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.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,181 papers · 148 categories
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48 results for “stable dynamical systems”
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.
This work extracts stochastic dynamical systems with -stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for -stable Lévy noise.
result Effectiveness of the method confirmed by numerical experiments.
Proposes a method to learn stable invariant sets in dynamical systems.
problem Learning stable invariant sets in general dynamical systems.
method Generalizes Manek and Kolter's approach by introducing projection onto latent space shapes and using invertible neural networks.
result Validates the method and shows its usefulness for long-term prediction.
New algorithm learns stable LDSs with lower error and better control performance.
problem Learning stable LDSs from data with minimal reconstruction error and stability constraints.
method Proposes an optimization method using a recent characterization of stable matrices, iteratively improving reconstruction error and ensuring stability.
result Achieves orders-of-magnitude improvement in reconstruction error compared to existing methods.
CVF learns stable dynamical systems from trajectories.
problem Stable dynamical systems from sampled trajectories.
method Constructs vector fields with controlled contraction and curvature using convex optimization.
result CVF learns stable dynamical systems explicitly controlled by curvature and contraction.
Study learns dynamics of linear systems from multiple short trajectories.
problem Learning dynamics of autonomous linear systems from multiple short trajectories.
method Finite sample analysis for stable and unstable systems, adjusting trajectory length for marginally stable systems.
result Learning rate of for both stable and unstable systems.
The paper addresses online prediction in marginally stable systems with bounded perturbations.
problem Online prediction in marginally stable linear dynamical systems with adversarial or stochastic perturbations.
method The online least-squares algorithm is used to achieve sublinear regret, with a refined regret analysis and a structural lemma.
result The online least-squares algorithm achieves sublinear regret, with polynomial dependence on the system's parameters.
Method extracts stochastic systems with Lévy noise from data.
problem Identifying stochastic dynamical systems with Lévy noise from short data.
method Estimate Lévy jump measure and noise intensity, approximate drift coefficient.
result Accurate and effective method for discovering stochastic laws.
Proposes neural delay differential equations for stable system identification with partially observed states.
problem Learning stable models for systems with partial or delayed observations.
method Augments states with history, uses neural delay differential equations, and ensures stability through time delay analysis.
result The approach ensures stability of learned models for partially observed systems.
NAIS-Net stabilizes deep networks using non-autonomous dynamical systems.
problem Stabilizing deep neural networks to prevent vanishing/exploding gradients.
method NAIS-Net uses non-autonomous dynamical systems with skip connections to enforce stability.
result NAIS-Net proves to be globally asymptotically stable and reduces generalization gap.
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…
Stabilizes complex systems using diffusion models trained on Lyapunov functions.
problem Generating stabilizing controllers for complex dynamical systems.
method Trains a diffusion model on pairs of asymptotically stable vector fields and their Lyapunov functions to identify the closest stable field and adjust control functions.
result Efficient and rapid stabilization of unseen systems, showcasing generalizability.
Generative models for complex stochastic dynamics using adversarial learning.
problem Data-driven modeling of multistep stochastic dynamics.
method Adversarial learning with GANs and MMD for stable model classes.
result Stable generative models for long-time prediction and stochastic systems.
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
Anticorrelations, subbrownian stochastic drift, and 1/f-like spectra in stable financial systemscond-mat.dis-nn
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
Are large complex economic systems unstable ?physics.soc-ph
Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic n…
This paper addresses metaconsistency in Bayesian inference for metastable systems.
problem Inference for metastable systems may not be consistent, but can be metaconsistent over large but finite time intervals.
method Introduces metaconsistency in a Bayesian framework, discusses its relation to spectral properties of model dynamics.
result Metaconsistency can be exploited to infer sub-systems efficiently from larger systems.
PAC-Bayes bound for stable RNNs in time-series data.
problem Bounding generalization gap for stable RNNs in time-series data.
method Derived a PAC-Bayes bound with stability constraints for discrete-time non-linear dynamical systems, including stable RNNs.
result The bound converges to zero as dataset size increases, and does not grow with RNN steps.
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This comb…
Noise-robust Koopman operator framework for control with improved stability and performance.
problem Developing a stable and noise-robust Koopman operator for control tasks.
method Proposes a learning framework using Hankel matrix and neural network approximations for system dynamics, ensuring long-term stability and noise robustness.
result Demonstrates improved model performance and noise robustness in control tasks compared to existing methods.
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.
Model financial network dynamics to avoid systemic risk.
problem Avoid systemic risk in financial networks.
method Model financial network as random liability graph, agents adapt strategies based on learning, analyze using ODE.
result Emerging strategies converge to evolutionary stable strategies (all risky or all less risky agents).
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.
Paper generalizes Mochizuki's theorem to stable λ-flat bundles and explores applications to moduli spaces.
problem Stable λ-flat bundles and their moduli spaces.
method Generalization of Mochizuki's theorem to stable λ-flat bundles and applications to moduli spaces.
result Existence of harmonic metrics on stable λ-flat bundles and homeomorphism between moduli spaces.
First-order methods avoid saddle points for most initializations.
problem Avoiding saddle points in optimization problems.
method First-order methods, including gradient descent and variants, analyzed using dynamical systems and the Stable Manifold Theorem.
result First-order methods avoid saddle points for almost all initializations.
