Gaussian processes improve system identification models.
problem Improving system identification models for non-linear dynamics.
method Using Gaussian processes to create time series prediction models.
result Gaussian processes enhance model accuracy in system identification.
Study curvature and torsion in Gaussian distribution's dual coordinate system.
problem Characterize geometric invariants of Gaussian distribution.
method Investigate Riemannian curvature and torsion in a dual coordinate system of Gaussian distribution.
result Explicitly give Amari formulas in the new coordinate system.
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.
Proposes a new filtering method for dynamical systems that relaxes Gaussian and affine assumptions.
problem Inferring states of dynamical systems from observations with Gaussian and affine assumptions.
method Relaxes Gaussian and affine assumptions using deep, nonlinear, non-Gaussian models.
result Significant advantage over Gaussian Filtering and nonlinear fixed kernels.
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
New method uses Gaussian processes for solving linear PDEs with boundary conditions.
problem Solving linear PDEs with boundary conditions.
method Boundary Ehrenpreis--Palamodov Gaussian Processes (B-EPGPs).
result Significant accuracy and resource improvements over existing methods.
New analysis explains pathology of deep Gaussian processes.
problem Pathology of deep Gaussian processes reduces learning capacities with increased layers.
method Study nonlinear dynamic systems corresponding to DGPs, derive recurrence relations.
result Provide tighter bounds and rate of convergence for dynamic systems.
Proposes a Gaussian process model for constrained dynamics learning.
problem Challenges in identifying constrained dynamics of mechanical systems.
method Combines analytical mechanics with Gaussian process regression.
result Improves data efficiency and constraint integrity in predictions.
GP-SUM filters complex non-Gaussian states using Gaussian Processes.
problem Stochastic dynamic filtering and state propagation with complex beliefs.
method GP-SUM combines sampling and probabilistic Bayes filters, using Gaussian Processes for dynamic and observation models.
result GP-SUM outperforms other filters on benchmarks and predicts non-Gaussian states accurately.
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
Decentralized Gaussian processes for multi-agent systems.
problem Scalable and flexible learning solutions for multi-agent systems.
method Asymptotically exact decentralized solution to Gaussian processes, with online Bayesian model averaging for hyperparameter selection.
result Asymptotically exact decentralized Gaussian process approximation and online Bayesian model averaging.
Introduces numerical Gaussian process Kalman filtering for infinite-dimensional systems.
problem Kalman filtering on infinite-dimensional systems.
method Embedding numerical Gaussian processes into Kalman filter equations.
result Ability to perform Kalman filtering on infinite-dimensional systems using Gaussian processes.
Method extracts governing laws from non-Gaussian stochastic systems data.
problem Modeling complex dynamics with non-Gaussian Lévy noise.
method Data-driven method to extract stochastic dynamical systems from noisy data.
result Established a theoretical framework and numerical algorithm to compute Lévy jump measure, drift, and diffusion.
Gaussian process model learns Hamiltonian systems from noisy data.
problem Learning Hamiltonian systems from long, noisy trajectories.
method Efficient decoupled parameterisation, energy-conserving shooting method.
result Robust inference from short and long trajectories.
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.
Gaussian processes learn unknown ODE dynamics from sparse data.
problem Learning unknown ODE models with limited data.
method Nonparametric ODE modelling using Gaussian process vector fields.
result Model infers dynamics from sparse data and simulates future states.
Study of Ricci flow on discrete surfaces of revolution with constant Gaussian curvature.
problem Understanding Ricci flow on discrete surfaces of revolution.
method Explicit parametrizations and Ricci flow analysis for discrete surfaces of revolution.
result Discrete surfaces of revolution approach constant Gaussian curvature under Ricci flow.
Gaussian processes for dynamical systems with Koopman equivariance.
problem Forecasting and learning representations of nonlinear dynamical systems.
method Koopman-equivariant Gaussian processes with linear time-invariant responses and trajectory-based equivariance.
result Enhanced forecasting performance compared to kernel-based methods.
Gaussian Process improves tracking control for unknown systems.
problem Challenges in perfect tracking control for real-world Euler-Lagrange systems.
method Employing Gaussian Process regression for data-driven model of unknown dynamics and adaptive feedback gains.
result Guaranteed globally bounded tracking error with specific probability.
Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between n n n economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter ε ε ε . We demonstrate, that within Gaussian noise,…
New method calculates partial information for Gaussian systems based on dependency constraints.
problem Quantifying information sharing in multivariate Gaussian systems.
method Constructing maximum entropy models based on dependency constraints and deriving closed-form solutions.
result Closed-form solutions for Gaussian systems show differences in redundancy and synergy estimates compared to existing methods.
