A Riemmanian foliated dynamical system of 3-dimension is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. In the context of arithmetic topology, it is a geometric/analytic analogue of an arithmetic scheme with a conjectural dynamical system suggested by C. De…
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48 results for “Dynamic Systems”
Mechanical Hamiltonian systems with respect to linear Poisson structures and Jacobi-Reeb dynamicsmath.DG
Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
NDS learns dynamical models with prior knowledge, improving accuracy and efficiency.
problem Learning accurate dynamical models with limited data and varying dynamics.
method Neural Dynamical Systems (NDS) integrates prior knowledge in ODEs with neural networks to estimate parameters and predict states.
result NDS achieves higher accuracy and uses fewer samples compared to other methods.
Analog forecasting uses local dynamics to predict chaotic systems.
problem Theoretical connections between analog forecasting and dynamical systems are overlooked.
method Local approximations of the system's dynamics, linear regression, and estimation of analog forecasting errors.
result Analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
This work introduces a method to learn dynamical systems from noisy sensor measurements using multiple shooting.
problem Learning dynamical systems from noisy sensor measurements is challenging due to system instability.
method A scalable method based on multiple shooting.
result Robust learning of latent representations of dynamical systems from noisy measurements.
Abstract reviews symmetry and reduction in dynamical systems.
problem Understanding symmetries and reductions in dynamical systems.
method Algebraic formulation for dynamics of physical systems.
result Describes a reduction procedure for classical and quantum evolutions.
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by t…
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent dynamical system. Given trajectory data from two dynamical systems, we learn a …
This paper proposes a system-agnostic policy for dynamic scheduling.
problem Dynamic scheduling in changing systems is challenging due to system-specific optimal policies.
method Descriptive policy that learns a system-agnostic scheduling principle.
result System-agnostic meta-learning enables adaptation to unseen system characteristics.
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to determine whether arbitrary systems are governed by causal relations of the same form o…
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.
dynoNet learns dynamical systems using linear operators.
problem Learning complex dynamical systems.
method dynoNet uses linear dynamical operators for sequence modeling and system identification.
result dynoNet effectively identifies systems on benchmarks.
Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with dynamical systems with finite sets of observations and actions. We present an algorithm…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been difficult to make formal claims about the basic properties of the learned systems. In …
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.
New loss function helps learn unstable dynamical systems.
problem Gradient descent fails to learn unstable dynamical systems.
method Introduced a time-weighted logarithmic loss function.
result Time-weighted loss function effectively learns unstable systems.
DOODL learns shared spectral dynamics across related dynamical systems.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
New neural net learns time-reversible symplectic dynamics.
problem Lack of time-reversibility in neural networks for symplectic systems.
method Proposes a new neural network architecture for time-reversible symplectic systems.
result Demonstrates learning of time-reversible symplectic dynamics from data.
Paper proposes learning system dynamics from irregularly-sampled partial observations.
problem Capturing dynamics of multi-agent systems with irregular and partial observations.
method LG-ODE, a latent ordinary differential equation model using graph neural networks and neuralODE.
result Demonstrates effectiveness on motion capture, spring system, and charged particle datasets.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
A new metric compares dynamical systems using operator eigenvalues.
problem Comparing and interpolating nonlinear dynamical systems from trajectory data.
method Representing systems as distributions of operator eigenvalues and projectors, defining a spectral-Grassmann Wasserstein metric.
result The proposed metric outperforms standard operator-based distances in machine learning applications.
CoDA adapts dynamics models to new physical systems by conditioning on context.
problem Generalizing to new physical systems with shared dynamics but different contexts.
method Context-informed dynamics adaptation (CoDA) using multiple environments and a hypernetwork.
result State-of-the-art generalization results on nonlinear dynamics.
Proposes local coordinate frames for improving model performance in complex dynamical systems.
problem Improving model performance in complex, non-linear, and time-dependent dynamical systems.
method Introduces roto-translation invariant local coordinate frames for geometric graphs.
result The approach outperforms state-of-the-art models in various complex scenarios.
