update plotter
@@ -25,14 +25,13 @@ The problem definition
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The problem is written in the following form:
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.. math::
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\begin{equation}
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\begin{cases}
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\Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
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u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
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u(x, y, t) = 0 \quad \text{on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
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\end{cases}
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\end{equation}
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:raw-latex:`\begin{equation}
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\begin{cases}
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\Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
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u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
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u(x, y, t) = 0 \quad \text{on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
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\end{cases}
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\end{equation}`
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where :math:`D` is a square domain :math:`[0,1]^2`, and
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:math:`\Gamma_i`, with :math:`i=1,...,4`, are the boundaries of the
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@@ -149,7 +148,7 @@ approximately 3 minutes.
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 62.13it/s, v_num=0, mean_loss=0.0268, D_loss=0.0397, t0_loss=0.121, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000]
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Epoch 999: : 1it [00:00, 84.47it/s, v_num=0, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000, t0_loss=0.0419, D_loss=0.0307, mean_loss=0.0121]
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.. parsed-literal::
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@@ -158,7 +157,7 @@ approximately 3 minutes.
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 53.88it/s, v_num=0, mean_loss=0.0268, D_loss=0.0397, t0_loss=0.121, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000]
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Epoch 999: : 1it [00:00, 68.69it/s, v_num=0, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000, t0_loss=0.0419, D_loss=0.0307, mean_loss=0.0121]
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Notice that the loss on the boundaries of the spatial domain is exactly
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@@ -263,7 +262,7 @@ Now let’s train with the same configuration as thre previous test
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 48.54it/s, v_num=1, mean_loss=1.48e-8, D_loss=8.89e-8, t0_loss=0.000, gamma1_loss=2.06e-15, gamma2_loss=0.000, gamma3_loss=2.1e-15, gamma4_loss=0.000]
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Epoch 0: : 0it [00:00, ?it/s]Epoch 999: : 1it [00:00, 52.10it/s, v_num=1, gamma1_loss=1.97e-15, gamma2_loss=0.000, gamma3_loss=2.14e-15, gamma4_loss=0.000, t0_loss=0.000, D_loss=1.25e-7, mean_loss=2.09e-8]
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.. parsed-literal::
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@@ -272,7 +271,7 @@ Now let’s train with the same configuration as thre previous test
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 43.25it/s, v_num=1, mean_loss=1.48e-8, D_loss=8.89e-8, t0_loss=0.000, gamma1_loss=2.06e-15, gamma2_loss=0.000, gamma3_loss=2.1e-15, gamma4_loss=0.000]
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Epoch 999: : 1it [00:00, 45.78it/s, v_num=1, gamma1_loss=1.97e-15, gamma2_loss=0.000, gamma3_loss=2.14e-15, gamma4_loss=0.000, t0_loss=0.000, D_loss=1.25e-7, mean_loss=2.09e-8]
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We can clearly see that the loss is way lower now. Let’s plot the
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Before Width: | Height: | Size: 49 KiB After Width: | Height: | Size: 57 KiB |
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Before Width: | Height: | Size: 53 KiB After Width: | Height: | Size: 56 KiB |
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Before Width: | Height: | Size: 52 KiB After Width: | Height: | Size: 54 KiB |
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Before Width: | Height: | Size: 52 KiB After Width: | Height: | Size: 52 KiB |
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Before Width: | Height: | Size: 47 KiB After Width: | Height: | Size: 48 KiB |