Related papers: Riemannian Stochastic Interpolants for Amorphous P…

Using normalizing flows and reweighting, Boltzmann Generators enable equilibrium sampling from a Boltzmann distribution, defined by an energy function and thermodynamic state. In this work, we introduce Thermodynamic Interpolation (TI),…

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering…

We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…

We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an…

We are interested in the challenging problem of modelling densities on Riemannian manifolds with a known symmetry group using normalising flows. This has many potential applications in physical sciences such as molecular dynamics and…

Inorganic crystals are periodic, highly-symmetric arrangements of atoms in three-dimensional space. Their structures are constrained by the symmetry operations of a crystallographic \emph{space group} and restricted to lie in specific…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through…

A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field…

Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…

Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…

Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a…

We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for…

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

Using a well defined soft model glass in the framework of Molecular Dynamics simulations, the inherent structures are probed by means of a recently developed deformation protocol that aims to capture the Dynamical Heterogeneities (DH), as…