New method calibrates predictions in chaotic systems using variational inference.
problem Uncertainty in data assimilation for chaotic systems.
method Variational inference applied to multivariate Gaussian distribution.
result Nearly perfectly calibrated predictions in chaotic Lorenz-96 dynamics.
Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.
problem Challenging identification of governing equations from noisy and partial observations.
method Jointly learns inference model and governing laws using variational deep learning.
result Framework generalizes state-of-the-art methods and accounts for stochastic variabilities.
Extends tracking guarantees for time-varying variational inequalities.
problem Tracking solutions of time-varying variational inequalities.
method Extends existing results to sublinear solution paths and periodic problems.
result Discrete dynamical systems of periodic time-varying VI can exhibit chaotic behavior or converge to the solution.
A ML model accurately replicates chaotic dynamics across various parameters.
problem Replicating chaotic characteristics of non-linear dynamics using machine learning.
method A ML model trained to predict one-step-ahead states from historic states captures bifurcation diagrams and Lyapunov exponents universally.
result Variational quantum circuit outperforms classical models in reproducing long-term chaotic characteristics.
Deep learning improves chaotic dynamics filtering without ensemble.
problem Discovering efficient DA schemes for chaotic dynamics.
method Residual Convolutional Neural Network for the analysis step.
result Deep learning achieves ensemble filtering accuracy without an ensemble.
Novel framework for risk-sensitive reinforcement learning using martingale decomposition.
problem Risk sensitivity in sequential decision-making with uncertain rewards.
method Martingale decomposition and chaotic variation for reward uncertainty, integrated into model-free reinforcement learning algorithms.
result Demonstrated relevance of risk-sensitive reinforcement learning in grid world and portfolio optimization problems.
The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.
problem Modeling chaotic positional dynamics of stars in celestial systems.
method Discrete dynamical systems, Ricci flow, Perelman entropy, Lyapunov exponents, bifurcation analysis.
result Entropy increases exponentially, indicating challenging long-term star position prediction.
The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for fully-observed systems, {\em i.e.} large signal-to-noise ratios and high-frequency sampling …
Study chaotic behavior in homeomorphism groups of countable products of spaces.
problem Investigate chaotic behavior in homeomorphism groups of countable products of various metrizable topological spaces.
method Construct numerous examples of chaotic groups of homeomorphisms of countable products of spaces.
result New chaotic groups of homeomorphisms of countable products of various metrizable topological spaces are discovered.
Enhanced fuzzy system predicts chaotic time series with improved accuracy.
problem Forecasting chaotic time series with high uncertainty.
method Combines evolving fuzzy systems, participatory learning, KRLS, and type-2 fuzzy sets.
result Proposed model outperforms other methods in accuracy and complexity.
TSSC images enhance chaotic signal classification using ConvNets.
problem Classifying chaotic signals accurately and robustly.
method Triad State Space Construction (TSSC) for image encoding, Convolutional Neural Network (ConvNet) for classification.
result TSSC-ConvNet achieves high accuracy and robustness in chaotic signal classification.
We introduce a deep learning method to simulate the motion of particles trapped in a chaotic recirculating flame. The Lagrangian trajectories of particles, captured using a high-speed camera and subsequently reconstructed in 3-dimensional space, were used to train a variational autoencoder (VAE) which comprises multipl…
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural networks can efficiently model chaotic dynamics by becoming structurally chaotic t…
Reservoir computing predicts chaotic systems for long horizons with sparse updates.
problem Predicting chaotic systems with long horizons using limited data.
method Sparse, time-dependent data inputs into reservoir computing.
result Achieves arbitrarily long prediction horizons for chaotic systems.
Predicting unobserved bifurcations in time series with unsupervised parameter extraction.
problem Predicting system behavior with unknown parameters from time series data.
method Reservoir computing framework for unsupervised extraction of slowly varying system parameters.
result Model predicts unknown bifurcations not present in training data.
Bayesian ANN method predicts chaotic systems with uncertainty.
problem Estimating chaotic dynamical systems from noisy data.
method Bayesian Artificial Neural Networks for ODE inverse problems.
result Accurate time predictions and uncertainty bounds.
New risk models use chaotic attractors to predict extreme events.
problem Predicting Black Swan events in financial markets.
method Combining heavy-tailed priors with chaotic dynamics (Lorenz and Rossler systems).
result Models generate volatility clustering, fat tails, and extreme events.
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of eith…
Panda predicts chaotic systems without retraining, showing emergent properties.
problem Predicting chaotic systems with small errors.
method Trained on a synthetic dataset of chaotic dynamical systems using evolutionary algorithms.
result Panda predicts unseen chaotic systems with zero-shot learning.
Deep learning models learn chaotic system dynamics from real and simulated data.
problem Training deep learning models for chaotic systems requires big data.
method Jointly train deep neural networks on real and simulated data, enforcing physical laws.
result Proposes knowledge-based deep learning (KDL) for accurate forecasting of chaotic systems.
This paper considers the ideal gas-like model of trading markets, where each individual is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally this model introduces different rules of random selection and exchange between pair agents. Real economic …
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional lo…
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over conventional uni-dimensional approaches by harnessing the information from both …
Gradient descent with chaotic perturbations improves generalization.
problem Improving generalization of gradient descent.
method Introducing chaotic perturbations to gradient descent to achieve improved generalization.
result Gradient descent with chaotic perturbations converges to a heavy-tailed SDE, leading to improved generalization.
