arXiv research

Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical an…

Efficiently simulates slow dynamics of high-dimensional stochastic systems.

The paper proposes a method to improve Koopman operator estimation using indicator functions.

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…

Gating units in GRUs and LSTMs create slow modes and control phase-space complexity.

The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simpl…

Meta-CoTGAN improves adversarial text generation by preventing mode collapse.

Measures mode separation in high-dimensional densities via a reversible diffusion process.

This study examines memory effects in S&P500 market correlations using Langevin models.

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harm…

Accelerates optimal transport computation by 10x with spectral insights.

Develops an oblique projection technique to approximate a foliation for non-normal dynamics.

We find stationary distributions in a financial model with trends and mean-reversion.

Continuous Hidden Markov Models for Equity Returns

Modern medicine requires generalised approaches to the synthesis and integration of multimodal data, often at different biological scales, that can be applied to a variety of evidence structures, such as complex disease analyses and epidemiological models. However, current methods are either slow and expensive, or inef…

This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustai…

Markov state models (MSMs) and Master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variationa…

This paper analyzes GANs using Fourier modes to stabilize training.

New model reduces sampling cost in diffusion models, making them faster and applicable to real-world applications.

We analyze architectural features of Deep Neural Networks (DNNs) using the so-called Neural Tangent Kernel (NTK), which describes the training and generalization of DNNs in the infinite-width setting. In this setting, we show that for fully-connected DNNs, as the depth grows, two regimes appear: "order", where the (sca…

Improves DPGMM sampler by better initializing subclusters for more effective clustering.

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local…

Improved lower bound for parallel tempering's mixing time.

State-free reversible VAMPnets (SRVs) are a neural network-based framework capable of learning the leading eigenfunctions of the transfer operator of a dynamical system from trajectory data. In molecular dynamics simulations, these data-driven collective variables (CVs) capture the slowest modes of the dynamics and are…

This work interprets SFA through variational inference, relaxing linearity constraints.

Periodic surfaces have a limited number of bending modes, equal to their membrane modes.

Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.

Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range and distribution of weights in the current-mode design, it is shown that any we…

We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…

Method learns dynamics of slow variables from stochastic data.

Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the dynamics onto the dominant slow processes, or to separate superimposed signals. We …

We propose Power Slow Feature Analysis, a gradient-based method to extract temporally slow features from a high-dimensional input stream that varies on a faster time-scale, as a variant of Slow Feature Analysis (SFA) that allows end-to-end training of arbitrary differentiable architectures and thereby significantly ext…

Adaptive stopping in MCMC using classifier-based dynamics

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…

Characterizes neutral deformation modes of minimal surfaces.

Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.

Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.

Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a …

We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x' = f(x,y,ε), y' = εg(x,y,ε)$ with one-dimensional slow variable $y$. Our validation procedure is based on topological tools called isolatin…

Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.

Recent work by Brock et al. (2018) suggests that Generative Adversarial Networks (GANs) benefit disproportionately from large mini-batch sizes. Unfortunately, using large batches is slow and expensive on conventional hardware. Thus, it would be nice if we could generate batches that were effectively large though actual…

Derives a biologically plausible neural network for Slow Feature Analysis.

Geodesics connect model modes in neural network loss landscapes.

A new, efficient $k$-modes algorithm improves clustering of categorical data.

Multimodal clustering is an unsupervised technique for mining interesting patterns in $n$-adic binary relations or $n$-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…

EDLP samples flat modes in discrete spaces using entropy.

Paper introduces slow kill for efficient large-scale variable screening.

Proposes a Gaussian process for Koopman mode decomposition.