Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
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48 results for “nonlinear system identification”
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
Paper accelerates nonlinear mapping in online systems with lower time complexity.
problem Speeding up nonlinear mapping in online systems.
method Integrates an acceleration module into Dendrite Net (DD) to reduce time complexity.
result DD with AC has lower time complexity while maintaining nonlinear mapping and system identification properties.
Deep SSMs use neural networks to identify complex systems.
problem Identifying nonlinear systems with high uncertainty.
method Deep state space models with neural networks.
result Deep SSMs outperform traditional methods on benchmarks.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
Study on identifying and inferring nonlinear dynamics on unknown networks.
problem Identifying network structure in nonlinear dynamic systems with unknown interactions.
method Showed network structure is not generically identified, requiring sufficient spectral heterogeneity. Developed necessary and sufficient conditions for identification and proposed a semiparametric estimator.
result Necessary and sufficient conditions for identification of network structure in nonlinear dynamic systems.
CNN identifies nonlinear human posture control models efficiently.
problem Identifying nonlinear human posture control models.
method Convolutional Neural Networks (CNN) for model identification.
result Efficiently identifies nonlinear human posture control models.
Probabilistic Numeric SMC Sampling for Bayesian Nonlinear System Identification in Continuous Timestat.ML
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Unified framework identifies nonlinear systems using characteristic curves and neural networks.
problem Balancing interpretability and flexibility in nonlinear system identification.
method Combines differential equation structure with neural networks, using characteristic curves as modular components.
result NN-CC approach outperforms other methods in complex nonlinear systems.
New techniques improve the accuracy of identifying nonlinear systems from noisy data.
problem Identifying nonlinear dynamical systems from noisy state measurements.
method Comparative study of local and global smoothing techniques to denoise state measurements and improve sparse regression methods.
result Global smoothing methods outperform local methods in improving the accuracy of governing equation recovery.
One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estima…
Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a nonlinear system identification method for gray-box modeling. It consists of two int…
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of basis functions. We reconstruct the …
Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datastat.ML
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully …
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
This work uses a scalable approach to identify partially observed nonlinear systems.
problem Offline identification of partially observed nonlinear systems.
method Certainty-equivalent expectation-maximization (CEEM) as block coordinate-ascent.
result The CEEM approach can identify high-dimensional systems reliably and efficiently.
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization…
QENDy learns quadratic dynamics from nonlinear systems data.
problem Identifying governing equations of highly nonlinear dynamical systems.
method QENDy embeds nonlinear dynamics into a quadratic feature space, requiring trajectory data and preselected basis functions.
result QENDy accurately identifies quadratic dynamics and outperforms SINDy and deep learning methods.
The Duffing oscillator's parameters are identified online using variational message passing.
problem Estimating parameters of a nonlinear Duffing oscillator in real-time.
method Variational message passing on a factor graph of the Duffing oscillator's generative model.
result The online inference procedure performs as well as offline methods.
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computationa…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability forms. The biggest obstacle of the probability model is the probability distribu…
dynoGP uses deep Gaussian processes for dynamic system identification.
problem System identification for complex dynamical systems.
method Interconnecting linear dynamic GPs and static GPs to model dynamic and static nonlinearities.
result Demonstrates effectiveness of the approach using both simulated and real-world data.
We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamic…
A tutorial on non-asymptotic system identification methods.
problem Identifying system parameters in linear models.
method Covering technique, Hanson-Wright Inequality, method of self-normalized martingales.
result Streamlined proofs of least-squares based estimator performance.
Sparse Identification of Nonlinear Dynamical Systems via Reweighted -regularized Least Squaresstat.ML
Method improves SINDy for noisy nonlinear systems.
problem Recover nonlinear dynamical systems from noisy data.
method Reweighted -regularized least squares.
result Improved accuracy and robustness in noisy conditions.
