Paper shows leafwise cohomological expression for dynamical zeta functions.
problem Analyzing dynamical zeta functions on foliated dynamical systems.
method Leafwise cohomological approach.
result Leafwise cohomological expression of dynamical zeta functions.
Method learns to map dynamics of different systems.
problem Mapping dynamics of different systems.
method Learned latent dynamical system for mapping.
result Learned correspondences enable imagined motions and bisimulation.
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.
Dynamic systems linked to infinite permutation matrices.
problem Dynamic equivalence of control systems.
method Association of infinite permutation matrices.
result Relationship between dynamic equivalences and permutation matrices.
Stable deep models learn dynamical systems with formal stability guarantees.
problem Difficulties in making formal claims about stability of deep network dynamics models.
method Jointly learning a dynamics model and Lyapunov function to ensure non-expansiveness.
result Proposes an approach for stable deep learning of dynamical systems.
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.
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…
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.
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.
Neural circuits integrate continuous dynamics efficiently.
problem Efficiently integrating continuous neural dynamics for simulation and learning.
method Compact neural circuits for Runge-Kutta and Adams-Bashforth-Moulton methods.
result Equivalence of neural and numerical integration for polynomial systems.
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.
This work improves neural network models of dynamical systems by regularizing the tangent space of the dynamics function.
problem Improving neural network models of dynamical systems to learn correct input-output Jacobians without overfitting.
method Regularization of the model Jacobian along system trajectories using assumptions on the tangent space of the dynamics.
result Different network architectures learn models with correct input-output Jacobians under different conditions.
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…
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.
This work identifies eigenvalues of unknown linear dynamics without full system identification.
problem Identifying parameters of a linear dynamical system is challenging.
method Developed a computationally efficient algorithm to estimate eigenvalues of the state-transition matrix.
result The algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths.
Learning machines can mimic the dynamics of black systems without knowing their equations.
problem Simulating black systems without knowing their equations of motion.
method Train a learning machine with input-output responses or time series of a black system.
result Learning machines can mimic the dynamics of various black systems and their evolution history.
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.
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 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.
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.
Study of Sard problem in Carnot groups using dynamical systems.
problem Sard problem in sub-Riemannian Carnot groups.
method Dynamical-systems approach to study singular curves.
result Positively answer the Sard problem in some Carnot groups.
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.
Develops interpretable model for latent stochastic systems from noisy data.
problem Learning interpretable models of latent stochastic dynamical systems from noisy data.
method Semi-parametric model using Gaussian process for drift, inference of latent paths with sparse variational description.
result Flexible nonparametric model of dynamics with interpretable portraits.
Switching linear dynamics improves model-based reinforcement learning and system identification.
problem Complex and nonlinear systems can be approximated by linear dynamical systems.
method Bayesian inference, Variational Autoencoders, Concrete relaxations.
result Improved accuracy in learning dynamics from partial and high-dimensional observations.
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…
Develops methods to model and forecast inter-sectoral balance dynamics.
problem Modeling and forecasting the dynamics of inter-sectoral balance in macroeconomic systems.
method Approach to specification and identification of a weakly formalized dynamical system, matching procedure for parameters, detection of significant harmonic waves.
result Effective methods for detecting and modeling significant harmonic waves in macroeconomic systems.
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.
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.
Deep learning networks are approximated using dynamical systems theory.
problem Understanding the approximation capabilities of deep learning networks.
method Modeling deep residual networks as continuous-time dynamical systems and using approximation theories in Lp. result Established general sufficient conditions for universal approximation of deep residual networks.
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.
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.
New tools for uncertainty in dynamical systems without distribution assumptions.
problem Uncertainty representation in dynamical systems without distributional assumptions.
method Kernel mean embedding and kernel probabilistic programming.
result Distribution-free representation, comparison, and propagation of uncertainties.
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.
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.
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.
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.
SRNNs learn dynamics of physical systems from data.
problem Learning dynamics of complex, noisy Hamiltonian systems.
method SRNNs model Hamiltonian functions with neural networks, using symplectic integration and optimization.
result SRNNs reliably learn dynamics of complex and noisy Hamiltonian systems.