. While the machine learning force field achieves the accuracy of ab initio calculations, its implementation in...

46. Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective

Davide Ghio (EPFL)

18/09/2023 10:00

Result Communication

Recent years witnessed the development of powerful generative models based on flows, diffusion or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical analysis of the performance and understanding of the limitations of these methods remain, however, challenging.

In this talk, I present our...

24. Disentangling representations in RBMs without adversaries

Jorge Fernández de Cossío Díaz (PSL)

18/09/2023 10:30

Result Communication

A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. The methods for disentangling representations often rely on an adversarial...

41. Learning in Restricted Boltzmann Machines: The Critical Role of Sampling Processes

Aurélien DECELLE (Universidad Complutense de Madrid)

19/09/2023 10:00

Faraday discussion

Generative models aim to learn the empirical distribution of a given data set in order to build a probabilistic model capable of generating new samples that are statistically similar to the data set. One can also assume that one can obtain an approximately tractable analytical description of this distribution.

In this presentation, I will specifically consider the case of the so-called...

14. Renormalization Group Approach for Machine Learning Hamiltonian

Misaki Ozawa (CNRS, Univ. Grenoble Alpes, France)

20/09/2023 10:00

Result Communication

Reconstructing, or generating, high dimensional probability distributions starting from data is a central problem in machine learning and data sciences.
We will present a method —The Wavelet Conditional Renormalization Group —that combines ideas from physics (renormalization group theory) and computer science (wavelets, Monte-Carlo sampling, etc.). The Wavelet Conditional Renormalization...

31. Sampling with Neural Hamiltonian Flows

Vincent Souveton (LMBP - Université Clermont Auvergne)

20/09/2023 10:30

Result Communication

Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced, Neural Hamiltonian Flows (NHF) are Hamiltonian dynamics-based flows, which are continuous, volume-preserving and invertible and thus make for natural...

38. Rare events, large deviation and sampling

Alberto ROSSO (LPTMS-CNRS)

20/09/2023 15:30

Colloquium

In many systems exceptional events can have a crucial impact, while the routine is peaceful and with no consequences. Well known examples are the earthquakes in the Earth's lithosphere or the events of extreme weather. Predicting their magnitude or their occurrence rate is a major challenge for human security and economy. Large deviation theory is the branch of probabilities that adresses...

48. Conditioning and variance reduction schemes for more accurate estimation of thermodynamic and transport properties of metal alloys - Manuel Athènes

21/09/2023 10:00

Result Communication

The Monte Carlo method is a stochastic simulation approach mainly used to estimate multi-dimensional integrals. This is traditionally done by generating a Markov chain of states and then implementing an estimator. In this context, conditioning is a trick consisting in doing part of the job in closed form, through numerical quadrature, so as to reduce the statistical variance associated with...

49. Active particle systems through the lens of piecewise deterministic Markov processes

Léo Hahn (Université Clermont Auvergne)

22/09/2023 10:00

Result Communication

Run-and-tumble particles are a paradigmatic model in out-of-equilibrium physics that exhibits interesting phenomena not found in their passive counterparts such as motility-induced phase separation. I will present the long-time behavior of a pair of such particles with hard-core interactions on a unidimensional torus and on a line by casting them as a piecewise deterministic Markov process. I...

50. Splitting schemes for second order approximations of piecewise-deterministic Markov processes

Andrea Bertazzi (CMAP École polytechnique)

22/09/2023 10:30

Result Communication

Piecewise deterministic Markov processes (PDMPs) received substantial interest in recent years as an alternative to classical Markov chain Monte Carlo algorithms. While theoretical properties of PDMPs have been studied extensively, their practical implementation remains limited to specific applications in which bounds on the gradient of the negative log-target can be derived. In order to...

22. Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori-Zwanzig formulation

David Aristoff

Result Communication

Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. Summarizing and analyzing the results of such simulations is often challenging, due to the high dimension in which simulations are carried out (and consequently to the very large amount of data that is typically generated).
Coarse graining is a popular technique for addressing this problem by...