Jove
Visualize
Contact Us

Related Concept Videos

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.8K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.8K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

136
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
136
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.5K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.5K
Gauss's Law01:07

Gauss's Law

8.1K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
8.1K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

109
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
109
Navier–Stokes Equations01:28

Navier–Stokes Equations

869
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
869

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

Dynamical thermalization and turbulence in social stratification models.

Chaos (Woodbury, N.Y.)·2026
Same journal

Endogenous regime switching driven by scalar-irreducible learning dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

The coherence analysis and Laplacian spectrum applications of cycle-based iterative networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Hitting times, recurrence, and local dimension under nonstationary forcing with applications to climate data.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multiscale deep reservoir computing for predicting chaotic dynamical systems.

Chaos (Woodbury, N.Y.)·2026
Same journal

Chaotic decoherence under finite resolution: Lyapunov-controlled interference suppression.

Chaos (Woodbury, N.Y.)·2026
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Sep 28, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K

Data driven adaptive Gaussian mixture model for solving Fokker-Planck equation.

Wenqing Sun1, Jinqian Feng1, Jin Su1

  • 1School of Science, Xi'an Polytechnic University, Xi'an 710048, China.

Chaos (Woodbury, N.Y.)
|April 2, 2022
PubMed
Summary
This summary is machine-generated.

A new machine learning approach using an adaptive Gaussian mixture model (AGMM) effectively solves the complex Fokker-Planck (FP) equation for stochastic systems. This method integrates data and models, offering improved accuracy and interpretability for nonlinear dynamics.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.6K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K

Related Experiment Videos

Last Updated: Sep 28, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.6K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K

Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Machine Learning

Background:

  • The Fokker-Planck (FP) equation models probability density functions in stochastic differential equations (SDEs).
  • Analytical solutions for the FP equation are limited, necessitating numerical methods for complex nonlinear systems.

Purpose of the Study:

  • To propose a novel machine learning method for approximating general Fokker-Planck equations.
  • To enhance the integration of data-driven approaches with mathematical models for improved interpretability and performance.

Main Methods:

  • Development of an adaptive Gaussian mixture model (AGMM) for solving FP equations.
  • Seamless integration of prior mathematical model knowledge with machine learning algorithms.
  • Numerical simulations on one- and two-dimensional SDEs with varying noise levels.

Main Results:

  • The AGMM technique demonstrates effectiveness and robustness in solving the FP equation for diverse SDEs.
  • The proposed method shows superior performance compared to traditional numerical discretization techniques.
  • The integration of models enhances the interpretability of the machine learning approach.

Conclusions:

  • The AGMM method offers a powerful and interpretable tool for tackling complex FP equations in nonlinear dynamical systems.
  • This approach advances the application of machine learning in solving challenging mathematical models.
  • Further discussion on computational complexity and optimization algorithms is provided.