New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.
problem Random dynamical systems of polynomial automorphisms on C^2.
method Generic random dynamical systems of polynomial automorphisms are shown to have mean stability.
result A generic random dynamical system of polynomial automorphisms on C^2 has mean stability.
We investigate i.i.d. random complex dynamical systems generated by probability measures on finite unions of the loci of holomorphic families of rational maps on the Riemann sphere. We show that under certain conditions on the families, for a generic system, (especially, for a generic random polynomial dynamical system…
Deep neural nets approximate random dynamical system trajectories uniformly in time.
problem Approximating trajectories of random dynamical systems over infinite time horizons.
method Recurrent neural networks with simple feedback structures.
result Certain random trajectories can be approximated uniformly in time to any desired accuracy.
Random feature maps improve forecasting of chaotic dynamical systems.
problem Forecasting chaotic dynamical systems with high accuracy.
method Data-driven random feature maps with tanh activation, skip connections, and localization.
result Effective forecasting skill for dynamical systems with dimensions up to 512.
Paper develops metrics for random dynamical systems using vector-valued RKHSs.
problem Creating metrics for random nonlinear dynamical systems.
method Develops metrics on random dynamical systems using Perron-Frobenius operators in vector-valued reproducing kernel Hilbert spaces (vvRKHSs). Uses operator-valued kernels and time-wise independence criteria.
result Extends existing metrics for deterministic systems and introduces kernel maximal mean discrepancy for random processes.
Machine learning identifies chimera states in complex dynamical systems.
problem Chimera states are hard to identify due to their varied appearance and peculiar nature.
method Machine learning techniques, specifically random forest and oblique random forest with null space regularization.
result High accuracy in identifying chimera states across different dynamical models.
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
Randomized feature models learn interaction kernels from agent paths.
problem Learning interaction kernels from noisy agent paths.
method Randomized feature algorithm and sparse regression.
result Pruned features reduce overfitting and lower simulation cost.
Generative adversarial network for probabilistic forecasting of random systems.
problem Forecasting random dynamical systems without distributional assumptions.
method Recurrent neural network and generative adversarial network (GAN) with regularization based on maximum mean discrepancy (MMD).
result The proposed model successfully forecasts complex stochastic processes with multiple-step predictions.
Overview of high-dimensional dynamical systems and their applications to machine learning.
problem Characterizing behavior of high-dimensional dynamical systems driven by random matrices.
method Cavity method arguments, path integrals, dynamical mean field theory (DMFT), and random matrix resolvents.
result Connections between random matrix resolvents and DMFT response, and non-monotonic loss curves in training.
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…
We consider a multivariate default system where random environmental information is available. We study the dynamics of the system in a general setting and adopt the point of view of change of probability measures. We also make a link with the density approach in the credit risk modelling. In the particular case where …
Develops a Krylov subspace method for estimating nonlinear systems with random noise.
problem Estimating nonlinear dynamical systems with random noise.
method Lifted representation of nonlinear dynamical systems using transfer operators, extended Arnoldi method, and shift-invert Arnoldi method.
result Empirical validation of methods on synthetic and real-world healthcare data.
New approach to concentration inequalities for unbounded state space dynamical systems.
problem Concentration inequalities for unbounded state space dynamical systems.
method Functional analytic framework, transport-entropy inequality.
result Exponential concentration inequalities for sampling from stationary distribution.
The supplement proves the existence and properties of a dynamical system related to asset price bubbles.
problem Modeling asset price bubbles using liquidity and random matching.
method Proves the existence and properties of a dynamical system D.
result Existence and properties of the dynamical system D are proven.
A new method for decision tree selection in recommendation systems.
problem Feature-based selection of a single tree from an ensemble for dynamic interpretation.
method A multi-armed contextual bandit recommendation framework that trains a system on top of Random Forests to identify the most relevant tree.
result The dynamic method outperforms an independent CART tree and is comparable to Random Forest in predictive performance.
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
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).
New algorithm shows how networked agents can protect against systemic risk.
problem Understanding and managing systemic risk in networked systems.
method Developed a simple algorithm to model protection dynamics in networked agents.
result Protection mechanisms can emerge even in random networks, reducing systemic risk.
