scholarly journals Bayesian differential programming for robust systems identification under uncertainty

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200290
Author(s):  
Yibo Yang ◽  
Mohamed Aziz Bhouri ◽  
Paris Perdikaris
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Nonlinear Dynamical ◽  
Predator Prey ◽  
Learning Framework ◽  
Numerical Studies ◽  
Recent Developments ◽  
Systems Identification ◽  
Robust Systems

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Mapping the dynamics of a bursting neuron

1993 ◽  
Vol 341 (1298) ◽  
pp. 345-359 ◽  
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Model Neuron ◽  
Neural Model ◽  
Model Parameters ◽  
Nonlinear Dynamical ◽  
Bursting Neuron ◽  
Channel Blocking ◽  
Real Neuron ◽  
Intrinsic Firing

The anterior burster (AB) neuron of the lobster stom atogastric ganglion displays varied rhythmic behavior when treated with neuromodulators and channel-blocking toxins. We introduce a channelbased model for this neuron and show how bifurcation analysis can be used to investigate the response of this model to changes of its parameters. Two dimensional maps of the parameter space of the model were constructed using com putational tools based on the theory of nonlinear dynamical systems. Changes in the intrinsic firing and oscillatory properties of the model AB neuron were correlated with the boundaries of Hopf and saddle-node bifurcations on these maps. Complex rhythmic patterns were observed, with a bounded region of the parameter plane producing bursting behavior of the model neuron. Experiments were performed by treating an isolated AB cell with 4-am inopyridine which selectively reduces gλ, the conductance of the transient potassium channel. The model accurately predicts the qualitative changes in the neuronal voltage oscillations that are observed over a range of reduction of gλ in the neuron. These results dem onstrate the efficacy of dynamical systems theory as a means of determ ining the varied oscillatory behaviors inherent in a channel-based neural model. Further, the maps of bifurcations provide a useful tool for determining how these behaviors depend upon model parameters and comparing the model to a real neuron.

Updating Nonlinear Dynamical Models Using Response Measurements Only

2003 ◽  
Author(s):  
Ka-Veng Yuen ◽  
James L. Beck
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Simulated Data ◽  
Model Parameters ◽  
Response Signal ◽  
Dynamical Models ◽  
Nonlinear Dynamical ◽  
Uncertain Input ◽  
Measured Response

A spectral density approach for the identification of linear systems is extended to nonlinear dynamical systems using only incomplete noisy response measurements. A stochastic model is used for the uncertain input and a Bayesian probabilistic approach is used to update the uncertainties in the model parameters. The proposed spectral-based approach utilizes important statistical properties of the Fast Fourier Transform and their robustness with respect to the probability distribution of the response signal in order to calculate the updated probability density function for the parameters of a nonlinear model conditional on the measured response. This probabilistic approach is well suited for the identification of nonlinear systems and does not require huge amounts of dynamic data. The formulation is presented directly for multiple-degree-of freedom systems. Examples using simulated data for a Duffing oscillator and a four-DOF inelastic structure are presented to illustrate the proposed approach.

scholarly journals NOISE IMMUNITY RESEARCH FOR NONLINEAR DYNAMICAL SYSTEMS IDENTIFICATION BASED ON VOLTERRA MODEL IN FREQUENCY DOMAIN

2014 ◽  
pp. 34-41
Author(s):  
Vitaliy Pavlenko ◽  
Sergei Pavlenko ◽  
Viktor Speranskyy
Keyword(s):  
Dynamical Systems ◽  
Frequency Domain ◽  
Noise Immunity ◽  
Nonlinear Dynamical Systems ◽  
Interpolation Method ◽  
Test System ◽  
Volterra Model ◽  
Third Order ◽  
Nonlinear Dynamical ◽  
Systems Identification

The accuracy and noise immunity of the interpolation method of nonlinear dynamical systems identification based on the Volterra model in the frequency domain is studied in this paper. The polyharmonic signals are used for the testing the method. The algorithmic and software toolkit in Matlab is developed for the identification procedure. This toolkit is used to construct the informational models of test system and communication channel. The model is built as a first-, second- and third-order amplitude–frequency and phase–frequency characteristics. The comparison of obtained characteristics with previous works is given. Wavelet denoising is studied and applied to reduce measurement noise.

Sign in / Sign up

Export Citation Format

Share Document