Paper proves non-equivalence of RKHS stability and kernel absolute summability.
problem Equivalence of RKHS stability and kernel absolute summability.
method Analyzes Reproducing Kernel Hilbert spaces and positive semidefinite kernels.
result Stable RKHSs can be induced by non-absolutely summable kernels.
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.
This work analyzes how users and services adapt to reduce risk, leading to specialization.
problem Adaptation of users and services to reduce risk affects learning and performance.
method Analyzed a class of dynamics where users allocate participation and services update parameters.
result Repeated myopic updates with multiple learners lead to better outcomes than repeated risk minimization.
CausalKinetiX identifies stable kinetic models from noisy data.
problem Learning stable and predictive kinetic models from noisy data.
method CausalKinetiX framework for identifying structure from discrete time, noisy observations.
result Causal approach improves generalization and prediction in kinetic systems.
Model financial network dynamics to avoid systemic risk.
problem Emergence of systemic risk in financial networks.
method Derive solutions of random fixed point equations, analyze replicator dynamics, derive conditions for evolutionary stable strategies, verify with simulations.
result Emerging strategies converge to an attractor of an ODE, avoiding systemic risk.
This work tackles learning stable Koopman operators from data.
problem Learning stable Koopman operators from data with guaranteed stability.
method Formalizes Koopman operator learning with deep neural networks, enforcing stability through structural parameterization and hierarchical Bayesian inference.
result Demonstrates a stable autoencoder architecture for learning Koopman operators and quantifying uncertainties.
GRUs exhibit diverse dynamical behaviors but cannot mimic continuous attractors.
problem Understanding and predicting the dynamics of GRUs for neural data.
method Continuous time dynamical systems analysis of GRU networks.
result GRUs can represent stable limit cycles, multi-stable dynamics, and homoclinic bifurcations but not continuous attractors.
Efficient online control algorithms for noisy systems with quadratic losses.
problem Controlling linear systems with known dynamics and adversarial losses.
method Novel SDP relaxation for steady-state distribution, ensuring strongly stable policies.
result Guaranteed regret for online learning algorithms.
Stabilized neural differential equations enforce constraints on dynamical systems.
problem Ensuring dynamical systems preserve known constraints like conservation laws.
method SNDEs with a stabilization term to enforce manifold constraints.
result SNDEs outperform existing methods and broaden constraint types.
New insights into gradient descent and ascent dynamics in min-max optimization.
problem Understanding the convergence and limit points of gradient descent and ascent methods in min-max optimization problems.
method Characterization of limit points using dynamical systems perspective for GDA and OGDA.
result Both GDA and OGDA dynamics avoid unstable critical points and have a superset of local min-max solutions.
Direct Mapping Hidden Excited State Interaction Patterns from ab initio Dynamics and Its Implications on Force Field Developmentphysics.chem-ph
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
KCRL learns stable policies for nonlinear systems with formal guarantees.
problem Lack of stabilization guarantees in RL methods for safety-critical systems.
method KCRL uses Krasovskii's Lyapunov functions as a stability constraint and a primal-dual approach to learn stabilizing policies.
result KCRL guarantees learning a stabilizing policy in a finite number of interactions.
Predictive coding networks are shown to be stable, robust, and converge faster than backpropagation.
problem Stability, robustness, and convergence of predictive coding networks.
method Dynamical systems theory and Lyapunov stability analysis.
result Predictive coding networks are Lyapunov stable and converge faster than backpropagation.
Paper solves tracking control for -flat systems using classical states.
problem Tracking control for -flat systems.
method Quasi-static feedback of classical states.
result Achieves linear, decoupled and asymptotically stable tracking error dynamics.
Stable topological summary captures evolving dependency structure in dynamic Bayesian networks.
problem Missing larger-scale patterns in evolving dependency structures in dynamic Bayesian networks.
method Topological approach using Dynamic Bayesian Graphs and persistent homology.
result Stable topological summary (barcodes) captures evolving dependency structure in DBNs.
Cryptocurrency stability modeled using dynamical systems theory.
problem Stability of cryptocurrencies in the absence of traditional financial metrics.
method Modeling cryptocurrency assets as asset flow equations and analyzing stability of resulting ordinary differential equations.
result Conditions for system stability identified, with trends and liquidity affecting stability.
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical systems, construct their cross-products, and introduce representation theory of …
Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approachstat.ML
Study non-asymptotic bounds on correlation in high-dimensional linear systems, revealing invariant subspaces and bottlenecks.
problem Understanding correlation and mixing in high-dimensional linear systems with Gaussian noise.
method Sampling from sub-trajectories, using Talagrand's inequality, and analyzing invariant subspaces.
result Large discrepancy between algebraic and geometric multiplicity leads to bottlenecks between invariant subspaces.
Study stabilizes second-order systems to first-order dynamics.
problem Stabilizing second-order systems to first-order dynamics.
method Feedback control of second-order systems on manifolds.
result Second-order systems can globally exponentially stabilize first-order dynamics for fully actuated systems.
Next-gen reservoir computing models dynamical systems from time-series data.
problem Modeling dynamical systems from time-series data.
method Pseudorandom nonlinear projection of time-delay embedded inputs.
result Models remain stable over long rollouts and generalize beyond training data.