In this tutorial we will solve a RODE with
NNRODE. Consider the equation:
\[du = f(u,p,t,W)dt\]
where $f(u,p,t,W)=2u\sin(W)$ and $W(t)$ is a Noise process.
f = (u,p,t,W) -> 2u*sin(W) tspan = (0.00f0, 1.00f0) u0 = 1.0f0 dt = 1/20f0
We start off by defining the
NoiseProcess $W(t)$. In this case, we define a simple Gaussian Process. See Noise Processes for defining other types of processes.
W = WienerProcess(0.0,0.0,nothing)
Then, we need to define our model. In order to define a model, we can use
chain = Flux.Chain(Dense(2,5,elu),Dense(5,1)) #Model using Flux
chain = FastChain(FastDense(2,50,tanh), FastDense(50,2)) #Model using DiffEqFlux
And let's define our optimizer function:
opt = ADAM(1e-3)
Now, let's pass all the parameters to the algorithm and then call the solver. If we already have some initial parameters, we can pass them into the
NNRODE as well.
alg = NNRODE(chain , W , opt , init_params)
sol = solve(prob, NeuralPDE.NNRODE(chain,W,opt), dt=dt, verbose = true, abstol=1e-10, maxiters = 15000)