Related papers: Multiscale Computations on Neural Networks: From t…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
Over the past few years it has been demonstrated that "coarse timesteppers" establish a link between traditional numerical analysis and microscopic/ stochastic simulation. The underlying assumption of the associated…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for {\it heterogeneous} populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each…
Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between neural…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free- energy…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are…
Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…
Recent years have seen dramatic progress in the development of techniques for measuring the activity and connectivity of large populations of neurons in the brain. However, as these techniques grow ever more powerful---allowing us to even…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to…
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a…
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain. Inspired by our early study in \cite{li2018data}, we…