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.
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 …
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.
Chimera state refers to coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of Chimera, on one hand is essential due to its applicability in various areas including neuroscience, and on other hand is challenging due to its wid…
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.
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…
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).
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.
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…
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.
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…
Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states of the system's components over time, but also describe how their evolution is af…
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.
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random…
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 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…
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…
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.
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.
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than researchers understood them to be. In this paper, we show how to construct a large vari…
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…
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.
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.
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.
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.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
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.
Improved averaging method for noisy observations converges strongly.
problem Noisy observations from random dynamical systems require stable estimates.
method Introduced p-EMA, a modified exponential moving average with subharmonic weight decay. result Stochastic convergence guarantees for p-EMA under mild assumptions. Domain randomization (DR) is a successful technique for learning robust policies for robot systems, when the dynamics of the target robot system are unknown. The success of policies trained with domain randomization however, is highly dependent on the correct selection of the randomization distribution. The majority of…