Related papers: Stable Invariant Models via Koopman Spectra

This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak…

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this…

Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven…

Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large…

With the development of end-to-end control based on deep learning, it is important to study new system modeling techniques to realize dynamics modeling with high-dimensional inputs. In this paper, a novel Koopman-based deep convolutional…

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such…

In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady 3D fluid-structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a…

We study the learning problem associated with spiking neural networks. Specifically, we focus on spiking neural networks composed of simple spiking neurons having only positive synaptic weights, equipped with an affine encoder and decoder;…

In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

In this article, we present a framework for designing neural networks that remain consistent with the underlying principles of agent-based models. We begin by highlighting the limitations of standard neural differential equations in…

Stacked intelligent metasurfaces (SIMs) facilitate computation by cascaded programmable layers so that part of the signal processing can be performed in the wave domain during signal propagation, rather than solely after reception. This…

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated…

The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…

Stacked intelligent metasurfaces (SIMs) have recently emerged as a promising metasurface-based physical-layer paradigm for wireless communications, enabling wave-domain signal processing through multiple cascaded metasurface layers.…

Experimental manipulations perturb the neuronal activity. This phenomenon is manifested in the fMRI response. Dynamic causal model and its variants can model these neuronal responses along with the BOLD responses [1, 2, 3, 4, 5] .…

Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…

Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior…

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…