Exact analytical expression for the time-dependent maximum Lyapunov exponent during transients in a network supporting dynamics-based computation.
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Modern koopman theory for dynamical systems
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A real Schur decomposition projection maps the state matrix of discrete-time state-space layers onto its nearest stable counterpart, delivering accuracy comparable to prior stable identification methods with fewer weights.
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
DiffSRDA uses denoising diffusion models to perform uncertainty-aware spatiotemporal super-resolution data assimilation, achieving EnKF-like quality from low-resolution forecasts on an ocean jet testbed.
QIML uses a quantum-trained Q-Prior to enhance classical autoregressive predictions of spatiotemporal chaos, improving accuracy by up to 17.25% and full-spectrum fidelity by up to 29.36% while enabling stable forecasts for 3D turbulent channel flow.
Graph State-Space Models jointly learn state-space dynamics and latent relational graphs end-to-end from time series for forecasting and structure extraction.
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
Derives optimality constraints for nonnegative joint dictionary learning that explain observed SAE behaviors such as feature splitting, absorption, and dense antipodal features.
For a stochastic double-well system, the first nonzero Koopman eigenvalue and its mode recover mean escape times and basin boundaries without knowing the equations.
ASACK provides a unified online adaptation method for Koopman models of uncertain nonlinear systems that combines contractive learning laws, active excitation, and robust MPC safety bounds.
Non-conserved biased tracers debias more rapidly than conserved tracers, leading to time-dependent suppression of large-scale power.
Weak-DMD applies a Galerkin weak form to Dynamic Mode Decomposition to eliminate timestep constraints and filter noise in modal analysis.
Koopman operators identified from Bekker-Wong terramechanics simulations enable short-horizon prediction and constrained MPC for stable tracking of aggressive maneuvers by off-road vehicles on deformable terrain.
Self-supervised residual learning from trajectory data forms a hybrid dynamics model that enables trajectory optimization to produce aggressive yet precisely trackable motions for quadrotors.
Characteristic roots govern dynamics in linear forecasting models but noise induces spurious roots; rank reduction and Root Purge regularization mitigate this for more robust predictions.
Presents DHPO and a pretrained DeepONet inverse modeling framework that discovers unknown PDE terms and infers parameters across equation families with O(10^-2) solution and O(10^-3) parameter errors on benchmarks.
SHRED reconstructs full power system state from limited PMU data, outperforming a shallow decoder benchmark on the IEEE 39-bus system under nonlinear disturbances.
An integral formulation of QENDy is introduced that eliminates the need for time derivatives to achieve greater robustness against noise in nonlinear system identification.
Proves SCI upper bounds for regularized and closed approximate point ε-pseudospectra plus the approximate point spectrum of Koopman operators in L^p (1<p<∞) for four classes of maps via dictionaries and tagged quadrature residuals.
A SA-KLQR controller with tactile feedback enables real-time regulation of angle, pressure, and coverage for a deformable swab tool in food-safety sampling.
Proposes a two-step test for adequacy/reliability of stochastic dynamical system reconstruction from noisy data while discussing limits from degeneracy and non-identifiability.
A literature review of safe RL using Lyapunov and barrier functions that identifies a shift to model-free methods since 2017, well-defined open problems per approach class, and high-dimensional scalability as the main barrier.
citing papers explorer
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Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Exact analytical expression for the time-dependent maximum Lyapunov exponent during transients in a network supporting dynamics-based computation.
-
A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures
A real Schur decomposition projection maps the state matrix of discrete-time state-space layers onto its nearest stable counterpart, delivering accuracy comparable to prior stable identification methods with fewer weights.
-
Is Flow Matching Just Trajectory Replay for Sequential Data?
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
-
Uncertainty-Aware Spatiotemporal Super-Resolution Data Assimilation with Diffusion Models
DiffSRDA uses denoising diffusion models to perform uncertainty-aware spatiotemporal super-resolution data assimilation, achieving EnKF-like quality from low-resolution forecasts on an ocean jet testbed.
