Related papers: A gradient flow formulation of the Lohe matrix mod…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
We develop a gradient flow on the space of probability measures defined on matrix-valued parameters induced by regularized Muon, an analytically smoothed version of the idealized Muon optimizer. The key observation is that the regularized…
The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
The paper contains an application of the generalized lattice model to multicomponent systems with internal degrees of freedom. The short-range inter-atomic repulsions and smooth long-range parts of the inter-atomic potentials are considered…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the…
We prove a compactness result for gradient flow lines in a general set-up which comprises both the situation of Morse gradient flow lines as well as Floer cylinders converging to a critical submanifold respectively. For the compactness…
We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state…
A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers' law as an…
We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a…
Fermionic gradient flow in combination with the short-flow-time expansion provides a computational method where the renormalisation of hadronic matrix elements on the lattice can be simplified to address e.g. the issue that operators with…
The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions…
The gradient (Wilson) flow has been introduced recently in order to provide a solid theoretical framework for the smoothing of ultraviolet noise in lattice gauge configurations. It is interesting to ask how it compares with other, more…
We present the first proof of principle that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model - a key framework for describing the electronic structure of graphene and related materials.…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…