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142283425566 · Jun 202019922001200920172026
48 results for nonlinear dynamical systems

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.

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.

Breaks down complex nonlinear dynamics into simpler components.

problem Control of nonlinear dynamical systems remains challenging.
method Inspired by hybrid switching systems, decomposes dynamics into simpler stochastic switching linear dynamical systems.
result Extracts hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts.

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.

New method identifies key genes affecting phenotypes in biological systems.

problem Identifying genes that drive specific phenotypes in complex biological systems.
method Data-driven observability decomposition using Koopman operators.
result Koopman operator representation identifies genes that drive phenotypes.

D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.

problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.

New method learns nonlinear systems from single finite trajectory samples.

problem Learning stabilizable nonlinear systems from single finite trajectory samples.
method Gradient-based algorithms with noise-sensitive uniform convergence guarantees.
result Efficient learning of general nonlinear systems with high accuracy and small sample complexity.

Improved robust latent variable estimation for neural dynamics.

problem Inconsistent results due to noise and nonlinearity in existing models.
method Probabilistic approach to latent variable estimation in decomposed models.
result More accurate latent variable inference in nonlinear systems with diverse noise conditions.

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.

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.

Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.

problem Challenges in time-dependent reliability analysis of nonlinear dynamical systems.
method Koopman operator approach for transforming nonlinear systems into linear ones, combined with deep learning for intrinsic coordinates.
result Robust and generalizable approach for time-dependent reliability analysis, superior to purely data-driven methods.

KCRL learns stable policies for nonlinear systems with formal guarantees.

problem Lack of stabilization guarantees in RL methods for safety-critical systems.
method KCRL uses Krasovskii's Lyapunov functions as a stability constraint and a primal-dual approach to learn stabilizing policies.
result KCRL guarantees learning a stabilizing policy in a finite number of interactions.

This research improves dynamical systems understanding by identifying latent states and their nonlinear transitions.

problem Previous work on dynamical systems could not identify nonlinear transition dynamics, leading to unreliable predictions.
method Proposes a state-space modeling framework using variational auto-encoders to identify latent states and their nonlinear transition functions.
result Demonstrates high accuracy in recovering latent state dynamics and future prediction accuracy.

Algorithm learns weight matrix from single trajectory of nonlinear dynamical system.

problem Learning weight matrix from a single trajectory of nonlinear dynamical system.
method Algorithm uses global stability and well-conditioned covariance to recover weight matrix.
result Algorithm recovers weight matrix with optimal sample complexity and linear running time.

GD-VAEs learn dynamics from observations using geometric and topological information.

problem Learning parsimonious representations of nonlinear dynamics from observations.
method Develops data-driven methods incorporating geometric and topological information using Variational Autoencoders (VAEs).
result GD-VAEs provide methods for learning reduced dimensional representations of nonlinear dynamics.

A novel model uses ODE-based random features to model nonlinear dynamical systems.

problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.

The paper introduces reservoir computing models for complex systems.

problem Modeling complex engineering systems using nonlinear autoregression.
method Introduces reservoir computing with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models.
result Demonstrates versatility of classical and quantum reservoir computers in modeling synthetic and real data.

Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.

problem Detecting change-points and estimating parameters in nonlinear dynamical systems with regime transitions.
method Residual-loss anomaly analysis of physics-informed neural networks, two-stage strategy.
result The method outperforms traditional approaches in change-point localization and parameter estimation accuracy.

This paper presents a method for efficient density estimation in nonlinear systems.

problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.

New method learns nonlinear projections for reduced-order modeling of complex dynamical systems.

problem Modeling transient dynamics near a manifold in nonlinear systems.
method Constrained autoencoder neural networks with invertible activation functions and biorthogonal weight matrices.
result Demonstrated effectiveness on a vortex shedding model, learning oblique fibers for fast dynamics.

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.

Enhances RSCNs with hybrid regularization for nonlinear dynamics.

problem Modeling nonlinear dynamic systems with uncertainties.
method Recurrent stochastic configuration networks with hybrid regularization.
result The method outperforms other models in nonlinear system identification and industrial tasks.

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…

2017-12-27abs ↗pdf ↗

DeepRSCN models nonlinear systems using stochastic configurations.

problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.

A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.

problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.

DeepONet accelerates reliability analysis of stochastic nonlinear systems.

problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.

Study chaotic dynamics in social stratification models leading to thermalization and turbulence.

problem Understanding social stratification dynamics through chaotic nonlinear systems.
method Modeling social network links with oscillators and energies, studying Hamiltonian evolution and nonlinear interactions.
result Chaotic dynamics leads to dynamical thermalization and Kolmogorov-Zakharov turbulence, with implications for wealth inequality.

Novel method estimates complex nonlinear systems with stochastic differential equations.

problem Handling complex nonlinear dynamical systems with strong learning guarantees.
method Estimates drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations.
result Strong theoretical guarantees including finite-sample bounds for various metrics.