-
Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage
QIML uses a quantum-trained Q-Prior to enhance classical autoregressive predictions of spatiotemporal chaos, improving accuracy by up to 17.25% and full-spectrum fidelity by up to 29.36% while enabling stable forecasts for 3D turbulent channel flow.
-
Graph State-Space Models and Latent Relational Inference
Graph State-Space Models jointly learn state-space dynamics and latent relational graphs end-to-end from time series for forecasting and structure extraction.
-
Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
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How Optimality Structures Sparse Dictionaries: A Theory for Understanding SAE Representations
Derives optimality constraints for nonnegative joint dictionary learning that explain observed SAE behaviors such as feature splitting, absorption, and dense antipodal features.
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Data-driven analysis of metastability in a stochastic bistable system
For a stochastic double-well system, the first nonzero Koopman eigenvalue and its mode recover mean escape times and basin boundaries without knowing the equations.
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ASACK : Adaptive Safe Active Continual Koopman Learning for Uncertain Systems with Contractive Guarantees
ASACK provides a unified online adaptation method for Koopman models of uncertain nonlinear systems that combines contractive learning laws, active excitation, and robust MPC safety bounds.
-
Non-conservation and time non-locality of biased tracers
Non-conserved biased tracers debias more rapidly than conserved tracers, leading to time-dependent suppression of large-scale power.
-
Weak-DMD: A Galerkin approach to the problem of noise in the Dynamic Mode Decomposition algorithm
Weak-DMD applies a Galerkin weak form to Dynamic Mode Decomposition to eliminate timestep constraints and filter noise in modal analysis.
-
Koopman Operator Framework for Modeling and Control of Off-Road Vehicle on Deformable Terrain
Koopman operators identified from Bekker-Wong terramechanics simulations enable short-horizon prediction and constrained MPC for stable tracking of aggressive maneuvers by off-road vehicles on deformable terrain.
-
Optimizing Control-Friendly Trajectories with Self-Supervised Residual Learning
Self-supervised residual learning from trajectory data forms a hybrid dynamics model that enables trajectory optimization to produce aggressive yet precisely trackable motions for quadrotors.
-
Characteristic Root Analysis and Regularization for Linear Time Series Forecasting
Characteristic roots govern dynamics in linear forecasting models but noise induces spurious roots; rank reduction and Root Purge regularization mitigate this for more robust predictions.
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Learning Hidden Physics and System Parameters with Deep Operator Networks
Presents DHPO and a pretrained DeepONet inverse modeling framework that discovers unknown PDE terms and infers parameters across equation families with O(10^-2) solution and O(10^-3) parameter errors on benchmarks.
-
A Shallow Recurrent Decoder for Dynamic State Estimation with a Limited Number of PMUs in Power Systems
SHRED reconstructs full power system state from limited PMU data, outperforming a shallow decoder benchmark on the IEEE 39-bus system under nonlinear disturbances.
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Integral Formulation of QENDy for Robust Nonlinear System Identification
An integral formulation of QENDy is introduced that eliminates the need for time derivatives to achieve greater robustness against noise in nonlinear system identification.
-
Residual SCI Upper Bounds And Lower Witnesses For Koopman Approximate Point Spectra In $L^p$ For $1<p<\infty$: Extended Version
Proves SCI upper bounds for regularized and closed approximate point ε-pseudospectra plus the approximate point spectrum of Koopman operators in L^p (1<p<∞) for four classes of maps via dictionaries and tagged quadrature residuals.
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Data-Driven Contact-Aware Control Method for Real-Time Deformable Tool Manipulation: A Case Study in the Environmental Swabbing
A SA-KLQR controller with tactile feedback enables real-time regulation of angle, pressure, and coverage for a deformable swab tool in food-safety sampling.
-
Data-Based Dynamical Systems Reconstruction: An Adequacy/Reliability Test
Proposes a two-step test for adequacy/reliability of stochastic dynamical system reconstruction from noisy data while discussing limits from degeneracy and non-identifiability.
-
A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions
A literature review of safe RL using Lyapunov and barrier functions that identifies a shift to model-free methods since 2017, well-defined open problems per approach class, and high-dimensional scalability as the main barrier.