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We outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we showed that the effective potential can be probabilistically…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone…
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…
Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…
Interacting particle or agent systems that display a rich variety of swarming behaviours are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and…
We consider a special type of Restricted Boltzmann machine (RBM), namely a Gaussian-spherical RBM where the visible units have Gaussian priors while the vector of hidden variables is constrained to stay on an ${\mathbbm L}_2$ sphere. The…
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…
Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…
Random reshuffling with momentum (RRM) corresponds to the SGD optimizer with momentum option enabled, as found in many machine learning libraries like PyTorch and TensorFlow. Despite its widespread use, the convergence properties of RRM do…
This review deals with Restricted Boltzmann Machine (RBM) under the light of statistical physics. The RBM is a classical family of Machine learning (ML) models which played a central role in the development of deep learning. Viewing it as a…
In this book chapter, we review how systems of simple motile agents can be used as a pathway to intelligent systems. It is a well known result from nature that large groups of entities following simple rules, such as swarms of animals, can…
Restricted Boltzmann Machines (RBMs) are a common family of undirected graphical models with latent variables. An RBM is described by a bipartite graph, with all observed variables in one layer and all latent variables in the other. We…
In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number of particles with expectation greater…
This study analyses a method to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by the improper discretisation of required source terms. The work focuses on…
Last years have seen a regain of interest for the use of stochastic block modeling (SBM) in recommender systems. These models are seen as a flexible alternative to tensor decomposition techniques that are able to handle labeled data. Recent…
Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to math finance, and under general stability conditions, it has a unique stationary distribution.…