tweaked DP burgers settings
This commit is contained in:
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f939b89ecd
commit
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1 file changed
+24
-26
+24
-26
@@ -35,7 +35,7 @@
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"N = 128\n",
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"STEPS = 32\n",
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"DT = 1./STEPS\n",
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"NU = 0.01/np.pi\n",
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"NU = 0.2/np.pi\n",
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"\n",
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"DOMAIN = Domain(x=N, boundaries=PERIODIC, bounds=Box[-1:1])\n",
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"\n",
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@@ -105,7 +105,7 @@
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"with math.record_gradients(velocity.values):\n",
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"\n",
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" for time_step in range(STEPS):\n",
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" v1 = diffuse.explicit(1.0*velocities[-1], NU, DT)\n",
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" v1 = diffuse.explicit(1.0*velocities[-1], NU, DT, substeps=1)\n",
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" v2 = advect.semi_lagrangian(v1, v1, DT)\n",
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" velocities.append(v2)\n",
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"\n",
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@@ -138,7 +138,7 @@
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"image/png": 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truncated
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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@@ -195,10 +195,10 @@
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"output_type": "stream",
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"text": [
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"Optimization step 0, loss: 0.382915\n",
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"Optimization step 1, loss: 0.326966\n",
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"Optimization step 2, loss: 0.281119\n",
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"Optimization step 3, loss: 0.242881\n",
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"Optimization step 4, loss: 0.210734\n"
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"Optimization step 1, loss: 0.329677\n",
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"Optimization step 2, loss: 0.284684\n",
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"Optimization step 3, loss: 0.246604\n",
|
||||
"Optimization step 4, loss: 0.214305\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -239,7 +239,7 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
@@ -291,16 +291,16 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Optimization step 0, loss: 0.183535\n",
|
||||
"Optimization step 5, loss: 0.096258\n",
|
||||
"Optimization step 10, loss: 0.054813\n",
|
||||
"Optimization step 15, loss: 0.032847\n",
|
||||
"Optimization step 20, loss: 0.020363\n",
|
||||
"Optimization step 25, loss: 0.012899\n",
|
||||
"Optimization step 30, loss: 0.008259\n",
|
||||
"Optimization step 35, loss: 0.005283\n",
|
||||
"Optimization step 40, loss: 0.003360\n",
|
||||
"Runtime 29.89s\n"
|
||||
"Optimization step 0, loss: 0.186823\n",
|
||||
"Optimization step 5, loss: 0.098101\n",
|
||||
"Optimization step 10, loss: 0.055802\n",
|
||||
"Optimization step 15, loss: 0.033452\n",
|
||||
"Optimization step 20, loss: 0.020761\n",
|
||||
"Optimization step 25, loss: 0.013248\n",
|
||||
"Optimization step 30, loss: 0.008643\n",
|
||||
"Optimization step 35, loss: 0.005733\n",
|
||||
"Optimization step 40, loss: 0.003848\n",
|
||||
"Runtime 47.50s\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -344,7 +344,7 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
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||||
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
@@ -378,7 +378,7 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
@@ -406,8 +406,6 @@
|
||||
"source": [
|
||||
"Naturally, this is a tougher task: the optimization receives direct feedback what the state at $t=0.5$ should look like, but due to the non-linear model equation, we typically have a large number of solutions that exactly or numerically very closely satisfy the constraints. Hence, our minimizer not necessarily finds the exact state we started from. However, it's still quite close in this Burgers scenario.\n",
|
||||
"\n",
|
||||
"_Note_: for the current phiflow version (2.0) the intial solution actually contains some high frequency oscillations in the peaks. These oscilllations disappear over the course of the simulation due to numerical diffusions, and hence represent a _null space_ of the solution. They could be removed by introducing regularization.\n",
|
||||
"\n",
|
||||
"Before measuring the overall error of the reconstruction, let's visualize the full evolution of our system over time as this also yields the solution in the form of a numpy array that we can compare to the other versions:"
|
||||
]
|
||||
},
|
||||
@@ -418,7 +416,7 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x360 with 2 Axes>"
|
||||
]
|
||||
@@ -478,7 +476,7 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x360 with 2 Axes>"
|
||||
]
|
||||
@@ -523,14 +521,14 @@
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"MAE PINN: 0.22991 \n",
|
||||
"MAE DP: 0.05909\n",
|
||||
"MAE DP: 0.05811\n",
|
||||
"\n",
|
||||
"Error GT to PINN (top) , DiffPhys (bottom):\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x360 with 2 Axes>"
|
||||
]
|
||||
|
||||
Reference in new issue
Block a user