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.
Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant str…
Climate projections suffer from uncertain equilibrium climate sensitivity. The reason behind this uncertainty is the resolution of global climate models, which is too coarse to resolve key processes such as clouds and convection. These processes are approximated using heuristics in a process called parameterization. Th…
DD-SP uses ML to improve SP for Lorenz 96 systems, outperforming LR and DD-P.
Combining LETKF and RC improves chaotic system prediction from noisy, sparse data.
EnEMF uses Epanechnikov kernel for high-dimensional filtering, improving accuracy and robustness.
In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural n…
New method calibrates predictions in chaotic systems using variational inference.
Analog methods improve forecast accuracy in complex models.
CG-EnKF and NS-EnKF outperform deep learning-based SF in data assimilation.
Deep learning improves chaotic dynamics filtering without ensemble.
A new method predicts non-Markovian closure terms for complex systems.
E&E uses contrastive learning to speed up SBI for high-dimensional systems.
A hybrid method combines data assimilation and machine learning to predict chaotic dynamics from sparse noisy data.
Develops theory for data-driven methods in dynamical systems.
New parameterization tackles stochasticity in weather models.
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…
Proposes a new method for data assimilation using closed-form conditional diffusion models.
A new ML-based filter improves data assimilation for nonlinear systems.
Enhanced ensemble filters use machine learning to improve accuracy in filtering models.
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from proba…
New satellite knots counter a conjecture about Lorenz knots.
While most classical approaches to Granger causality detection repose upon linear time series assumptions, many interactions in neuroscience and economics applications are nonlinear. We develop an approach to nonlinear Granger causality detection using multilayer perceptrons where the input to the network is the past t…
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
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.
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…
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-…
This is a review article on Lorenz knots.
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.
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…
Study of Lorenz links and T-links, showing equivalence and unique presentations.
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
AD-EnKFs use machine learning to improve data assimilation in high-dimensional systems.
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.
In this article the Lorenz dynamical system is revived and revisited and the current state of the art results for one step ahead forecasting for the Lorenz trajectories are published. Multitask learning is shown to help learning the hard to learn z trajectory. The article is a reflection upon the evolution of neural ne…
New findings on T-links derived from torus links.
Unified framework for blending ML and mechanistic models in dynamical systems.
New satellite knots found that can't be represented by positive braids with full twists.
This paper learns state, dynamics, and filtering algorithms together for data assimilation.
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…
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.
Deep density methods improve filtering in high-dimensional systems.
Improved algorithm for modular links provides upper volume bounds.
New method uses neural networks to efficiently approximate Bayesian inference for complex models.
GC-KAN uses KANs to detect Granger causality in time series data.
A new framework reduces inconsistencies in chaotic surrogate modeling.
Long-lead forecasting for spatio-temporal systems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often highly parameterized and thus, challenging to implement from a computational perspective. One potential parsim…