Evaluating Stochastic Gradient with Random Grid

[Heimdall]

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

 

[makc]

how to deal with grid boundaries

how about $$u_{-1}:=2u_{0}-u_{1}$$, etc? I mean (linear) extrapolation.

 

[tacman]

for your question and for sharing your approach to evaluating the gradient with a random grid. Evaluating gradients with random grids can indeed be challenging due to the fluctuations in the data. It is important to take into consideration the nature of the data and the specific problem at hand when choosing a method for evaluating the gradient.

One approach that could potentially work well for this problem is using a moving average method. This involves taking an average of the data points within a moving window and using that as the gradient value. The size of the window can be adjusted to find a balance between smoothing out fluctuations and maintaining the overall trend of the data. This method can also be applied at the boundaries by using a smaller window size or by padding the data with zeros.

Another approach could be to use a Gaussian filter to smooth out the data before calculating the gradient. This can help reduce the impact of fluctuations and provide a more accurate gradient value.

Ultimately, the best method for evaluating the gradient with a random grid will depend on the specific characteristics of the data and the desired outcome. It may require some experimentation and fine-tuning to find the most effective approach. I hope this helps and good luck with your evaluation!