Differences in graph between true and predicted solution

[richieakka]

Dear LuLu,

We are trying to sole the following set of equations

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def de_system(x, y): r = y[:, 0:1] p = y[:, 1:2] d_r_over_d_t = tf.gradients(r, x)[0] d_p_over_d_t = tf.gradients(p, x)[0] return [ d_r_over_d_t - (r - (rr)/26 - 0.1211rp), d_p_over_d_t - (0.278p(1 - 0.0862p) - 0.0105rp) ]

def boundary(_, on_initial): return on_initial

geom = dde.geometry.TimeDomain(0, 200) ic1 = dde.IC(geom, lambda X: 1, boundary, component=0) ic2 = dde.IC(geom, lambda X: 1, boundary, component=1)

data = dde.data.PDE(geom, de_system, [ic1, ic2], 5000, 2, num_test=200) #change here, 4000 traininng points

layer_size = [1] + [50] * 5 + [2] # change here, layers are made 5 instaed of 3. activation = "tanh" initializer = "Glorot normal" #uniform" net = dde.maps.FNN(layer_size, activation, initializer)

model = dde.Model(data, net) model.compile("adam", lr=0.001) losshistory, train_state = model.train(epochs=40000) model.compile('L-BFGS-B') losshistory, train_state = model.train()

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The training loss we are achieving if o order 10^-8. But despite this, the predicted solution deviates largely from true solution. Also, just for fyi, we have normalized this DEs. Can you please let me know where I am wrong.

Thanking you in advance Richa Gupta

[lululxvi]

Your code dosen't have any BC.

[richieakka]

Yes LuLu, this problem does not have any BC. We have only ICs which we have mentioned. We get the correct exact solution using solve_ivp function, but predicted solution becomes flat and does not match the exact solution. Kindly help!!!

[richieakka]

Hi LuLu,

Please help in what could be the issue with this problem.

[lululxvi]

Try a smaller time domain like [0, 1] first.

[richieakka]

Dear LuLu,

The problem is working for domain [0,20] but not beyond that. We need the results in domain of [0,300]. Please guide how to approach it.

[lululxvi]

Check FAQ for scaling.