Calculates local Granger causality for Gaussian and nonlinear systems.
problem Understanding causal influence in complex systems.
method Vector autoregression and information-theoretic approach.
result Local Granger causality offers a robust and fast method for time-directed information transfer.
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.
Unified Bayesian framework for LTV system identification using neural networks and Gaussian Processes.
problem Identifying Linear Time-Varying systems from input-output data.
method Bayesian modeling of impulse response as a stochastic process, using neural networks and Gaussian Processes for inference.
result Framework can infer LTI system properties from a single noisy input-output pair, achieving lower error than classical methods.
LqgOpt learns optimal control in unknown LQG systems with minimal regret.
problem Adaptive control in partially observable linear quadratic Gaussian systems with unknown dynamics.
method Optimism in the face of uncertainty, predictor state evolution, closed-loop system identification, confidence bounds.
result Proves a regret upper bound of i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) for LQG systems. Bayesian approach for solving systems of linear PDEs with boundary conditions.
problem Modeling data efficiently with prior knowledge from systems of linear PDEs.
method Construct multi-output Gaussian process priors using Gröbner bases and pullback parametrizations.
result Gaussian process priors can represent solutions to systems of linear PDEs adhering to boundary conditions.
New method learns dynamical systems efficiently using active learning.
problem Efficiently learning dynamical systems from data.
method Active learning strategies leveraging Gaussian process regression.
result Data-efficient training of the model through exploratory sampling.
The study sets limits on how well systems can be controlled adaptively.
problem Learning to control unknown linear Gaussian systems with quadratic costs.
method Combining ideas from experiment design, estimation theory, and perturbation bounds of information matrices.
result Regret lower bounds of the order of T \sqrt{T} T in the time horizon T T T accurately capture control-theoretic parameters. A new method eliminates miscalibration in Gaussian process models for dynamical systems.
problem Miscalibration and overestimation of transition function parameters in Gaussian process models.
method Explicitly models the dependence between state trajectories and Gaussian process posterior, eliminating factorization.
result Better predictive performance and more calibrated estimates of the transition function.
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
Paper develops a new state estimation method for nonlinear systems.
problem State estimation for nonlinear state-space models is intractable.
method Developed a variational inference approach based on Gaussian approximations.
result The method outperforms alternative Gaussian approaches in various examples.
Gaussian process framework learns interaction kernels in multi-species particle systems.
problem Learning interaction kernels in multi-species interacting particle systems from trajectory data.
method Nonparametric Bayesian approach with Gaussian processes.
result Established rigorous statistical guarantees for recoverability and optimality of interaction kernels.
This paper uses Gaussian Process and converse Lyapunov function to estimate power system ROA.
problem Estimating the region of attraction (ROA) for power systems with conservative and limited analytical methods.
method Combining converse Lyapunov theorem and Gaussian Process to estimate ROA without needing an analytic Lyapunov function.
result The approach can significantly enlarge the estimated ROA compared to analytical methods.
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.
Paper analyzes a generalized EM algorithm for Gaussian mixtures in control systems.
problem Parametric distribution-based clustering in unsupervised learning.
method Proposes a generalized EM (GEM) algorithm for Gaussian mixture models, analyzing its convergence properties using control theory.
result GEM algorithm can be understood as a linear time-invariant system with feedback nonlinearity.
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.
GP-NODE combines Gaussian processes and NeuralODEs for Bayesian system identification.
problem Bayesian systems identification from partial, noisy and irregular observations.
method Differentiable programming, Hamiltonian Monte Carlo, Gaussian Process priors, sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Method extracts stochastic systems with Lévy noise from data.
problem Identifying stochastic dynamical systems with Lévy noise from short data.
method Estimate Lévy jump measure and noise intensity, approximate drift coefficient.
result Accurate and effective method for discovering stochastic laws.
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.
The article develops models for learning and controlling physical systems with unknown inputs.
problem Learning and controlling physical systems with unknown inputs.
method Gaussian process latent force models (GP-LFMs) combining first-principles models and non-parametric GP components.
result Theoretical observability and controllability results for GP-LFMs.
Paper uses black-box inference to estimate non-linear latent force models.
problem Estimating posterior state and forcing term in non-linear systems with unknown forcing terms.
method Black-box variational inference with local inverse autoregressive flows.
result Demonstrates effectiveness of approximation on known posterior systems and non-linear dynamics.
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after …
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…
Efficient inference for multimodal Gaussian mixture models of interacting dynamical systems.
problem Efficient inference for multimodal distributions in stochastic dynamical systems.
method Graph neural networks with moment matching for sample-free inference and structured covariance approximations.
result Sample-free inference with improved efficiency and stability compared to Monte Carlo alternatives.
This work extracts stochastic dynamical systems with α \alpha α -stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for α \alpha α -stable Lévy noise. result Effectiveness of the method confirmed by numerical experiments.
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.