SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
Bayesian-SINDy learns differential equations from noisy data quickly.
problem Learning correct model equations from limited and noisy data.
method Bayesian-SINDy framework using Gaussian approximations.
result Bayesian-SINDy is more robust and accurate in learning correct model equations from noisy data.
Bayesian autoencoders discover physics from noisy data.
problem Challenges in identifying governing equations and coordinates from noisy, low-data real-world data.
method Bayesian SINDy autoencoders with hierarchical Bayesian sparsifying prior and adaptive empirical Bayesian method.
result Better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification.
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems…
This work improves SINDy-type algorithms for system identification using score-guided dictionary selection.
problem Improving accuracy and interpretability in dynamical system identification.
method Score-guided library selection to refine dictionary terms in sparse regression.
result Score-guided methods enhance SINDy's robustness in discovering governing equations.
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
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.
Paper discovers governing equations from data using differential invariants.
problem Discovering partial differential equations from data is challenging.
method The paper proposes a pipeline based on differential invariants to reduce the search space and adhere to symmetry.
result DI-SINDy method outperforms other symmetry-informed methods in PDE discovery.
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 method recovers BSDE from financial data without ergodicity.
problem Discovering probabilistic laws from financial data.
method Stochastic SINDy method under risk-neutral measure.
result Recovery of BSDE from limited financial data.
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 algorithm STCV improves sparse model discovery from normalised data.
problem Distortion of sparse model discovery due to data scaling.
method STCV, a novel sparse regression algorithm robust to data scaling.
result STCV outperforms standard methods on normalised, noisy datasets.
New method learns differential equations from data with hidden variables.
problem Learning differential equations from data with hidden variables.
method Sparse linear regression optimization problem with higher order time derivatives and dictionary of functions.
result High quality short-term forecasts with orders of magnitude faster than competing methods.
A new method ODR-BINDy improves model discovery from noisy data.
problem Discovering models from noisy datasets with error-in-variable problem.
method ODR-BINDy uses orthogonal distance regression with Bayesian model selection.
result ODR-BINDy consistently outperforms existing methods in recovering correct models.
WSINDy for PDEs robustly identifies models from noisy data.
problem Identifying nonlinear dynamics from noisy partial differential equations data.
method Weak formulation of PDEs, Fourier-based model identification, sequential-thresholding least-squares.
result WSINDy enables robust identification of PDEs in noisy conditions.
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data is challenging without simultaneously proposing an accompanying discrepancy model…
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.
Reactmine infers chemical reactions from time series data, overcoming sparse model limitations.
problem Inferring chemical reaction networks from time series data, especially when initial conditions are not varied.
method Sequential reaction inference in a search tree, ranking and re-optimizing kinetics.
result Reactmine successfully infers preponderant regulations in real datasets, matching model-based analyses.
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 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…
Optimizes basis functions for learning dynamical systems from data.
problem Learning suitable basis functions for dynamical systems from data.
method Gradient-based optimization framework for learning basis functions.
result Efficacy demonstrated on various benchmark problems.
First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-kn…
New method stabilizes model selection with theoretical guarantees.
problem Stability of model selection methods in the face of noisy or incomplete data.
method Combines bagging with an 'inflated' argmax operation to select a stable set of models.
result Stable model selection with high probability of overlap after removing any data point.
PASTIS method selects simple models from noisy data.
problem Selecting correct models from large candidate libraries.
method PASTIS (Parsimonious Stochastic Inference) using extreme value theory.
result PASTIS outperforms other methods in model identification and predictive capability.
Bayesian framework identifies dynamical systems from noisy data.
problem Identifying dynamical systems from time-series data with uncertainty quantification.
method Bayesian maximum a posteriori (MAP) framework, including JMAP and VBA algorithms.
result Robust model selection metric based on Gaussian posterior norm.
SIP framework discovers governing equations in uncertain systems.
problem Discovering governing equations in systems with input variability and noisy data.
method SIP framework treats unknown coefficients as random variables and infers their posterior distribution by minimizing Kullback-Leibler divergence.
result SIP consistently identifies correct equations and lowers coefficient error by 82% relative to SINDy.
Bayesian system ID improves robustness to sparse, noisy data.
problem Robust system identification with sparse, noisy data.
method Probabilistic formulation of system identification using Bayesian posterior.
result The log posterior is more robust and less affected by multiple minima.
Modeling air pollutants using data-driven techniques and sparse identification of nonlinear dynamics.
problem Predicting concentrations of air pollutants using hidden physical laws.
method Sparse identification of nonlinear dynamics (SINDy) for parsimonious systems of ordinary differential equations.
result More than half of the critical points are saddle points, indicating system instability.
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
problem Estimating quasi-potential and drift components in stochastic systems.
method Sparse identification of non-linear dynamics (SINDy) combined with action minimization methods.
result Evaluation of quasi-potential landscape from a single trajectory.
Data-driven control of robotic systems using Koopman operators with error bounds.
problem Real-time control of nonlinear robotic systems with unknown dynamics.
method Constructing a Koopman operator-based linear representation using higher-order derivatives of nonlinear dynamics, with error bounds derived from Taylor series accuracy analysis.
result The Koopman model provides marginally better performance than competing nonlinear modeling methods and can be efficiently controlled using linear control design tools.
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.
EML-CD discovers causal mechanisms from neural networks in a structured way.
problem Extracting causal mechanisms from neural network weights is ill-posed.
method Integrates EML operator into causal structure learning, representing each edge mechanism as a gated EML binary tree.
result Achieves SHD=11.2 +/- 0.4 on real data, matching or outperforming existing methods.
A new method selects variables efficiently for fast and accurate dynamic system identification.
problem Efficiently selecting variables for scalable Gaussian processes.
method Forward variable selection using Karhunen-Loève decomposition and Gibbs sampling.
result Method yields competitive accuracies and inference times for dynamic systems.
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of these methods on complex engineered systems. Dynamics of these systems play a cru…