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
17 Pith papers cite this work. Polarity classification is still indexing.
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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.
Data-driven Koopman analysis of a bistable stochastic system recovers large deviation theory escape time statistics and basin structure via the subdominant mode.
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.
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.
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.
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.
-
Data-driven analysis of metastability in a stochastic bistable system
Data-driven Koopman analysis of a bistable stochastic system recovers large deviation theory escape time statistics and basin structure via the subdominant mode.
-
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.
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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.
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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.
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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.
-
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.
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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.
-
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.