Related papers: Dual Geometric Worm Algorithm for Two-Dimensional …
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even…
Lattice formulation of a fermionic field theory defined on a randomly triangulated compact manifold is discussed, with emphasis on the topological problem of defining spin structures on the manifold. An explicit construction is presented…
In this paper a class of dynamical systems describing deterministic neural network models are formulated from a viewpoint of differential geometry. This class includes the Hopfield model and gradient systems, and is such that the so-called…
Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
We discuss worm algorithms for the 3-state Potts model with external field and chemical potential. The complex phase problem of this system can be overcome by using a flux representation where the new degrees of freedom are dimer and…
In this study, we evaluate the performance of three algorithms as computational models of trabecular bone architecture, through systematic evaluation of morphometric, topological, and mechanical properties. Here, we consider the widely-used…
A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this…
The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…
In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the best algorithm in the literature for solving this problem. In light…
In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…
We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square…