Neural networks improve Lorenz trajectory prediction.
problem Predicting the Lorenz dynamical system's future states.
method Multitask learning to improve prediction of the z trajectory.
result Neural networks enhance forecasting performance.
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48 results for “Lorenz system”
Deep learning models predict chaotic Lorenz 96 system accurately.
problem Predicting short-term and long-term statistics of a multi-scale chaotic system.
method Reservoir computing (RC-ESN), ANN, RNN-LSTM.
result RC-ESN outperforms ANN and RNN-LSTM for short-term prediction.
Proves stability of Minkowski space-time in Einstein-Yang-Mills system.
problem Stability of Minkowski space-time governed by Einstein-Yang-Mills system.
method Null frame decomposition, well-posedness of Cauchy development, convergence to Minkowski space-time.
result Exterior stability of Minkowski space-time in Lorenz gauge without spherical symmetry.
During this last decades, several attempts to construct slow invariant manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many two-time scales singularly perturbed dynamical systems the various asymptotic p…
Lorenz links, T-links, Minimal Braids, Positive braids with a full twist, and Geometric Typesmath.GT
Study of Lorenz links and T-links, showing equivalence and unique presentations.
problem Understanding equivalence and uniqueness of T-link presentations for Lorenz links.
method Minimal-braid approach, V-link braids, T-link parameters, geometric type criteria.
result Explicit correspondence between V-links and T-links, criteria for equivalence and uniqueness.
Geometrical Objects on the First Order Jet Space Produced by the Lorenz Atmospheric DEs Systemmath.DG
The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where , like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atm…
Deep networks infer parameters for chaotic dynamics in climate models.
problem Uncertainty in climate sensitivity due to coarse model resolution.
method Three deep network algorithms (fully-connected, 1D, 2D convolutional) trained on Lorenz-96 model.
result Convolutional networks outperform fully-connected and 1D networks in parameter recovery.
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.
Satellites and Lorenz knotsmath.GT
New satellite knots counter a conjecture about Lorenz knots.
problem A conjecture about satellite knots and Lorenz knots was disproven.
method Constructed infinitely many counterexamples of satellite knots that are not cables.
result The conjecture was amended and shown to hold for many Lorenz knots.
Physics-informed ESNs improve chaotic system prediction accuracy.
problem Predicting chaotic systems while adhering to physical laws.
method Integrates physics constraints into ESN training through an additional loss function.
result Physics-informed ESNs predict chaotic systems with a 2 Lyapunov time improvement.
VSE estimates complex processes from noisy measurements without a model.
problem Estimating states of complex, model-free processes from noisy data.
method Variational state estimation using recurrent neural networks (RNNs) in both learning and inference phases.
result VSE provides a competitive state estimate for a benchmark process (Lorenz system) compared to known and data-driven methods.
New methods distill dynamical system equations from data.
problem Discovering governing equations of dynamical systems from data.
method Sparse regression, LASSO, dual LASSO optimization, STRidge algorithm.
result Improved accuracy and stability in learning dynamical system equations.
DD-SP uses ML to improve SP for Lorenz 96 systems, outperforming LR and DD-P.
problem Improving computational efficiency in weather/climate modeling.
method Data-driven super-parameterization using recurrent neural networks.
result DD-SP is more accurate and cheaper than SP, especially with scale separation.
We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.
Proposes a new method for data assimilation using closed-form conditional diffusion models.
problem Data assimilation for systems with complex, non-Gaussian probability distributions.
method Uses kernel density estimation to model joint distributions and leverages the score function for efficient evaluation.
result Outperforms ensemble Kalman and particle filters in nonlinear data assimilation problems.
Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Modelphysics.ao-ph
GANs improve stochastic parameterization of the Lorenz '96 model.
problem Improving stochastic parameterizations for sub-grid processes.
method Developed a GAN-based stochastic parameterization for the Lorenz '96 model.
result GAN configurations outperform a bespoke parameterization in skillful forecasts and climate simulations.
Low-connectivity reservoirs outperform standard designs in chaotic system forecasting.
problem Forecasting chaotic systems with high accuracy and low computational resources.
method Used Bayesian optimization to find optimal reservoir configurations, focusing on global system climate rather than short-term prediction.
result Optimized reservoirs with very low connectivity perform well in forecasting chaotic systems, challenging existing design heuristics.
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.
We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots code…
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
A new twist on Lorenz linksmath.GT
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T--links are a natural generalization, given by repeated positive twisting. We establish a one-to-one correspondence between positive braid representatives of Lorenz links and T--links, so Lorenz links and T-…
Deep neural networks classify chaotic time series.
problem Classifying chaotic time series with high accuracy.
method Train neural networks on simpler systems to classify more complex ones.
result Convolutional neural networks outperform other networks for time series classification.
Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.
problem Stability of Minkowski space-time solution to Einstein-Yang-Mills equations in higher dimensions.
method Global stability proof for arbitrary small perturbations using wave coordinates and gauge invariant norms.
result Global stability of Minkowski space-time in higher dimensions for arbitrary small perturbations.
Lorenz knotsmath.GT
This is a review article on Lorenz knots.
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.
