dynamical systems
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Related Articles from SNS
Let the Dynamics Flow: Stable Flow Matching Dynamical Systems
Announce Type: new Abstract: Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, incorporating formal stability guarantees into these generative models, a prerequisite to ensure safe and generalizable robot behaviors, remains a significant challenge. While modeling robot motions as dynamical systems allows for such stability-based inductive biases, existing frameworks struggle to capture the...
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
arXiv:2412.12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach,...
State-Coupled Volatility in Latent Dynamical Systems: Recovery Under Partial Observation
Announce Type: cross Abstract: Latent state-space models are widely used to study partially observed dynamical systems, yet most formulations assume that process variability is independent of latent-state position. In many biological, behavioral, and physiological systems, however, variability may depend systematically on the underlying dynamical state, producing structured stochasticity that is not captured by constant-variance models. We introduce a state-coupled stochastic volatility...
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
arXiv:2604.06881v2 Announce Type: replace Abstract: Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, Fourier-based variants inherently truncate high-frequency components in spectral space, resulting in the loss of small-scale structures and degraded prediction quality at high resolutions when trained on low-resolution data.
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
arXiv:2604.06881v2 Announce Type: replace-cross Abstract: Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, Fourier-based variants inherently truncate high-frequency components in spectral space, resulting in the loss of small-scale structures and degraded prediction quality at high resolutions when trained on low-resolution data.
SpectraLDS: Provable Distillation for Linear Dynamical Systems
arXiv:2505.17868v2 Announce Type: replace Abstract: We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that represents symmetric LDSs as convolutions learnable via fixed spectral transformations. We show how to invert this representation, thereby recovering an LDS model from its spectral transform and yielding an...
Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling
Announce Type: replace Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective.
Optimal Control and Dissipativity of Linear Hermitian Matrix-Valued Dynamical Systems
arXiv:2606.08856v1 Announce Type: cross Abstract: We develop a unified framework for linear-cost optimal control, finite-time optimal steering, dissipativity analysis, and zero-sum differential games for linear impulsive systems whose state is a Hermitian matrix evolving in $\mathbb{H}^{n+m}_{\succeq0}$, a class that encompasses continuous- and discrete-time linear systems and switched systems as degenerate cases, and includes the second-order moment dynamics of linear (stochastic) hybrid...
Self-Supervised Dynamical System Representations for Physiological Time-Series
Announce Type: replace Abstract: The effectiveness of self-supervised learning (SSL) for physiological time series depends on the ability of a pretraining objective to preserve information about the underlying physiological state while filtering out unrelated noise. However, existing strategies are limited due to reliance on heuristic principles or poorly constrained generative tasks. To address this limitation, we propose a pretraining framework that exploits the information structure of a...
Loop Current Extension as an Effective Delayed Dynamical System
Announce Type: cross Abstract: The Loop Current is the dominant circulation feature of the Gulf of Mexico and exhibits pronounced variability associated with northward extension, retraction, and eddy shedding. Despite decades of study, the extent to which this variability admits a reduced dynamical description remains unclear. We investigate this question using delayed-coordinate representations constructed from satellite-altimetry observations of Loop Current extension.