The paper analyzes methods for sparse Bayesian regression in nonlinear system identification.
problem Learning sparse models in Bayesian regression with nonlinear applications.
method Two classes of methods: regularization and thresholding based, built on automatic relevance determination (ARD).
result Analytical demonstration of favorable performance with sparse solutions in linear problems.
Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures …
Bayesian framework for robust model discovery from noisy data.
problem Robust model discovery from noisy, sparse and irregular observations of nonlinear systems.
method Bayesian differential programming using Hamiltonian Monte Carlo and sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Bayesian neural networks with nonparametric noise models for system identification.
problem Estimating parameters and noise processes in stochastic dynamic systems.
method Bayesian nonparametric approach using neural networks and Gibbs sampler.
result The method converges to full nonparametric Bayesian regression model.
Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general nonlinear system, as they have proven to be very effective in approximating comple…
Online algorithm identifies PDEs from noisy data snapshots.
problem Identifying PDEs from sequential solution snapshots.
method Combines weak-form discretization with online proximal gradient descent.
result Efficiently identifies and tracks systems with time-varying coefficients.
A method for identifying NPWARX models with arbitrary domains using probabilistic mixture models.
problem Identifying hybrid system models with discontinuous maps.
method Probabilistic mixture model with a neural network for nonlinear partitioning and Expectation Maximization for parameter estimation.
result Demonstrated on a nonlinear piece-wise problem with discontinuous maps.
Proposes a method to learn system dynamics and region of attraction from trajectories.
problem Learning accurate dynamics and region of attraction from system trajectories.
method Uses local stability information as a prior to learn vector field and region of attraction.
result Efficient sampling and accurate estimate of dynamics in inner approximation of region of attraction.
Herein, we propose a spatio-temporal extension of RBFNN for nonlinear system identification problem. The proposed algorithm employs the concept of time-space orthogonality and separately models the dynamics and nonlinear complexities of the system. The proposed RBF architecture is explored for the estimation of a highl…
Identification of Gaussian Process State-Space Models with Particle Stochastic Approximation EMstat.ML
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlostat.ML
BINDy uses Bayesian methods to identify nonlinear dynamics from data.
problem Learning sparse representations of complex dynamics from data.
method Bayesian treatment of dictionary learning system identification using reversible-jump Markov-chain Monte-Carlo.
result BINDy produces models that are sparse in model space rather than parameter space.
New algorithms for interpreting complex multivariate functions.
problem Hard interpretation of multivariate functions due to many parameters.
method Filtered tensor decompositions of derivative information.
result Nonparametric estimates of smooth decoupled functions.
A new method reduces Volterra kernel complexity and uncertainty quantification.
problem Challenges in modeling nonlinear systems with Volterra series due to high model order.
method Bayesian Tensor Network Volterra kernel machines (BTN-V) using canonical polyadic decomposition.
result Competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.
New method integrates sparse parametric and nonparametric techniques for complex system modeling.
problem Lack of accurate modeling for complex biological systems due to nonlinearities.
method Sparse nonparametric estimation framework combining parametric and nonparametric techniques.
result Accurately captures nonlinearities in complex systems without prior information.
The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.
problem Learning nonparametric nonlinear operators from data.
method NVKM model using Volterra series and Gaussian processes for unobserved and observed input functions.
result The NVKM model can perform both single and multiple output regression and system identification.
Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to solve this task and includes powerful estimators such as regularization network…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfu…
Incremental Nonlinear System Identification and Adaptive Particle Filtering Using Gaussian Processstat.ML
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …
This work proposes a new method for simultaneous probabilistic identification and control of an observable, fully-actuated mechanical system. Identification is achieved by conditioning stochastic process priors on observations of configurations and noisy estimates of configuration derivatives. In contrast to previous w…
The paper proposes a new system ID method from noisy data.
problem System identification of linear and nonlinear non-autonomous systems from noisy and sparse data.
method Bayesian formulation for learning a hidden Markov model with stochastic dynamics, analyzed in the context of least squares and multiple shooting approaches.
result The proposed approach outperforms existing methods in terms of mean squared error and model generalizability.
Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based met…