f(x, y) function approximation in 3D space

[tesnikio]

Hey @rlorigro , thanks for your work, I didn't find a way to contact you, so I opened an issue here, sorry :)

How to extend your code so it could approximate 2 variable functions in 3D space?

For example: f(x, y) = x^2 + x + ycos(x) + sin(y)

[rlorigro]

Hi Nikita, no worries, this is as good a place as any. You would have to do 2 things to make this work:

1. Edit the data generation code to create your own training/testing set for your function
2. Modify the dimensions of the network layers to match the dimensions of your inputs and outputs

For 1, it looks like you are already generating data based on the plot you showed me, so you would just have to sample randomly from your x,y space and generate z values (ideally with some noise added). You would probably want to format your x,y pairs as a single matrix where one of its dimensions is size=2 so it can easily be handed to the NN forward method. You'll have to verify which orientation pytorch wants the matrix to be.

For 2, all fully connected networks like this one are essentially compound functions, so there is a pretty straightforward way to adapt it to approximate any other continuous function.

For the sin function, the number of inputs and outputs is 1:

D_in, H1, D_out = [1, 8, 1] # These numbers correspond to each layer: [input, hidden_1, output]

Where D_in and D_out are 1. Your function has 2 inputs and 1 output, so you would just have to change D_in to 2, and then when you call the forward method be sure to pass in the appropriate shaped x vector.

[tesnikio]

Hi Nikita, no worries, this is as good a place as any. You would have to do 2 things to make this work:

1. Edit the data generation code to create your own training/testing set for your function
2. Modify the dimensions of the network layers to match the dimensions of your inputs and outputs

For 1, it looks like you are already generating data based on the plot you showed me, so you would just have to sample randomly from your x,y space and generate z values (ideally with some noise added). You would probably want to format your x,y pairs as a single matrix where one of its dimensions is size=2 so it can easily be handed to the NN forward method. You'll have to verify which orientation pytorch wants the matrix to be.

For 2, all fully connected networks like this one are essentially compound functions, so there is a pretty straightforward way to adapt it to approximate any other continuous function.

For the sin function, the number of inputs and outputs is 1:

D_in, H1, D_out = [1, 8, 1] # These numbers correspond to each layer: [input, hidden_1, output]

Where D_in and D_out are 1. Your function has 2 inputs and 1 output, so you would just have to change D_in to 2, and then when you call the forward method be sure to pass in the appropriate shaped x vector.

Thank you so much, Ryan! It worked out :)
The loss isn't that good as for the initial case, but I'll play around with params to get it better

[rlorigro]

Cool, I'm glad to hear it is running. I would be curious to see the output of the trained model if you have a plot. Also if you want to add your notebook to the repo, feel free to make a PR.

[tesnikio]

Ok, I'll upload it when I'm finished.

[tesnikio]

As for the plot, here you go, the first one is a generated function, the second one is prediction.

[rlorigro]

Nice, it looks like it is performing well. I think the 3D example is a much more impressive demonstration than the sin function