33 ms·
There are two ways differential equations can involve more than one variable. dx/dt = stuff dy/dt = stuff OR dt/dx = stuff dt/dy = stuff Require very diff
by freemint 4y ago
There are two ways differential equations can involve more than one variable.
dx/dt = stuff
dy/dt = stuff
OR
dt/dx = stuff
dt/dy = stuff
Require very different approaches.
- wheelinsupial 4y agoI think they might be asking about PDEs instead of ODEs in this case when they mentioned x, y, z as being multivariable.
- naillo 4y agoI wasn't actually gonna use them to solve a diff equation though to be honest :) I was just experimenting with denoising diffusion and instead of a u-net to infer the denoising step, I was thinking about using a multivariate polynomial. (Since if you express the output denoising as a linear combination of polynomials finding the denoiser just turns into linear algebra. Might be a big solve etc but inferene is way fast and it's nice to know that you have the global opimum.) I'm sitting at the code right this instant and was using x, y, xy, x^2y, xy^2, etc, but this thread inspired me to try out chebychev as a possible alternative. :)
- johnbcoughlin 4y agoAny orthogonal polynomial family can be combined into a simple tensor product basis. So in your case you could try T_1(x), T_1(y), T_1(x)T_1(y), T_2(x), T_2(x)T_1(y), and so on.