In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e. systems dynamically equivalent to linear control systems, the advantage of this a…
Model captures system input variations in latent space for actionable dynamics.
problem Learning dynamical systems from data without prescribing a mathematical model.
method Structured latent ODE model with stochastic factors of variation for each input.
result Improves generation of time-series data and inference of system inputs over baselines.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
problem Whether 2-valued dynamics can be defined by the action of a 2-valued group.
method Construction of examples of dynamics that are or are not group actions.
result Some 2-valued dynamics on complex plane cannot be defined by the action of a 2-valued group.
Easy conditions found for simplifying complex systems.
problem Linearizing complex two-input systems.
method Endogenous dynamic feedback with a dimension of at most two.
result Necessary and sufficient conditions for linearizability.
New Y-systems for Miquel dynamics are Möbius invariant.
problem Miquel dynamics circle centers are not Möbius invariant.
method Introduced new Y-systems involving only intersection points.
result New Y-systems are Möbius invariant and satisfy the transformation group principle.
Cross-validation methods help learn dynamical systems from data.
problem Learning surrogate models for dynamical systems from limited data.
method Variants of cross-validation (Kernel Flows, MMD, Lyapunov exponents).
result Simple approaches for kernel selection in dynamical system emulators.
Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamicsstat.ML
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.
Transformer model for probabilistic dynamical systems.
problem Modeling high-dimensional dynamical systems from noisy observations.
method Parallel between dynamical systems and language modeling; transformer-based model with geometrical properties; iterative training algorithm.
result Fine-grid approximation of conditional probabilities for high-dimensional systems.
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
Study uses auxiliary data to estimate system dynamics, reducing noise error.
problem Estimating system dynamics from similar but not identical systems.
method Weighted least squares approach with performance guarantees.
result Effective use of auxiliary data reduces estimation error due to process noise.
Deep learning detects bifurcations in dynamical systems.
problem Predicting catastrophic changes in dynamical systems across sciences.
method Data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries.
result Extracts topologically invariant features to detect bifurcation boundaries in unseen systems.
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
New method infers dynamical systems from population data.
problem Inferring dynamical systems from population data.
method Deducing and estimating Fokker-Planck equation, projecting to test functions, sparse inference.
result Induces driving forces of dynamical systems.
This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.
problem Identifying latent variables in sequential data models.
method Proved identifiability of Markov Switching Models and established conditions for Switching Dynamical Systems.
result Identifiability of latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations.
Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputsnlin.CD
Extremely accurate prediction of dynamical system bifurcations using control inputs.
problem Predicting complex bifurcation structures in dynamical systems.
method Extending extreme learning machines with control inputs to model system dynamics.
result The model can nearly reproduce the entire structure of bifurcations using only a few parameter values.
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…
The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.
problem Random dynamical systems of polynomial automorphisms on C^2.
method Generic random dynamical systems of polynomial automorphisms are shown to have mean stability.
result A generic random dynamical system of polynomial automorphisms on C^2 has mean stability.
Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.
problem Finding invariant measures for contact Hamiltonian systems.
method Splitting the system into Reeb and Liouville dynamics; using invariant measures and symplectic sandwiches.
result Invariant measure found for Reeb dynamics; characterization of Liouville dynamics invariant measure.
Uncertainty modeling for dynamical systems
problem Uncertainty modeling for dynamical systems
method Discussing sources of uncertainty, their nature, and task-specific objectives
result Identifying the types of uncertainty needed for dynamical systems
Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemsmath.DS
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
Learning non-stationary Langevin dynamics from stochastic observations of latent trajectoriesstat.ML
Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
Defines hybrid systems on principal bundles and studies impact effects.
problem Understanding impact effects in hybrid mechanical systems.
method Defines hybrid systems on principal bundles, studies underlying geometry, and finds conditions for impact preservation.
result Conditions for preservation of both exterior and interior impacts by mechanical connections.