Related papers: Forward sensitivity analysis of the FitzHugh-Nagum…

Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

Accurate trajectory prediction is vital for autonomous driving, robotics, and intelligent decision-making systems, yet traditional models typically rely on fixed-length output predictions, limiting their adaptability to dynamic real-world…

This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this regime, the time step can be subject to stability…

The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model is analyzed. We show that the firing rate is diminished as the ratio of the high-frequency amplitude to its frequency is increased. Moreover, it is demonstrated…

Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect…

In this work, a three-dimensional multicomponent reaction-diffusion model has been developed, combining excitable-system dynamics with diffusion processes and sharing conceptual features with the FitzHugh-Nagumo model. Designed to capture…

The challenges in feature selection, particularly in balancing model accuracy, interpretability, and computational efficiency, remain a critical issue in advancing machine learning methodologies. To address these complexities, this study…

We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the…

Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…

Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump…

This perspective article investigates how auditory stimuli influence neural network dynamics using the FitzHugh-Nagumo (FHN) model and empirical brain connectivity data. Results show that synchronization is sensitive to both the frequency…

This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…

We propose a novel inverse-modelling approach which estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable physics-based forward model. The governing equations are expressed within a…

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory…

We study invasion fronts in the FitzHugh--Nagumo equation in the oscillatory regime using singular perturbation techniques. Phenomenologically, localized perturbations of the unstable steady-state grow and spread, creating temporal…

Brain operates at remarkably low signal power. It has been noted that noise may play a constructive role in neural networks and facilitate the subthreshold signaling. The process of spiking pattern excitation at the characteristic neuronal…

The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the formation and bifurcation structure of spatially localized states…

In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first…

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity…