high-dimensional semilinear pde solver using deep bsde algorithm #9
Conversation
added test cases
-fixed the mistake with the neural network -fixed the mistake with dimensional of Brownian motion process
KirillZubov
changed the title
KirillZubov
requested review from
ChrisRackauckas and
akaysh
and removed request for
ChrisRackauckas and
akaysh
| x_sde(x_dim,t,dwa) = [x_dim[i] + μ(t,x_dim[i])*dt + σ(t,x_dim[i])*dwa[i] for i = 1: d] | ||
|
|
||
| get_x_sde(x_cur,l,dwA) = [x_sde(x_cur[i], ts[l] , dwA[i]) for i = 1: m] | ||
| reduceN(x_dim, l, dwA) = sum([gradU*dwA[i] for (i, gradU) in enumerate(chains[l](x_dim))]) |
| opt = neuralNetworkParams[2] | ||
|
|
||
| U0(hide_layer_size, d) = neuralNetworkParams[3](hide_layer_size, d) | ||
| gradU(hide_layer_size, d) = neuralNetworkParams[4](hide_layer_size, d) |
There was a problem hiding this comment.
I think this is a good spot for unicode on the grad.
| function sol() | ||
| x_cur = x_0 | ||
| U = [chainU(x)[1] for x in x_0] | ||
| global x_prev |
There was a problem hiding this comment.
why global this? that shouldn't be needed. local x_prev should be fine.
| U0(hide_layer_size, d) = neuralNetworkParams[3](hide_layer_size, d) | ||
| gradU(hide_layer_size, d) = neuralNetworkParams[4](hide_layer_size, d) | ||
|
|
||
| chains = [gradU(hide_layer_size, d) for i=1:length(ts)] |
There was a problem hiding this comment.
I think it be much easier to read if it was just
u0 = neuralNetworkParams[3](hide_layer_size, d)
∇u = [neuralNetworkParams[4](hide_layer_size, d) for i=1:length(ts)]since then it would be notationally a lot closer.
| ps = Flux.params(chainU, chains...) | ||
|
|
||
| # brownian motion | ||
| dw(dt) = sqrt(dt) * randn() |
There was a problem hiding this comment.
delete this so you can just use dW for the Brownian motions. It took a bit to see that dwa was just a renaming of dw array since dw was taken.
| # the Euler-Maruyama scheme | ||
| x_sde(x_dim,t,dwa) = [x_dim[i] + μ(t,x_dim[i])*dt + σ(t,x_dim[i])*dwa[i] for i = 1: d] | ||
|
|
||
| get_x_sde(x_cur,l,dwA) = [x_sde(x_cur[i], ts[l] , dwA[i]) for i = 1: m] |
There was a problem hiding this comment.
this is going to need to be iterating through time. I am not sure how x_cur[i] is supposed to act as the previous value here?
|
|
||
| get_x_sde(x_cur,l,dwA) = [x_sde(x_cur[i], ts[l] , dwA[i]) for i = 1: m] | ||
| reduceN(x_dim, l, dwA) = sum([gradU*dwA[i] for (i, gradU) in enumerate(chains[l](x_dim))]) | ||
| getN(x_cur, l, dwA) = [reduceN(x_cur[i], l, dwA[i]) for i = 1: m] |
There was a problem hiding this comment.
I'm not sure what this is doing. What equation does this correspond to?
| # brownian motion | ||
| dw(dt) = sqrt(dt) * randn() | ||
| # the Euler-Maruyama scheme | ||
| x_sde(x_dim,t,dwa) = [x_dim[i] + μ(t,x_dim[i])*dt + σ(t,x_dim[i])*dwa[i] for i = 1: d] |
There was a problem hiding this comment.
sigma is not necessarily diagonal, so you cannot essentially broadcast along the dimensions here.
prototype of one-dimensional pde solver using deep bsde algorithm