The geometry of oscillatory integrals on manifolds with intermediate symmetry.
problem Classification of curvature conditions in Sogge's program.
method Proposing a classification of curvature conditions.
result No manifolds satisfy the chaotic curvature condition of order 1.
Investigates chaotic financial time series with monthly contributions and devaluation.
problem Analyzing chaotic behavior in financial processes with piecewise contributions and negative interest rates.
method Examines a financial process with monthly contributions and devaluation, showing dichotomy in behavior.
result Financial time series exhibit either periodic sequences or Cantor set of ω-limit points, with chaotic behavior at points of a Cantor attractor.
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some of the most challenging real-life applications is to train different neural netwo…
RNNs struggle with chaotic dynamics due to exploding gradients, but we found a way to optimize training.
problem Challenging training of RNNs with chaotic dynamics due to exploding gradients.
method Relating loss gradients to Lyapunov spectrum to optimize training on chaotic data.
result RNNs with chaotic dynamics always have diverging gradients, while stable ones have bounded gradients.
This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.
problem Ensuring long-term accuracy of ensemble Kalman filters for complex dynamical systems.
method Established conditions for long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems.
result Ensemble Kalman filters maintain small estimation error over long time horizons for chaotic and machine-learned systems.
Apparently random financial fluctuations often exhibit varying levels of complexity, chaos. Given limited data, predictability of such time series becomes hard to infer. While efficient methods of Lyapunov exponent computation are devised, knowledge about the process driving the dynamics greatly facilitates the complex…
Modeling bank leverage dynamics using dynamical systems and neural networks.
problem Understanding leverage dynamics in financial systems.
method Dynamical systems, deep neural networks, adaptive expectation scheme.
result Chaotic behavior in leverage dynamics for a significant fraction of banks.
FCOC framework improves financial volatility forecasting.
problem Tackles dual challenges of feature fidelity and model responsiveness in financial volatility forecasting.
method Synergizes fractal feature extraction and dynamic chaotic oscillation processing.
result Demonstrates profound and generalizable impact on S\&P 500 and DJI datasets.
A new framework reduces inconsistencies in chaotic surrogate modeling.
problem Consistency issues between probabilistic objectives and dynamical system dynamics.
method KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter.
result KAFFEE mitigates the dynamic-probabilistic consistency gap, improving reconstruction and predictive scores.
A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time…
A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial ti…
ESNs with transfer learning predict long-term chaotic patterns in spatiotemporal dynamical systems.
problem Predicting long-term statistical patterns of spatiotemporally chaotic dynamical systems.
method Echo state networks (ESNs) with transfer learning.
result ESNs with transfer learning accurately predict long-term statistical properties of spatiotemporally chaotic PDEs.
Combining LETKF and RC improves chaotic system prediction from noisy, sparse data.
problem Improving chaotic system prediction from imperfect observations and models.
method Combining LETKF and RC to predict spatio-temporal chaotic systems from noisy and sparsely distributed observations.
result The proposed method using LETKF and RC outperforms LETKF in predicting chaotic systems from noisy and sparse observations.
Transfer learning improves chaotic dynamics predictions with less data.
problem Efficiently predicting chaotic dynamics with limited data.
method Transfer learning for nonlinear dynamics, optimizing transfer rate and leveraging small-scale turbulence universality.
result Significantly more accurate inference of chaotic dynamics achieved.
Analog forecasting uses local dynamics to predict chaotic systems.
problem Theoretical connections between analog forecasting and dynamical systems are overlooked.
method Local approximations of the system's dynamics, linear regression, and estimation of analog forecasting errors.
result Analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.
Agent-based models have demonstrated their power and flexibility in Econophysics. However their major challenge is still to devise more realistic simulation scenarios. The complexity of Economy makes appealing the idea of introducing chaotic number generators as simulation engines in these models. Chaos based number ge…
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…
In a recent paper we constructed a family of foliated 2-complexes of thin type whose typical leaves have two topological ends. Here we present simpler examples of such complexes that are, in addition, symmetric with respect to an involution and have the smallest possible rank. This allows for constructing a 3-periodic …
This paper presents a novel study on gas-like models for economic systems. The interacting agents and the amount of exchanged money at each trade are selected with different levels of randomness, from a purely random way to a more chaotic one. Depending on the interaction rules, these statistical models can present dif…
Study chaotic dynamics in social stratification models leading to thermalization and turbulence.
problem Understanding social stratification dynamics through chaotic nonlinear systems.
method Modeling social network links with oscillators and energies, studying Hamiltonian evolution and nonlinear interactions.
result Chaotic dynamics leads to dynamical thermalization and Kolmogorov-Zakharov turbulence, with implications for wealth inequality.
New method learns chaotic dynamics from single noisy trajectory.
problem Chaos in complex systems is hard to model accurately with machine learning.
method Adversarial optimal transport objectives to learn summary statistics and emulator from single noisy data.
result Emulators trained with proposed objectives have significantly improved long-term statistical fidelity.
Unified theory of θ-expectations derived from chaotic dynamics.
problem Non-convex stochastic control problems outside G-expectations.
method Spectral theory of transfer operators for uniformly hyperbolic flows, viscosity solutions to HJB equations.
result Affine Hessian, non-convex gradient structure of θ-expectation. This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.
problem Estimating chaotic dynamics and parameters from observations.
method Local ensemble Kalman filters with covariance and local domain localisation.
result Rigorously updating global parameters using a local domain ensemble Kalman filter.
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference fro…