Develops theory for data-driven methods in dynamical systems.
problem Lack of analysis for data-driven methods in dynamical systems.
method Establishes existence of mapping and properties of operator learning architecture.
result Novel universal approximation theorems for smoothing and forecasting.
The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a different method, find their unknotting numbers in terms of their positions on the Lorenz attractor.
Les noeuds de Lorenzmath.GT
This article is a survey on Lorenz knots. We describe the original construction, prove several classical properties, in particular the fact that the closure of a positive braid is a fibered knot, and describe Ghys'correspondance between modular knots and Lorenz knots. We also prove two new properties, namely that follo…
We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant , in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from old. Using this result we obtain explicit form…
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
In paper "A new twist on Lorenz links" (Journal of Topology 2(2009), 227-248) Joan Birman and Ilya Kofman prove the coincidence of the class of Lorenz links and the class of twisted links. The proof in that work is algebraic. We will identify this class in terms of grid diagrams and provide a transparent geometric argu…
Computed linking number of modular knots and Lorenz links.
problem Computing the linking number of modular knots in a specific space.
method Using correspondence between modular links and Lorenz links, and intersection number involving Conway topographs.
result Computed linking number of modular knots and compared to a previous formula.
New findings on T-links derived from torus links.
problem Difficulty in determining geometric type of T-links.
method Examined T-links obtained by full twists along torus links.
result T-links obtained by full twists are not torus links.
New satellite knots found that can't be represented by positive braids with full twists.
problem Satellite knots that cannot be represented by positive braids with full twists.
method Analyzing positive minimal braids and their closures to find satellite knots.
result Infinitely many satellite knots with Lorenz patterns and companions are not Lorenz knots.
In this paper we study the Lorenz equations using the perspective of the Conley index theory. More specifically, we examine the evolution of the strange set that these equations posses throughout the different values of the parameter. We also analyze some natural Morse decompositions of the global attractor of the syst…
EnEMF uses Epanechnikov kernel for high-dimensional filtering, improving accuracy and robustness.
problem Suboptimal Gaussian mixture kernel density estimates in high-dimensional settings.
method Ensemble Epanechnikov mixture filter (EnEMF) using optimal Epanechnikov kernel.
result EnEMF reduces error per particle on high-dimensional systems like Lorenz '96.
We show that the zeroes of the Alexander polynomial of a Lorenz knot all lie in some annulus whose width depends explicitly on the genus and the braid index of the considered knot.
E&E uses contrastive learning to speed up SBI for high-dimensional systems.
problem Challenges in training high-dimensional emulators for complex systems.
method Contrastive learning for low-dimensional latent embedding and fast emulator.
result Superior performance in non-identifiable parameter estimation tasks.
Improved algorithm for modular links provides upper volume bounds.
problem Understanding the geometry of modular links and Lorenz links.
method Bunch algorithm to study modular links and provide upper volume bounds.
result First upper volume bound independent of word exponents and quadratic in braid index.
A new method predicts non-Markovian closure terms for complex systems.
problem Predicting the effect of unresolved variables on resolved dynamics in high-dimensional systems.
method Mamba-Assisted Closure (MAC) framework: sequence model trained to predict closure from resolved trajectory, coupled with reduced-order equations.
result Substantially outperforms existing methods in predictive accuracy and long-time stability.
Kernel embedding of maps for sequential Bayesian inference: The variational mapping particle filterstat.ML
In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…
Stability of Minkowski space-time in Einstein-Yang-Mills system proven.
problem Stability of Minkowski space-time in Einstein-Yang-Mills system.
method Null frame decomposition, wave coordinates, dispersive estimates.
result Solutions converge to zero Yang-Mills curvature and Minkowski space-time.
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
problem Low accuracy in high-dimensional, nonlinear filtering problems.
method Score-based diffusion model, mini-batch Monte Carlo estimator.
result EnSF outperforms state-of-the-art methods in tracking high-dimensional systems.
Applying machine learning to improve simulations of a chaotic dynamical system using empirical error correctionphysics.ao-ph
Machine learning improves chaotic dynamical system simulations with empirical error correction.
problem Improving chaotic dynamical system simulations using machine learning.
method Combining machine learning with physically-derived models to correct timestep errors.
result The approach yields stable models with improved long-term statistics and single time-step tendencies.
Wealth Thermalization Hypothesis and Social Networkscond-mat.stat-mech
The study applies wealth thermalization hypothesis to social networks and explains inequality.
problem Explains inequality in human society through wealth thermalization hypothesis.
method Uses Random Matrix Theory and social networks with nonlinear perturbation.
result Shows that wealth distribution follows Rayleigh-Jeans distribution, leading to inequality.
TreeDOX predicts chaotic systems without hyperparameter tuning.
problem Forecasting chaotic systems requires hyperparameter tuning, limiting adoption.
method TreeDOX uses time delay overembedding and Extra-Trees Regressors.
result TreeDOX achieves state-of-the-art performance on chaotic systems.
This work discusses a closed-loop control strategy for complex systems utilizing scarce and streaming data. A discrete embedding space is first built using hash functions applied to the sensor measurements from which a Markov process model is derived, approximating the complex system's dynamics. A control strategy is t…
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.