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Ultrastable glasses have risen to prominence due to their potentially useful material properties and the tantalizing possibility of a general method of preparation via vapor deposition. Despite the importance of this novel class of…

Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…

Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down…

Stochastic interpolants unify flows and diffusions, popular generative modeling frameworks. A primary hyperparameter in these methods is the interpolation schedule that determines how to bridge a standard Gaussian base measure to an…

In addressing the challenge of Crystal Structure Prediction (CSP), symmetry-aware deep learning models, particularly diffusion models, have been extensively studied, which treat CSP as a conditional generation task. However, ensuring…

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

Determining whether a candidate crystalline material is thermodynamically stable depends on identifying its true ground-state structure, a central challenge in computational materials science. We introduce CrystalGRW, a diffusion-based…

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of…

In this study, a new alternative model algorithm has been proposed for assembling amorphous structures, unifying the bosonic paradigm applicable at low temperatures with crystalline models relevant at room and higher temperatures. Physical…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in…

Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…

Auto encoding models have been extensively studied in recent years. They provide an efficient framework for sample generation, as well as for analysing feature learning. Furthermore, they are efficient in performing interpolations between…

One of the greatest challenges facing our society is the discovery of new innovative crystal materials with specific properties. Recently, the problem of generating crystal materials has received increasing attention, however, it remains…

This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…

In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems…

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic…

Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation,…