Evaluating Stochastic Gradient with Random Grid

  • Context: Graduate 
  • Thread starter Thread starter Heimdall
  • Start date Start date
  • Tags Tags
    Gradient Stochastic
Click For Summary
SUMMARY

The discussion focuses on evaluating the gradient of a random grid using numerical methods. The user initially applied the Euler formula for gradient estimation but encountered issues with fluctuations. They proposed using a five-point stencil method to mitigate these fluctuations and sought advice on handling grid boundaries. The conversation highlights the importance of boundary conditions in numerical methods and suggests linear extrapolation as a potential solution.

PREREQUISITES
  • Understanding of numerical differentiation techniques, specifically Euler's method and five-point stencil.
  • Familiarity with concepts of grid boundaries in numerical analysis.
  • Knowledge of linear extrapolation methods for boundary condition handling.
  • Basic proficiency in programming for implementing numerical methods.
NEXT STEPS
  • Research the implementation of the five-point stencil method for gradient evaluation.
  • Study boundary condition techniques in numerical analysis, focusing on extrapolation methods.
  • Explore advanced numerical differentiation techniques to reduce fluctuations in gradient calculations.
  • Learn about the stability and accuracy of different numerical methods in random grids.
USEFUL FOR

Mathematicians, data scientists, and engineers involved in numerical analysis, particularly those working with random grids and gradient evaluations.

Heimdall
Messages
38
Reaction score
0
Hi,

I have a random grid, meaning that each cell consists of a random number. I need to evaluate the gradient.

I've tried to apply a basic Euler formula (u_(i+1) - u_(i-1))/2dx but since the values can fluctuate a lot, fluctuations are even stronger for the gradient...
I'm thinking about using a "smoother" method like a five point stencil, which could be better to avoid strong fluctuations... but then I can't find out how to deal with grid boundaries (for Euler method I use (u_(i+1)-u(i))/dx or (u_(i)-u_(i-1))/dx )

How would you do, is there a specific method for this kind of problem ?

Thanks a lot
 
Physics news on Phys.org
how to deal with grid boundaries
how about [tex]u_{-1}:=2u_{0}-u_{1}[/tex], etc? I mean (linear) extrapolation.
 

Similar threads

Graduate Methods to interpolate surfaces from gradient field?
  • · Replies 1 ·
Replies
1
Views
2K
High School Adding random noise to a gradient
  • · Replies 22 ·
Replies
22
Views
2K
RHS of Laplace's Equation is f(u(x,y))
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to compute phase gradient from Snell's law?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Some notes on stochastic physics
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Non-locality by memory (Jung, 2020) applied to stochastic mechanics
  • · Replies 5 ·
Replies
5
Views
2K
Calculus Differential Equations book recommendations
  • · Replies 5 ·
Replies
5
Views
5K
WaveGrid - Non-equilibrium Emergence Sandbox
  • · Replies 1 ·
Replies
1
Views
3K
Graduate The Blessings of Dimensionality and Hilbert's 6th Problem
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Discretizing a Fluctuation Dissipation Theorem
  • · Replies 1 ·
Replies
1
Views
2K