Related papers: Discrete-Time Fractional-Order Dynamical Networks …
Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
This paper focuses on analysis and design of time-varying complex networks having fractional order dynamics. These systems are key in modeling the complex dynamical processes arising in several natural and man made systems. Notably,…
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Accurate estimation of the State of Charge (SOC) is critical for ensuring the safety, reliability, and performance optimization of lithium-ion battery systems. Conventional data-driven neural network models often struggle to fully…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
Accumulated detailed knowledge about the neuronal activities in human brains has brought more attention to bio-inspired spiking neural networks (SNNs). In contrast to non-spiking deep neural networks (DNNs), SNNs can encode and transmit…
State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
With the advances in high resolution neuroimaging, there has been a growing interest in the detection of functional brain connectivity. Complex network theory has been proposed as an attractive mathematical representation of functional…
We devise neuro-dynamic state estimation (Neuro-DSE), a learning-based dynamic state estimation (DSE) algorithm for networked microgrids (NMs) under unknown subsystems. Our contributions include: 1) a data-driven Neuro-DSE algorithm for NMs…
Fluctuation theorems (FTs) quantify the thermodynamic reversibility of a system, and for deterministic systems they are defined in terms of the dissipation function. However, in a nonequilibrium steady state of deterministic dynamics, the…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…
This paper investigates typical behaviors like damped oscillations in fractional order (FO) dynamical systems. Such response occurs due to the presence of, what is conceived as, pseudo-damping and meta-damping in some special class of FO…
To ensure frequency security in power systems, both the rate of change of frequency (RoCoF) and the frequency nadir (FN) must be explicitly accounted for in real-time frequency-constrained optimal power flow (FCOPF). However, accurately…
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…