3 ms·
In theory, they can (Universal approximation theorem ). But those spatio-temporal systems are highly complex and consist of a very big number of variables (curs
by lagrange77 4y ago
In theory, they can (Universal approximation theorem
). But those spatio-temporal systems are highly complex and consist of a very big number of variables (curse of dimensionality). That's part of why weather forecasting is so hard.
So, to not have to use a gigantic neural network at the problem, you use some clever 'tricks', like dimensionality reduction and decomposing the problem. For example you can separate the spacial domain from the time domain and predict those with dedicated models, before joining the solutions again.
- d0mine 4y agoIs the number of variables really big or is it because no one ever tried large models with billions of parameters for this purpose (too expensive) like it was done with GPT?
- lagrange77 4y agoThe number is really big. GPT uses Transformers, which are kind of the successor to RNNs. Both are good at modelling sequences, like sentences or the temporal evolution of a dynamical system.
- d0mine 4y agoIt look like something GPT wrote. There are 3 spacial dimensions + one time dimension in Navier-Stokes equations. Not billions.
- lagrange77 3y agoLol, i guess we'll hear this allegation more often in the future. I'm talking about 3 variables for the velocity and 1 variable for the pressure at every point in space(typically a cartesian grid in numerical fluid simulation) and every time step of the solution.