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Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
Cosmologists aim to model the evolution of initially low amplitude Gaussian density fluctuations into the highly non-linear "cosmic web" of galaxies and clusters. They aim to compare simulations of this structure formation process with…
The prediction of dynamical stability of power grids becomes more important and challenging with increasing shares of renewable energy sources due to their decentralized structure, reduced inertia and volatility. We investigate the…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…
We consider global and gravitational lensing properties of the recently suggested Einstein clusters of WIMPs as galactic dark matter halos. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
This study presents residual U-Net (U-ResNet), a deep learning surrogate model for predicting steady hemodynamic fields in two-dimensional asymmetric stenotic channels at Reynolds numbers ranging from 200 to 800. By integrating residual…
Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…
The prediction of the electric field (E-field) plays a crucial role in monitoring radiofrequency electromagnetic field (RF-EMF) exposure induced by cellular networks. In this paper, a deep learning framework is proposed to predict E-field…
An exact and explicit ladder-tensor-network ansatz is presented for the non-equilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges…
We consider a deep structured linear network under sparsity constraints. We study sharp conditions guaranteeing the stability of the optimal parameters defining the network. More precisely, we provide sharp conditions on the network…
This paper establishes a theoretical framework to describe the transition from consensus to stable clustering in multi-agent systems with nonlinear, cooperative interactions. We first establish a sharp threshold for consensus. For a broad…
The stability of a class of electrically charged fluid spheres under radial perturbations is studied. Among these spheres there are regular stars, overcharged tension stars, regular black holes, quasiblack holes, and quasinonblack holes,…
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…
Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and…
We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…
Deep neural networks have shown remarkable performance across a wide range of vision-based tasks, particularly due to the availability of large-scale datasets for training and better architectures. However, data seen in the real world are…
Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field…
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…