218 research outputs found
Parameter identification in networks of dynamical systems
Mathematical models of real systems allow to simulate their behavior in conditions that are not easily or affordably reproducible in real life. Defining accurate models, however, is far from trivial and there is no one-size-fits-all solution.
This thesis focuses on parameter identification in models of networks of dynamical systems, considering three case studies that fall under this umbrella: two of them are related to neural networks and one to power grids.
The first case study is concerned with central pattern generators, i.e. small neural networks involved in animal locomotion. In this case, a design strategy for optimal tuning of biologically-plausible model parameters is developed, resulting in network models able to reproduce key characteristics of animal locomotion.
The second case study is in the context of brain networks. In this case, a method to derive the weights of the connections between brain areas is proposed, utilizing both imaging data and nonlinear dynamics principles.
The third and last case study deals with a method for the estimation of the inertia constant, a key parameter in determining the frequency stability in power grids. In this case, the method is customized to different challenging scenarios involving renewable energy sources, resulting in accurate estimations of this parameter
Low-dimensional models of single neurons: A review
The classical Hodgkin-Huxley (HH) point-neuron model of action potential
generation is four-dimensional. It consists of four ordinary differential
equations describing the dynamics of the membrane potential and three gating
variables associated to a transient sodium and a delayed-rectifier potassium
ionic currents. Conductance-based models of HH type are higher-dimensional
extensions of the classical HH model. They include a number of supplementary
state variables associated with other ionic current types, and are able to
describe additional phenomena such as sub-threshold oscillations, mixed-mode
oscillations (subthreshold oscillations interspersed with spikes), clustering
and bursting. In this manuscript we discuss biophysically plausible and
phenomenological reduced models that preserve the biophysical and/or dynamic
description of models of HH type and the ability to produce complex phenomena,
but the number of effective dimensions (state variables) is lower. We describe
several representative models. We also describe systematic and heuristic
methods of deriving reduced models from models of HH type
Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models
We introduce a new approach for solving forward systems of differential
equations using a combination of splitting methods and physics-informed neural
networks (PINNs). The proposed method, splitting PINN, effectively addresses
the challenge of applying PINNs to forward dynamical systems and demonstrates
improved accuracy through its application to neuron models. Specifically, we
apply operator splitting to decompose the original neuron model into
sub-problems that are then solved using PINNs. Moreover, we develop an
scheme for discretizing fractional derivatives in fractional neuron models,
leading to improved accuracy and efficiency. The results of this study
highlight the potential of splitting PINNs in solving both integer- and
fractional-order neuron models, as well as other similar systems in
computational science and engineering
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