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Found 23 papers, 6 papers with code
Stochastic parameter reduced-order model based on hybrid machine learning approaches
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction.
Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond.
Early Warning Prediction with Automatic Labeling in Epilepsy Patients
Early warning for epilepsy patients is crucial for their safety and well-being, in particular to prevent or minimize the severity of seizures.
Early warning indicators via latent stochastic dynamical systems
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability.
Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks
To that end, the observed randomness and spatial-correlations are captured by learning the drift and diffusion terms of the stochastic differential equation with a Gumble matrix embedding, respectively.
Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems.
Multi-task Meta Label Correction for Time Series Prediction
To address the above issues, we create a label correction method to time series data with meta-learning under a multi-task framework.
The most probable dynamics of receptor-ligand binding on cell membrane
We consider the dynamics of a receptor binding to a ligand on the cell membrane, where the receptor and ligand perform different motions and are thus modeled by stochastic differential equations with Gaussian noise or non-Gaussian noise.
Learning effective dynamics from data-driven stochastic systems
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications.
An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps
One of the challenges to calculate the most likely transition path for stochastic dynamical systems under non-Gaussian L\'evy noise is that the associated rate function can not be explicitly expressed by paths.
An Onsager-Machlup approach to the most probable transition pathway for a genetic regulatory network
We investigate a quantitative network of gene expression dynamics describing the competence development in Bacillus subtilis.
An end-to-end deep learning approach for extracting stochastic dynamical systems with $α$-stable Lévy noise
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields.
Neural network stochastic differential equation models with applications to financial data forecasting
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties.
Extracting stochastic dynamical systems with $α$-stable Lévy noise from data
Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) L\'evy noise are relatively few so far.
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
In this work, we propose a data-driven approach to extract stochastic governing laws with both (Gaussian) Brownian motion and (non-Gaussian) L\'evy motion, from short bursts of simulation data.
Learning the temporal evolution of multivariate densities via normalizing flows
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.
Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems
Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data.
Large Deviations for SDE driven by Heavy-tailed Lévy Processes
We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed L\'evy processes.
Probability 60H10, 60F10, 60J76
A Machine Learning Framework for Computing the Most Probable Paths of Stochastic Dynamical Systems
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems.
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants, hence requiring the development of a data-driven modeling approach.
A Logistic-Harvest Model with Allee Effect under Multiplicative Noise
This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect.
Populations and Evolution Dynamical Systems 2020 MSC: -Mathematics Subject Classification: 39A50, 45K05, 65N22
A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise
We then design a numerical algorithm to compute the drift, diffusion coefficient and jump measure, and thus extract a governing stochastic differential equation with Gaussian and non-Gaussian noise.
Most Probable Evolution Trajectories in a Genetic Regulatory System Excited by Stable Lévy Noise
We especially examine those most probable trajectories from low concentration state to high concentration state (i. e., the likely transcription regime) for certain parameters, in order to gain insights into the transcription processes and the tipping time for the transcription likely to occur.