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
This work extracts stochastic dynamical systems with α-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 α-stable Lévy noise. result Effectiveness of the method confirmed by numerical experiments.
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.
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationa…
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
problem Simulating dynamics on dense random matrix ensembles with high space and time complexity.
method Householder reflectors for adaptive and recursive construction, deferring decisions.
result Significant reductions in runtime and memory footprint for practical T≪n. We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an algorithm to generate complex dynamics for parameters and (both visible and hidde…
SDCMs model causal dynamics of interacting components over time.
problem Modeling and understanding causal relationships in dynamical systems.
method Structural dynamical causal models (SDCMs) that represent time-dependent stochastic processes.
result SDCMs extend SEMs to include time-dependence and provide a theory for their solutions.
Study rolling dynamics with random slipping and twisting using large deviation principles.
problem Analyzing the stability of a rolling model with random slipping and twisting.
method Modelled as a stochastic differential equation on the orthonormal frame bundle, examined via large deviations.
result Proved large deviation principles for projection curves and their horizontal lifts on the base manifold.
Researchers develop methods to learn neuron dynamics from colored noise.
problem Learning nonlocal stochastic neuron dynamics from colored noise.
method Proposed two methods for closing Fokker-Planck equations: nonlocal large-eddy-diffusivity closure and data-driven sparse regression.
result Mutual information and total correlation between stimulus and neuron states calculated for FHN neuron.
DeepRSCN models nonlinear systems using stochastic configurations.
problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.
RaNNDy uses randomized neural networks to learn transfer operators efficiently.
problem Efficiently learning transfer operators from data.
method Randomized neural network approach with randomly initialized hidden layers and trained output layer.
result Significant reduction in training time and resources with improved stability.
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the alg…
Analyze message passing algorithms using free probability theory.
problem Dynamics of message passing algorithms for probabilistic models.
method Use freeness assumptions of random matrix theory.
result Recover and analyze properties of message passing algorithms.
Study on estimating unstable open-loop matrices from state trajectories.
problem System identification for stochastic continuous-time dynamics.
method Employing randomized control inputs to estimate unstable open-loop matrix.
result Estimation error decays with trajectory length, signal-to-noise ratio, and excitability.
This work's purpose is to understand the dynamics of some social systems whose properties can be captured by certain iterated function systems. To achieve this intension, we start from the theory of iterated function systems, and then we study two specific economic models on random utility function and optimal stochast…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the averaged system disappears, due to the cooperation of the generators. We investi…
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
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.
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is studied by numerical simulations. The dynamics is so slow that one can meaningf…
DCRNN improves LSTM for chaotic dynamical system forecasting.
problem Modeling chaotic dynamical systems with recurrent neural networks.
method DCRNN incorporates learnable skip-connections and a Lyapunov stability regularization term.
result DCRNN outperforms LSTM in 100 out of 100 experiments, reducing mean squared error by 80.0%.
Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality (SOC) is one of the most popular theories able to explain this intermittent char…
A new method de-randomizes MCMC dynamics using the Stein operator.
problem Estimating complex target distributions in Bayesian inference.
method De-randomized kernel-based particle samplers that discretize the fiber-gradient Hamiltonian flow.
result GSVGD de-randomizes complex MCMC dynamics, maintaining high sample quality.
A GAN method for stochastic boundary conditions in fast dynamics.
problem Uncertainty quantification in fast dynamics and wave propagation.
method Physics-informed GANs for stochastic boundary conditions.
result Improved convergence and better stochastic boundary conditions.
Kernel test evaluates dynamical system data streams.
problem Evaluate if data streams from dynamical systems are from the same distribution.
method Proposes a novel kernel two-sample test for dynamical systems, addressing independence and autocorrelation challenges.
result Data-driven method with theoretical guarantees for anomaly detection.
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.
The paper explores how complex models can improve system identification beyond traditional limits.
problem Balancing model richness and spurious learning in system identification.
method Investigates the double-descent phenomenon in the context of dynamic systems.
result Complex models can improve system identification performance beyond the point of interpolation.
Random feature maps improve forecasting with cheaper computation.
problem Improving forecasting accuracy with random feature maps.
method Developed a hit-and-run algorithm to select optimal internal weights.
result Optimal internal weights lead to superior forecasting skill.