update plotter

docs/source/_rst/tutorials/tutorial1/tutorial.rst

@@ -28,8 +28,8 @@ Build a PINA problem
 Problem definition in the **PINA** framework is done by building a
 python ``class``, which inherits from one or more problem classes
 (``SpatialProblem``, ``TimeDependentProblem``, ``ParametricProblem``, …)
-depending on the nature of the problem. Below is an example. Consider the following
-simple Ordinary Differential Equation:
+depending on the nature of the problem. Below is an example: ### Simple
+Ordinary Differential Equation Consider the following:
 
 .. math::
 
@@ -49,7 +49,7 @@ our ``Problem`` class is going to be inherited from the
 .. code:: python
 
    from pina.problem import SpatialProblem
-   from pina import CartesianProblem
+   from pina.geometry import CartesianProblem
 
    class SimpleODE(SpatialProblem):
        
@@ -73,7 +73,7 @@ What about if our equation is also time dependent? In this case, our
 .. code:: ipython3
 
     from pina.problem import SpatialProblem, TimeDependentProblem
-    from pina import CartesianDomain
+    from pina.geometry import CartesianDomain
     
     class TimeSpaceODE(SpatialProblem, TimeDependentProblem):
         
@@ -215,26 +215,26 @@ calling the attribute ``input_pts`` of the problem
 
 .. parsed-literal::
 
-    Input points: {'x0': LabelTensor([[[0.]]]), 'D': LabelTensor([[[0.8633]],
-                 [[0.4009]],
-                 [[0.6489]],
-                 [[0.9278]],
-                 [[0.3975]],
-                 [[0.1484]],
-                 [[0.9632]],
-                 [[0.5485]],
-                 [[0.2984]],
-                 [[0.5643]],
-                 [[0.0368]],
-                 [[0.7847]],
-                 [[0.4741]],
-                 [[0.6957]],
-                 [[0.3281]],
-                 [[0.0958]],
-                 [[0.1847]],
-                 [[0.2232]],
-                 [[0.8099]],
-                 [[0.7304]]])}
+    Input points: {'x0': LabelTensor([[[0.]]]), 'D': LabelTensor([[[0.7644]],
+                 [[0.2028]],
+                 [[0.1789]],
+                 [[0.4294]],
+                 [[0.3239]],
+                 [[0.6531]],
+                 [[0.1406]],
+                 [[0.6062]],
+                 [[0.4969]],
+                 [[0.7429]],
+                 [[0.8681]],
+                 [[0.3800]],
+                 [[0.5357]],
+                 [[0.0152]],
+                 [[0.9679]],
+                 [[0.8101]],
+                 [[0.0662]],
+                 [[0.9095]],
+                 [[0.2503]],
+                 [[0.5580]]])}
     Input points labels: ['x']
 
 
@@ -271,7 +271,8 @@ If you want to track the metric by yourself without a logger, use
 
 .. code:: ipython3
 
-    from pina import PINN, Trainer
+    from pina import Trainer
+    from pina.solvers import PINN
     from pina.model import FeedForward
     from pina.callbacks import MetricTracker
     
@@ -300,12 +301,11 @@ If you want to track the metric by yourself without a logger, use
     TPU available: False, using: 0 TPU cores
     IPU available: False, using: 0 IPUs
     HPU available: False, using: 0 HPUs
-    Missing logger folder: /Users/dariocoscia/Desktop/PINA/tutorials/tutorial1/lightning_logs
 
 
 .. parsed-literal::
 
-    Epoch 1499: : 1it [00:00, 316.24it/s, v_num=0, mean_loss=5.39e-5, x0_loss=1.26e-6, D_loss=0.000106] 
+    Epoch 1499: : 1it [00:00, 272.55it/s, v_num=3, x0_loss=7.71e-6, D_loss=0.000734, mean_loss=0.000371]
 
 .. parsed-literal::
 
@@ -314,7 +314,7 @@ If you want to track the metric by yourself without a logger, use
 
 .. parsed-literal::
 
-    Epoch 1499: : 1it [00:00, 166.89it/s, v_num=0, mean_loss=5.39e-5, x0_loss=1.26e-6, D_loss=0.000106]
+    Epoch 1499: : 1it [00:00, 167.14it/s, v_num=3, x0_loss=7.71e-6, D_loss=0.000734, mean_loss=0.000371]
 
 
 After the training we can inspect trainer logged metrics (by default
@@ -332,9 +332,9 @@ loss can be accessed by ``trainer.logged_metrics``
 
 .. parsed-literal::
 
-    {'mean_loss': tensor(5.3852e-05),
-     'x0_loss': tensor(1.2636e-06),
-     'D_loss': tensor(0.0001)}
+    {'x0_loss': tensor(7.7149e-06),
+     'D_loss': tensor(0.0007),
+     'mean_loss': tensor(0.0004)}
 
 
 
