Topological Detection of Phenomenological Bifurcations with Unreliable
Kernel Densities
- URL: http://arxiv.org/abs/2401.16563v1
- Date: Mon, 29 Jan 2024 20:59:25 GMT
- Title: Topological Detection of Phenomenological Bifurcations with Unreliable
Kernel Densities
- Authors: Sunia Tanweer and Firas A. Khasawneh
- Abstract summary: Phenomenological (P-type) bifurcations are qualitative changes in dynamical systems.
Current state of the art for detecting these bifurcations requires reliable kernel density estimates computed from an ensemble of system realizations.
This study presents an approach for detecting P-type bifurcations using unreliable density estimates.
- Score: 0.5874142059884521
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Phenomenological (P-type) bifurcations are qualitative changes in stochastic
dynamical systems whereby the stationary probability density function (PDF)
changes its topology. The current state of the art for detecting these
bifurcations requires reliable kernel density estimates computed from an
ensemble of system realizations. However, in several real world signals such as
Big Data, only a single system realization is available -- making it impossible
to estimate a reliable kernel density. This study presents an approach for
detecting P-type bifurcations using unreliable density estimates. The approach
creates an ensemble of objects from Topological Data Analysis (TDA) called
persistence diagrams from the system's sole realization and statistically
analyzes the resulting set. We compare several methods for replicating the
original persistence diagram including Gibbs point process modelling, Pairwise
Interaction Point Modelling, and subsampling. We show that for the purpose of
predicting a bifurcation, the simple method of subsampling exceeds the other
two methods of point process modelling in performance.
Related papers
- Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models [0.0]
We show how diffusion-based models can be repurposed for performing principled, identifiable Bayesian inference.
We show how such maps can be learned via standard DBM training using a novel noise schedule.
The result is a class of highly expressive generative models, uniquely defined on a low-dimensional latent space.
arXiv Detail & Related papers (2024-07-11T19:58:19Z) - Latent diffusion models for parameterization and data assimilation of facies-based geomodels [0.0]
Diffusion models are trained to generate new geological realizations from input fields characterized by random noise.
Latent diffusion models are shown to provide realizations that are visually consistent with samples from geomodeling software.
arXiv Detail & Related papers (2024-06-21T01:32:03Z) - Towards stable real-world equation discovery with assessing
differentiating quality influence [52.2980614912553]
We propose alternatives to the commonly used finite differences-based method.
We evaluate these methods in terms of applicability to problems, similar to the real ones, and their ability to ensure the convergence of equation discovery algorithms.
arXiv Detail & Related papers (2023-11-09T23:32:06Z) - Sobolev Space Regularised Pre Density Models [51.558848491038916]
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density.
This method is statistically consistent, and makes the inductive validation model clear and consistent.
arXiv Detail & Related papers (2023-07-25T18:47:53Z) - Score-based Data Assimilation [7.215767098253208]
We introduce score-based data assimilation for trajectory inference.
We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments.
arXiv Detail & Related papers (2023-06-18T14:22:03Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - MAntRA: A framework for model agnostic reliability analysis [0.0]
We propose a novel model data-driven reliability analysis framework for time-dependent reliability analysis.
The proposed approach combines interpretable machine learning, Bayesian statistics, and identifying dynamic equation.
Results indicate the possible application of the proposed approach for reliability analysis of insitu and heritage structures from on-site measurements.
arXiv Detail & Related papers (2022-12-13T00:57:09Z) - Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain.
We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions.
We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
arXiv Detail & Related papers (2022-11-30T05:33:29Z) - Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning.
theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure.
This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
arXiv Detail & Related papers (2022-10-12T06:46:38Z) - Visualizing Confidence Intervals for Critical Point Probabilities in 2D
Scalar Field Ensembles [7.484221280249876]
We present an approach for the computation and visual representation of confidence intervals for the occurrence probabilities of critical points in ensemble data sets.
We demonstrate the added value of our approach over existing methods for critical point prediction in uncertain data on a synthetic data set and show its applicability to a data set from climate research.
arXiv Detail & Related papers (2022-07-13T12:54:27Z) - Gaussian Process States: A data-driven representation of quantum
many-body physics [59.7232780552418]
We present a novel, non-parametric form for compactly representing entangled many-body quantum states.
The state is found to be highly compact, systematically improvable and efficient to sample.
It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
arXiv Detail & Related papers (2020-02-27T15:54:44Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.