Related papers: Universal Approximation of Mean-Field Models via T…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…
Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…
A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff's mean-field approach with the model presented by one…
We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated…
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 study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a…
We demonstrate that a mean field approximation can be confidently employed in quasiperiodic moir\'e systems to treat interactions and quasiperiodicity on equal footing. We obtain the mean field phase diagram for an illustrative…
No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glass and jamming is a mean field theory which attempts to do so by working in the limit of infinite dimensions, such that…
It is known that on directed graphs, the correlations between neighbours of a given site vanish and thus simple mean-field-like arguments can be used to describe exactly the behaviour of Ising-like systems. We analyse heterogeneous…
Transformer architectures have achieved remarkable empirical success in modeling contextual relations, yet a clear understanding of their expressive power is still lacking. In this work, we introduce a measure-theoretic framework in which…
The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…
A brief, tutorial account is given of the differences between the near and far regions of the elec-tromagnetic field emphasizing the source-dependent behavior of the former and the universal properties of the latter. Field patterns of…
We develop theoretical diagnostics for the breakdown of mean-field theory, demonstrate how spatial structure and finite interaction ranges enter the effective description, and show how these scales qualitatively modify the…
Transformer-based models have transformed the landscape of natural language processing (NLP) and are increasingly applied to computer vision tasks with remarkable success. These models, renowned for their ability to capture long-range…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…