@@ -362,7 +362,7 @@ indistinguishable. We can also plot easily the loss:
 
 .. code:: ipython3
 
-    pl.plot_loss(trainer=trainer, label = 'mean_loss',  logy=True)
+    pl.plot_loss(trainer=trainer, label = 'mean_loss', logy=True)
 
 
 

docs/source/_rst/tutorials/tutorial2/tutorial.rst

@@ -31,16 +31,12 @@ The problem definition
 ----------------------
 
 The two-dimensional Poisson problem is mathematically written as:
-
-.. math::
-    \begin{equation}
-    \begin{cases}
-    \Delta u = \sin{(\pi x)} \sin{(\pi y)} \text{ in } D, \\
-    u = 0 \text{ on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
-    \end{cases}
-    \end{equation}
-
-where :math:`D` is a square domain :math:`[0,1]^2`, and
+:raw-latex:`\begin{equation}
+\begin{cases}
+\Delta u = \sin{(\pi x)} \sin{(\pi y)} \text{ in } D, \\
+u = 0 \text{ on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
+\end{cases}
+\end{equation}` where :math:`D` is a square domain :math:`[0,1]^2`, and
 :math:`\Gamma_i`, with :math:`i=1,...,4`, are the boundaries of the
 square.
 
@@ -127,7 +123,7 @@ These parameters can be modified as desired. We use the
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 152.98it/s, v_num=9, mean_loss=0.000239, D_loss=0.000793, gamma1_loss=8.51e-5, gamma2_loss=0.000103, gamma3_loss=0.000122, gamma4_loss=9.14e-5]  
+    Epoch 999: : 1it [00:00, 158.53it/s, v_num=3, gamma1_loss=5.29e-5, gamma2_loss=4.09e-5, gamma3_loss=4.73e-5, gamma4_loss=4.18e-5, D_loss=0.00134, mean_loss=0.000304]    
 
 .. parsed-literal::
 
@@ -136,7 +132,7 @@ These parameters can be modified as desired. We use the
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 119.21it/s, v_num=9, mean_loss=0.000239, D_loss=0.000793, gamma1_loss=8.51e-5, gamma2_loss=0.000103, gamma3_loss=0.000122, gamma4_loss=9.14e-5]
+    Epoch 999: : 1it [00:00, 105.33it/s, v_num=3, gamma1_loss=5.29e-5, gamma2_loss=4.09e-5, gamma3_loss=4.73e-5, gamma4_loss=4.18e-5, D_loss=0.00134, mean_loss=0.000304]
 
 
 Now the ``Plotter`` class is used to plot the results. The solution
@@ -162,10 +158,9 @@ is now defined, with an additional input variable, named extra-feature,
 which coincides with the forcing term in the Laplace equation. The set
 of input variables to the neural network is:
 
-.. math::
-    \begin{equation}
-    [x, y, k(x, y)], \text{ with } k(x, y)=\sin{(\pi x)}\sin{(\pi y)},
-    \end{equation}
+:raw-latex:`\begin{equation}
+[x, y, k(x, y)], \text{ with } k(x, y)=\sin{(\pi x)}\sin{(\pi y)},
+\end{equation}`
 
 where :math:`x` and :math:`y` are the spatial coordinates and
 :math:`k(x, y)` is the added feature.
@@ -219,7 +214,7 @@ new extra feature.
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 119.36it/s, v_num=10, mean_loss=8.97e-7, D_loss=4.43e-6, gamma1_loss=1.37e-8, gamma2_loss=1.68e-8, gamma3_loss=1.22e-8, gamma4_loss=1.77e-8]     
+    Epoch 999: : 1it [00:00, 111.88it/s, v_num=4, gamma1_loss=2.54e-7, gamma2_loss=2.17e-7, gamma3_loss=1.94e-7, gamma4_loss=2.69e-7, D_loss=9.2e-6, mean_loss=2.03e-6]     
 
 .. parsed-literal::
 
@@ -228,7 +223,7 @@ new extra feature.
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 95.23it/s, v_num=10, mean_loss=8.97e-7, D_loss=4.43e-6, gamma1_loss=1.37e-8, gamma2_loss=1.68e-8, gamma3_loss=1.22e-8, gamma4_loss=1.77e-8] 
+    Epoch 999: : 1it [00:00, 85.62it/s, v_num=4, gamma1_loss=2.54e-7, gamma2_loss=2.17e-7, gamma3_loss=1.94e-7, gamma4_loss=2.69e-7, D_loss=9.2e-6, mean_loss=2.03e-6] 
 
 
 The predicted and exact solutions and the error between them are
@@ -254,10 +249,9 @@ Another way to exploit the extra features is the addition of learnable
 parameter inside them. In this way, the added parameters are learned
 during the training phase of the neural network. In this case, we use:
 
