Regression of complex functions over the sphere using neural networks
$begingroup$
I am kinda new to Neural Networks and I am currently learning using TensorFlow.
My problem involves functions : $f : S^2 to mathbb{C}^2$ with some additionnal properties, $S^2$ being the unit sphere of $mathbb{R}^3$. My goal is, from (relatively few) discretizations points of the function $f$, to interpolate it over the sphere (or a portion of the sphere).
As I said, $f$ cannot be any function, it has some special properties. Lets pretend I have a way to generate a whole collection of functions ${f_1,dots,f_N}$ satisfying those properties.
What I would like to do it the following :
- Training a Neural Network on $f_i$ with a pre-defined discretization pattern over $S^2$,
- Giving as input a discretization (not on the same pattern as the training one) of a function $f$ I want to interpolate,
- Getting the value at any point I want on $S^2$.
Is it possible ? If yes, how ?
Thank you.
neural-network tensorflow interpolation
asked 6 mins ago
nicomezinicomezi
1011
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nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$begingroup$
I am kinda new to Neural Networks and I am currently learning using TensorFlow.
My problem involves functions : $f : S^2 to mathbb{C}^2$ with some additionnal properties, $S^2$ being the unit sphere of $mathbb{R}^3$. My goal is, from (relatively few) discretizations points of the function $f$, to interpolate it over the sphere (or a portion of the sphere).
As I said, $f$ cannot be any function, it has some special properties. Lets pretend I have a way to generate a whole collection of functions ${f_1,dots,f_N}$ satisfying those properties.
What I would like to do it the following :
- Training a Neural Network on $f_i$ with a pre-defined discretization pattern over $S^2$,
- Giving as input a discretization (not on the same pattern as the training one) of a function $f$ I want to interpolate,
- Getting the value at any point I want on $S^2$.
Is it possible ? If yes, how ?
Thank you.
neural-network tensorflow interpolation
asked 6 mins ago
nicomezinicomezi
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am kinda new to Neural Networks and I am currently learning using TensorFlow.
My problem involves functions : $f : S^2 to mathbb{C}^2$ with some additionnal properties, $S^2$ being the unit sphere of $mathbb{R}^3$. My goal is, from (relatively few) discretizations points of the function $f$, to interpolate it over the sphere (or a portion of the sphere).
As I said, $f$ cannot be any function, it has some special properties. Lets pretend I have a way to generate a whole collection of functions ${f_1,dots,f_N}$ satisfying those properties.
What I would like to do it the following :
- Training a Neural Network on $f_i$ with a pre-defined discretization pattern over $S^2$,
- Giving as input a discretization (not on the same pattern as the training one) of a function $f$ I want to interpolate,
- Getting the value at any point I want on $S^2$.
Is it possible ? If yes, how ?
Thank you.
neural-network tensorflow interpolation
asked 6 mins ago
nicomezinicomezi
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am kinda new to Neural Networks and I am currently learning using TensorFlow.
My problem involves functions : $f : S^2 to mathbb{C}^2$ with some additionnal properties, $S^2$ being the unit sphere of $mathbb{R}^3$. My goal is, from (relatively few) discretizations points of the function $f$, to interpolate it over the sphere (or a portion of the sphere).
As I said, $f$ cannot be any function, it has some special properties. Lets pretend I have a way to generate a whole collection of functions ${f_1,dots,f_N}$ satisfying those properties.
What I would like to do it the following :
- Training a Neural Network on $f_i$ with a pre-defined discretization pattern over $S^2$,
- Giving as input a discretization (not on the same pattern as the training one) of a function $f$ I want to interpolate,
- Getting the value at any point I want on $S^2$.
Is it possible ? If yes, how ?
Thank you.
neural-network tensorflow interpolation
neural-network tensorflow interpolation
asked 6 mins ago
nicomezinicomezi
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
nicomezinicomezi
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
nicomezinicomezi
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
nicomezinicomezi
1011
asked 6 mins ago
nicomezinicomezi
1011
1011
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
nicomezi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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