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.
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
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.
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.
Improved RBFNN for nonlinear system identification.
problem Nonlinear system identification problem.
method Spatio-temporal extension of RBFNN with time-space orthogonality.
result Spatio-temporal RBFNN outperforms standard RBFNN in convergence and error reduction.
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.
Equation discovery method reconstructs model structure and parameters from data.
problem Nonlinear system identification challenges.
method Two interlaced parts: model structure identification and parameter estimation.
result Equation discovery method successfully reconstructs model structure and parameters from data.
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.
Develops method for learning complex nonlinear systems with multiple outputs and inputs.
problem Learning nonlinear systems with multiple outputs and inputs.
method Latent variable framework, maximum likelihood principle, majorization-minimization approach, convex majorization technique.
result Recursive identification of parsimonious predictive models.
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.
This paper uses RBM to calculate conditional probabilities for nonlinear system identification.
problem Challenges in obtaining probability distributions for nonlinear system identification.
method Modified RBM to calculate joint, input, and conditional probabilities.
result The method outperforms other black-box models in noisy, complex systems.
New method improves parameter identification for complex systems.
problem Parameter identification and comparison of nonlinear ODE systems.
method Gaussian process regression over time-series data.
result Better accuracy in state-of-the-art performance for nonlinear systems.
New method identifies Hammerstein systems using kernel-based approach.
problem Identifying Hammerstein systems with unknown nonlinearities and impulse responses.
method Overparameterized vector estimation with regularized kernel-based approach.
result Unique decomposition of overparameterized vector into impulse response and nonlinear coefficients.
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…
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.
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.
Researchers identify latent variables and causal structures from nonlinear hierarchical models.
problem Challenging task of identifying latent variables and causal structures from observational data, especially when relationships are nonlinear.
method Investigated nonlinear latent hierarchical causal models, developed identification criterion, and constructed an estimation procedure.
result Identifiability of causal structures and latent variables achieved under mild assumptions.
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.
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 …
Paper studies geometric properties of nonlinear Lebesgue spaces.
problem Geometric and analytic properties of nonlinear Lebesgue spaces.
method Formalizes pointwise description of geometric properties using a nonlinear Fubini-Lebesgue theorem.
result Definition of length structure, Alexandrov curvature bounds, and speed for absolutely continuous curves in nonlinear Lebesgue spaces.
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.
Unified kernel-based methods improve nonlinear causal discovery.
problem Identifying nonlinear causal relationships between time series variables.
method Unified Kernel Principal Component Regression (KPCR) and Gaussian Process score-based model with Smooth Information Criterion.
result Improved performance in time series nonlinear causal discovery.
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.
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.
Tensor completion method identifies nonlinear systems from input-output data.
problem Identifying nonlinear functions from input-output data pairs.
method Formulated as tensor completion problem with smoothness regularization and solved using block coordinate descent.
result Provable correct nonlinear system identification under certain conditions.
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.
A new kernel improves Volterra series model selection and prediction.
problem Hard identification of Volterra series from limited data.
method Proposes a novel regularization network using a multiplicative polynomial kernel.
result Better selection of influential monomials improves model prediction.
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.
Online learning improves state estimation of nonlinear systems.
problem Online learning of nonlinear state dynamics in Gaussian state space models.
method Stochastic variational sparse Gaussian process embedded in a particle filter framework, with model updating using stochastic gradient descent.
result State estimation performance significantly improves with online learning of state dynamics.
Algorithm identifies top M arms from K in stochastic bandits with limited budget.
problem Identifying the top M arms from K in a stochastic bandit setting with limited exploration budget.
method Develops an iterative algorithm that allocates budget nonlinearly to deactivate arms, deciding acceptance or rejection based on a decision rule.
result The algorithm effectively identifies the top M arms with a decay rate of misidentification probability characterized by nonlinear budget allocation.
Best-arm identification in bandits with sequential elimination.
problem Identifying the arm with the highest expected reward in a budget-limited exploration process.
method Unified sequential elimination algorithms, dividing budget based on nonlinear function of remaining arms.
result Improved theoretical guarantees and performance over state-of-the-art algorithms.
Convex optimization method identifies LTV models with smooth or discontinuous dynamics.
problem Identifying LTV dynamical models with smooth or discontinuous time evolution.
method Convex optimization to design cost functions promoting either continuous or discontinuous changes in model coefficients.
result Demonstrates identification of LTV models with either continuous or discontinuous dynamics.
Method improves SINDy for noisy nonlinear systems.
problem Recover nonlinear dynamical systems from noisy data.
method Reweighted ℓ1-regularized least squares. result Improved accuracy and robustness in noisy conditions.
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
JULIA combines multi-linear and nonlinear models for tensor completion.
problem Complex patterns in real-world tensors require a unified model.
method JULIA unifies multi-linear and nonlinear models with flexible component assignment and efficient alternating optimization.
result JULIA outperforms existing methods in large-scale tensor completion.
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.
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.
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.
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.
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.
Deep learning's convolutional networks improve system identification.
problem Nonlinear system identification problems.
method Exploration of relationships between TCN and Volterra series/block-oriented models.
result TCN outperforms traditional models in sequence modeling tasks.
A novel adaptive kernel improves RBF neural networks performance.
problem Improving performance of RBF neural networks.
method Adaptive fusion of Euclidean and cosine distance measures using gradient descent.
result The method outperforms manual fusion on three major problems.
New method discovers discrepancies between simplified models and experimental data.
problem Model discrepancies in nonlinear systems lead to significant deviations from true behavior.
method Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to discover sparse model terms.
result Improvement in performance with a discrepancy model in simulations.
New method identifies latent components in nonlinear mixtures without stringent assumptions.
problem Unraveling latent components in nonlinearly mixed data.
method Constrained autoencoder-based algorithm for identifiability under relaxed assumptions.
result Comprehensive sample complexity results and new identifiability conditions.
Develops a new econometric model to identify structural shocks.
problem Identifying structural shocks in nonlinear systems.
method Exploits variation in conditional distributions of independent shocks induced by an exogenous variable.
result Strengthens identification results to permutation and sign changes.