-.. math::
-    \begin{equation}
-    k(x, \mathbf{y}) = \beta \sin{(\alpha x)} \sin{(\alpha y)},
-    \end{equation}
+:raw-latex:`\begin{equation}
+k(x, \mathbf{y}) = \beta \sin{(\alpha x)} \sin{(\alpha y)},
+\end{equation}`
 
 where :math:`\alpha` and :math:`\beta` are the abovementioned
 parameters. Their implementation is quite trivial: by using the class
@@ -306,7 +300,7 @@ need, and they are managed by ``autograd`` module!
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 103.14it/s, v_num=14, mean_loss=1.39e-6, D_loss=6.04e-6, gamma1_loss=4.19e-7, gamma2_loss=2.8e-8, gamma3_loss=4.05e-7, gamma4_loss=3.49e-8]    
+    Epoch 999: : 1it [00:00, 119.29it/s, v_num=5, gamma1_loss=3.26e-8, gamma2_loss=7.84e-8, gamma3_loss=1.13e-7, gamma4_loss=3.02e-8, D_loss=2.66e-6, mean_loss=5.82e-7]  
 
 .. parsed-literal::
 
@@ -315,7 +309,7 @@ need, and they are managed by ``autograd`` module!
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 84.50it/s, v_num=14, mean_loss=1.39e-6, D_loss=6.04e-6, gamma1_loss=4.19e-7, gamma2_loss=2.8e-8, gamma3_loss=4.05e-7, gamma4_loss=3.49e-8] 
+    Epoch 999: : 1it [00:00, 85.94it/s, v_num=5, gamma1_loss=3.26e-8, gamma2_loss=7.84e-8, gamma3_loss=1.13e-7, gamma4_loss=3.02e-8, D_loss=2.66e-6, mean_loss=5.82e-7] 
 
 
 Umh, the final loss is not appreciabily better than previous model (with
@@ -355,7 +349,7 @@ removing all the hidden layers in the ``FeedForward``, keeping only the
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 130.55it/s, v_num=17, mean_loss=1.34e-14, D_loss=6.7e-14, gamma1_loss=5.13e-17, gamma2_loss=9.68e-18, gamma3_loss=5.14e-17, gamma4_loss=9.75e-18] 
+    Epoch 0: : 0it [00:00, ?it/s]Epoch 999: : 1it [00:00, 131.20it/s, v_num=6, gamma1_loss=2.55e-16, gamma2_loss=4.76e-17, gamma3_loss=2.55e-16, gamma4_loss=4.76e-17, D_loss=1.74e-13, mean_loss=3.5e-14] 
 
 .. parsed-literal::
 
@@ -364,7 +358,7 @@ removing all the hidden layers in the ``FeedForward``, keeping only the
 
 .. parsed-literal::
 
-    Epoch 999: : 1it [00:00, 104.91it/s, v_num=17, mean_loss=1.34e-14, D_loss=6.7e-14, gamma1_loss=5.13e-17, gamma2_loss=9.68e-18, gamma3_loss=5.14e-17, gamma4_loss=9.75e-18]
+    Epoch 999: : 1it [00:00, 98.81it/s, v_num=6, gamma1_loss=2.55e-16, gamma2_loss=4.76e-17, gamma3_loss=2.55e-16, gamma4_loss=4.76e-17, D_loss=1.74e-13, mean_loss=3.5e-14] 
 
 
 In such a way, the model is able to reach a very high accuracy! Of

docs/source/_rst/tutorials/tutorial3/tutorial.rst

@@ -25,14 +25,13 @@ The problem definition
 
 The problem is written in the following form:
 
-.. math::
-    \begin{equation}
-    \begin{cases}
-    \Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
-    u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
-    u(x, y, t) = 0 \quad \text{on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
-    \end{cases}
-    \end{equation}
+:raw-latex:`\begin{equation}
+\begin{cases}
+\Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
+u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
+u(x, y, t) = 0 \quad \text{on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
+\end{cases}
+\end{equation}`
 
 where :math:`D` is a square domain :math:`[0,1]^2`, and
 :math:`\Gamma_i`, with :math:`i=1,...,4`, are the boundaries of the
@@ -149,7 +148,7 @@ approximately 3 minutes.
 
 .. parsed-literal::
 
-    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] 
+    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]
 
 .. parsed-literal::
 
@@ -158,7 +157,7 @@ approximately 3 minutes.
 
 .. parsed-literal::
 
-    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]
+    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]
 
 
 Notice that the loss on the boundaries of the spatial domain is exactly
@@ -263,7 +262,7 @@ Now let’s train with the same configuration as thre previous test
 
 .. parsed-literal::
 
-    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]
+    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]
 
 .. parsed-literal::
 
@@ -272,7 +271,7 @@ Now let’s train with the same configuration as thre previous test
 
 .. parsed-literal::
 
-    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]
+    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]
 
 
 We can clearly see that the loss is way lower now. Let’s plot the