Related papers: Random batch methods (RBM) for interacting particl…
We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain a gradient flow that does so. By approximating the latter…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…
A multi-scale meshfree particle method for macroscopic mean field approximations of generalized interacting particle models is developed and investigated. The method is working in a uniform way for large and small interaction radii. The…
We report results from a computer simulation study on the rotational ratchet effect in systems of magnetic particles interacting via dipolar interactions. The ratchet effect consists of directed rotations of the particles in an oscillating…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…
The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the…
Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers…