Tutorials v0.1 (#178)
Tutorial update and small fixes * Tutorials update + Tutorial FNO * Create a metric tracker callback * Update PINN for logging * Update plotter for plotting * Small fix LabelTensor * Small fix FNO --------- Co-authored-by: Dario Coscia <dariocoscia@cli-10-110-13-250.WIFIeduroamSTUD.units.it> Co-authored-by: Dario Coscia <dariocoscia@dhcp-176.eduroam.sissa.it>
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Nicola Demo
Nicola Demo
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@@ -5,7 +5,8 @@ The problem definition
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~~~~~~~~~~~~~~~~~~~~~~
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This tutorial presents how to solve with Physics-Informed Neural
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Networks a 2D Poisson problem with Dirichlet boundary conditions.
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Networks a 2D Poisson problem with Dirichlet boundary conditions. Using
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extrafeatures.
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The problem is written as: :raw-latex:`\begin{equation}
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\begin{cases}
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@@ -24,9 +25,15 @@ First of all, some useful imports.
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from torch.nn import Softplus
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from pina.problem import SpatialProblem
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from pina.operators import nabla
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from pina.operators import laplacian
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from pina.model import FeedForward
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from pina import Condition, Span, PINN, LabelTensor, Plotter
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from pina.solvers import PINN
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from pina.trainer import Trainer
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from pina.plotter import Plotter
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from pina.geometry import CartesianDomain
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from pina.equation import Equation, FixedValue
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from pina import Condition, LabelTensor
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from pina.callbacks import MetricTracker
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Now, the Poisson problem is written in PINA code as a class. The
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equations are written as *conditions* that should be satisfied in the
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@@ -37,24 +44,20 @@ be compared with the predicted one.
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class Poisson(SpatialProblem):
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output_variables = ['u']
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spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
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spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
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def laplace_equation(input_, output_):
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force_term = (torch.sin(input_.extract(['x'])*torch.pi) *
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torch.sin(input_.extract(['y'])*torch.pi))
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nabla_u = nabla(output_, input_, components=['u'], d=['x', 'y'])
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return nabla_u - force_term
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def nil_dirichlet(input_, output_):
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value = 0.0
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return output_.extract(['u']) - value
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laplacian_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])
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return laplacian_u - force_term
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conditions = {
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'gamma1': Condition(location=Span({'x': [0, 1], 'y': 1}), function=nil_dirichlet),
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'gamma2': Condition(location=Span({'x': [0, 1], 'y': 0}), function=nil_dirichlet),
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'gamma3': Condition(location=Span({'x': 1, 'y': [0, 1]}), function=nil_dirichlet),
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'gamma4': Condition(location=Span({'x': 0, 'y': [0, 1]}), function=nil_dirichlet),
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'D': Condition(location=Span({'x': [0, 1], 'y': [0, 1]}), function=laplace_equation),
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'gamma1': Condition(location=CartesianDomain({'x': [0, 1], 'y': 1}), equation=FixedValue(0.)),
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'gamma2': Condition(location=CartesianDomain({'x': [0, 1], 'y': 0}), equation=FixedValue(0.)),
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'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [0, 1]}), equation=FixedValue(0.)),
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'gamma4': Condition(location=CartesianDomain({'x': 0, 'y': [0, 1]}), equation=FixedValue(0.)),
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'D': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1]}), equation=Equation(laplace_equation)),
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}
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def poisson_sol(self, pts):
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@@ -64,6 +67,12 @@ be compared with the predicted one.
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)/(2*torch.pi**2)
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truth_solution = poisson_sol
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problem = Poisson()
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# let's discretise the domain
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problem.discretise_domain(25, 'grid', locations=['D'])
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problem.discretise_domain(25, 'grid', locations=['gamma1', 'gamma2', 'gamma3', 'gamma4'])
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The problem solution
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~~~~~~~~~~~~~~~~~~~~
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@@ -73,73 +82,62 @@ the class ``FeedForward``. This neural network takes as input the
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coordinates (in this case :math:`x` and :math:`y`) and provides the
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unkwown field of the Poisson problem. The residual of the equations are
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evaluated at several sampling points (which the user can manipulate
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using the method ``span_pts``) and the loss minimized by the neural
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network is the sum of the residuals.
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using the method ``CartesianDomain_pts``) and the loss minimized by the
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neural network is the sum of the residuals.
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In this tutorial, the neural network is composed by two hidden layers of
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10 neurons each, and it is trained for 1000 epochs with a learning rate
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of 0.006. These parameters can be modified as desired. The output of the
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cell below is the final loss of the training phase of the PINN. We
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highlight that the generation of the sampling points and the train is
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here encapsulated within the function ``generate_samples_and_train``,
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but only for saving some lines of code in the next cells; that function
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is not mandatory in the **PINA** framework.
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of 0.006. These parameters can be modified as desired.
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.. code:: ipython3
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def generate_samples_and_train(model, problem):
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pinn = PINN(problem, model, lr=0.006, regularizer=1e-8)
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pinn.span_pts(20, 'grid', locations=['D'])
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pinn.span_pts(20, 'grid', locations=['gamma1', 'gamma2', 'gamma3', 'gamma4'])
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pinn.train(1000, 100)
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return pinn
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problem = Poisson()
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# make model + solver + trainer
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model = FeedForward(
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layers=[10, 10],
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func=Softplus,
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output_variables=problem.output_variables,
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input_variables=problem.input_variables
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output_dimensions=len(problem.output_variables),
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input_dimensions=len(problem.input_variables)
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)
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pinn = PINN(problem, model, optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})
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trainer = Trainer(pinn, max_epochs=1000, callbacks=[MetricTracker()])
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pinn = generate_samples_and_train(model, problem)
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# train
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trainer.train()
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.. parsed-literal::
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00000] 4.879922e-01 1.557781e-01 7.685463e-02 2.743466e-02 2.047883e-02 2.074460e-01
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00001] 2.610107e-01 1.067532e-03 8.390929e-03 2.391219e-02 1.467707e-02 2.129630e-01
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00100] 8.640952e-02 1.038323e-04 9.709063e-05 6.688796e-05 6.651071e-05 8.607519e-02
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00200] 2.996790e-02 4.977722e-04 6.639907e-04 5.634258e-04 7.204801e-04 2.752223e-02
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00300] 2.896983e-03 1.864277e-04 2.020803e-05 2.418693e-04 3.052877e-05 2.417949e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00400] 1.865673e-03 1.250375e-04 2.438288e-05 1.595948e-04 6.709602e-06 1.549948e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00500] 2.874877e-03 2.077810e-04 1.149128e-04 1.273361e-04 3.024802e-06 2.421822e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00600] 1.310072e-03 1.081258e-04 3.365631e-05 1.059794e-04 3.468987e-06 1.058841e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00700] 2.694587e-03 1.267468e-04 6.266955e-05 9.891923e-05 8.897325e-06 2.397354e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00800] 5.028690e-03 1.435707e-04 5.986574e-06 9.517078e-05 4.583780e-05 4.738124e-03
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00900] 9.997603e-04 9.684711e-05 9.155992e-06 8.875966e-05 1.261154e-05 7.923861e-04
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[epoch 01000] 2.362966e-02 1.157872e-04 7.812096e-06 8.004917e-05 9.947084e-05 2.332654e-02
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GPU available: False, used: False
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TPU available: False, using: 0 TPU cores
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IPU available: False, using: 0 IPUs
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HPU available: False, using: 0 HPUs
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/Users/dariocoscia/anaconda3/envs/pina/lib/python3.9/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:67: UserWarning: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default
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warning_cache.warn(
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| Name | Type | Params
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----------------------------------------
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0 | _loss | MSELoss | 0
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1 | _neural_net | Network | 151
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----------------------------------------
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151 Trainable params
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0 Non-trainable params
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151 Total params
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0.001 Total estimated model params size (MB)
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The neural network of course can be saved in a file. In such a way, we
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can store it after the train, and load it just to infer the field. Here
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we don’t store the model, but for demonstrative purposes we put in the
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next cell the commented line of code.
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.. parsed-literal::
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.. code:: ipython3
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Epoch 999: : 1it [00:00, 129.50it/s, v_num=45, mean_loss=0.00196, gamma1_loss=0.0093, gamma2_loss=0.000146, gamma3_loss=8.16e-5, gamma4_loss=0.000201, D_loss=8.44e-5]
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.. parsed-literal::
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`Trainer.fit` stopped: `max_epochs=1000` reached.
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 101.25it/s, v_num=45, mean_loss=0.00196, gamma1_loss=0.0093, gamma2_loss=0.000146, gamma3_loss=8.16e-5, gamma4_loss=0.000201, D_loss=8.44e-5]
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# pinn.save_state('pina.poisson')
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Now the *Plotter* class is used to plot the results. The solution
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predicted by the neural network is plotted on the left, the exact one is
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@@ -149,11 +147,11 @@ and the predicted solutions is showed.
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.. code:: ipython3
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plotter = Plotter()
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plotter.plot(pinn)
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plotter.plot(trainer)
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.. image:: tutorial_files/tutorial_13_0.png
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.. image:: tutorial_files/tutorial_11_0.png
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The problem solution with extra-features
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@@ -195,56 +193,65 @@ new extra feature.
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torch.sin(x.extract(['y'])*torch.pi))
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return LabelTensor(t, ['sin(x)sin(y)'])
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model_feat = FeedForward(
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layers=[10, 10],
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output_variables=problem.output_variables,
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input_variables=problem.input_variables,
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func=Softplus,
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extra_features=[SinSin()]
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)
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pinn_feat = generate_samples_and_train(model_feat, problem)
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# make model + solver + trainer
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model_feat = FeedForward(
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layers=[10, 10],
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func=Softplus,
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output_dimensions=len(problem.output_variables),
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input_dimensions=len(problem.input_variables)+1
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)
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pinn_feat = PINN(problem, model_feat, extra_features=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})
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trainer_feat = Trainer(pinn_feat, max_epochs=1000, callbacks=[MetricTracker()])
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# train
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trainer_feat.train()
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.. parsed-literal::
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00000] 1.309440e-01 2.335824e-02 3.823499e-03 1.878588e-05 2.002613e-03 1.017409e-01
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00001] 5.053994e-02 6.420787e-03 6.924602e-03 4.746807e-03 1.751946e-03 3.069580e-02
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00100] 7.484706e-06 1.889349e-07 4.289622e-07 3.610726e-07 3.611258e-07 6.144610e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00200] 6.941436e-06 4.738185e-07 4.590637e-07 5.098815e-07 5.365398e-07 4.962133e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00300] 6.147081e-06 6.213511e-07 5.576677e-07 6.256337e-07 6.572442e-07 3.685184e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00400] 6.056770e-06 7.646217e-07 6.377599e-07 7.242416e-07 7.616553e-07 3.168491e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00500] 6.751128e-06 8.011474e-07 6.283512e-07 7.652199e-07 7.226305e-07 3.833779e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00600] 2.839740e-05 5.422368e-06 4.058312e-06 4.664194e-06 4.984503e-06 9.268020e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00700] 1.221099e-05 3.654685e-06 3.195583e-07 2.717753e-06 2.381476e-06 3.137519e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00800] 5.423951e-06 6.111856e-07 4.348901e-07 5.353588e-07 5.398895e-07 3.302627e-06
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00900] 6.777007e-06 3.749606e-07 1.421852e-06 4.068826e-08 1.292241e-06 3.647265e-06
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[epoch 01000] 6.803403e-05 2.302543e-07 3.886034e-05 4.901193e-06 2.005441e-05 3.987827e-06
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GPU available: False, used: False
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TPU available: False, using: 0 TPU cores
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IPU available: False, using: 0 IPUs
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HPU available: False, using: 0 HPUs
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| Name | Type | Params
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----------------------------------------
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0 | _loss | MSELoss | 0
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1 | _neural_net | Network | 161
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----------------------------------------
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161 Trainable params
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0 Non-trainable params
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161 Total params
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0.001 Total estimated model params size (MB)
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 112.55it/s, v_num=46, mean_loss=2.73e-7, gamma1_loss=1.13e-6, gamma2_loss=7.1e-8, gamma3_loss=4.69e-8, gamma4_loss=6.81e-8, D_loss=4.65e-8]
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.. parsed-literal::
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`Trainer.fit` stopped: `max_epochs=1000` reached.
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.. parsed-literal::
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Epoch 999: : 1it [00:00, 92.69it/s, v_num=46, mean_loss=2.73e-7, gamma1_loss=1.13e-6, gamma2_loss=7.1e-8, gamma3_loss=4.69e-8, gamma4_loss=6.81e-8, D_loss=4.65e-8]
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The predicted and exact solutions and the error between them are
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represented below. We can easily note that now our network, having
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almost the same condition as before, is able to reach an additional
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order of magnitude in accuracy.
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almost the same condition as before, is able to reach additional order
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of magnitudes in accuracy.
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.. code:: ipython3
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plotter.plot(pinn_feat)
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plotter.plot(trainer_feat)
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.. image:: tutorial_files/tutorial_18_0.png
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.. image:: tutorial_files/tutorial_16_0.png
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The problem solution with learnable extra-features
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@@ -283,41 +290,50 @@ need, and they are managed by ``autograd`` module!
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return LabelTensor(t, ['b*sin(a*x)sin(a*y)'])
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model_learn = FeedForward(
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# make model + solver + trainer
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model_lean= FeedForward(
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layers=[10, 10],
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output_variables=problem.output_variables,
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input_variables=problem.input_variables,
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extra_features=[SinSinAB()]
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func=Softplus,
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output_dimensions=len(problem.output_variables),
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input_dimensions=len(problem.input_variables)+1
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)
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pinn_lean = PINN(problem, model_lean, extra_features=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})
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trainer_learn = Trainer(pinn_lean, max_epochs=1000)
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pinn_learn = generate_samples_and_train(model_learn, problem)
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# train
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trainer_learn.train()
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.. parsed-literal::
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00000] 7.147130e-02 1.942330e-03 7.350697e-03 2.868338e-03 1.184232e-03 5.812570e-02
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
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[epoch 00001] 2.814954e-01 7.300152e-03 5.510583e-04 2.262258e-03 7.287678e-04 2.706531e-01
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sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00100] 1.961870e-04 3.066778e-06 5.342949e-07 2.670689e-06 9.807675e-07 1.889345e-04
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00200] 1.208203e-04 3.096610e-06 1.253595e-06 2.603416e-06 1.962141e-06 1.119046e-04
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00300] 3.992990e-05 3.451424e-06 6.415143e-07 1.576505e-06 1.244609e-06 3.301585e-05
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00400] 3.466437e-04 1.722332e-06 1.461791e-05 3.052185e-06 8.755493e-06 3.184958e-04
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00500] 5.242374e-03 3.230991e-05 1.387528e-05 5.379211e-06 3.145076e-06 5.187664e-03
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00600] 1.027368e-03 1.448758e-06 2.165510e-05 5.197179e-05 3.823021e-05 9.140619e-04
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00700] 1.141694e-03 6.998039e-06 2.446730e-05 3.083524e-05 1.376935e-05 1.065624e-03
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00800] 3.619534e-04 3.120772e-06 1.223103e-05 2.211869e-05 9.567964e-06 3.149150e-04
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00900] 3.287693e-04 2.432459e-06 7.569996e-06 1.101516e-05 4.546776e-06 3.032049e-04
|
||||
[epoch 01000] 5.432598e-04 8.919213e-06 1.991732e-05 2.632461e-05 7.365395e-06 4.807333e-04
|
||||
GPU available: False, used: False
|
||||
TPU available: False, using: 0 TPU cores
|
||||
IPU available: False, using: 0 IPUs
|
||||
HPU available: False, using: 0 HPUs
|
||||
|
||||
| Name | Type | Params
|
||||
----------------------------------------
|
||||
0 | _loss | MSELoss | 0
|
||||
1 | _neural_net | Network | 161
|
||||
----------------------------------------
|
||||
161 Trainable params
|
||||
0 Non-trainable params
|
||||
161 Total params
|
||||
0.001 Total estimated model params size (MB)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Epoch 999: : 1it [00:00, 91.07it/s, v_num=47, mean_loss=2.11e-6, gamma1_loss=1.03e-5, gamma2_loss=4.17e-8, gamma3_loss=4.28e-8, gamma4_loss=5.65e-8, D_loss=6.21e-8]
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
`Trainer.fit` stopped: `max_epochs=1000` reached.
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Epoch 999: : 1it [00:00, 76.19it/s, v_num=47, mean_loss=2.11e-6, gamma1_loss=1.03e-5, gamma2_loss=4.17e-8, gamma3_loss=4.28e-8, gamma4_loss=5.65e-8, D_loss=6.21e-8]
|
||||
|
||||
|
||||
Umh, the final loss is not appreciabily better than previous model (with
|
||||
@@ -333,41 +349,50 @@ removing all the hidden layers in the ``FeedForward``, keeping only the
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
model_learn = FeedForward(
|
||||
# make model + solver + trainer
|
||||
model_lean= FeedForward(
|
||||
layers=[],
|
||||
output_variables=problem.output_variables,
|
||||
input_variables=problem.input_variables,
|
||||
extra_features=[SinSinAB()]
|
||||
func=Softplus,
|
||||
output_dimensions=len(problem.output_variables),
|
||||
input_dimensions=len(problem.input_variables)+1
|
||||
)
|
||||
pinn_learn = PINN(problem, model_lean, extra_features=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})
|
||||
trainer_learn = Trainer(pinn_learn, max_epochs=1000, callbacks=[MetricTracker()])
|
||||
|
||||
pinn_learn = generate_samples_and_train(model_learn, problem)
|
||||
# train
|
||||
trainer_learn.train()
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00000] 1.907039e+01 5.862396e-02 5.423664e-01 4.624593e-01 7.118504e-02 1.793576e+01
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00001] 1.698682e+01 3.348809e-02 4.943427e-01 3.972439e-01 6.141453e-02 1.600033e+01
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00100] 8.010766e-02 1.765875e-04 6.100491e-04 1.604862e-04 5.841496e-04 7.857639e-02
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00200] 5.057434e-02 6.479959e-05 6.590948e-05 6.376287e-05 5.975253e-05 5.032011e-02
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00300] 1.974927e-02 3.145394e-05 1.531348e-05 3.037518e-05 1.363940e-05 1.965849e-02
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00400] 1.763019e-03 3.408035e-06 8.902280e-07 3.228933e-06 7.512407e-07 1.754741e-03
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00500] 2.604023e-05 5.248935e-08 1.091775e-08 4.940254e-08 9.077334e-09 2.591834e-05
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00600] 7.279636e-08 1.490485e-10 3.004504e-11 1.392443e-10 2.490262e-11 7.245312e-08
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00700] 2.307051e-11 5.051121e-14 1.083412e-14 4.412749e-14 8.684963e-15 2.295635e-11
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00800] 9.755044e-12 1.745244e-14 3.232219e-15 1.735542e-14 3.347362e-15 9.713657e-12
|
||||
sum gamma1nil_di gamma2nil_di gamma3nil_di gamma4nil_di Dlaplace_equ
|
||||
[epoch 00900] 5.909113e-12 1.112281e-14 2.037945e-15 1.107687e-14 2.124603e-15 5.882751e-12
|
||||
[epoch 01000] 3.220371e-12 5.622761e-15 1.002551e-15 5.519723e-15 9.455284e-16 3.207280e-12
|
||||
GPU available: False, used: False
|
||||
TPU available: False, using: 0 TPU cores
|
||||
IPU available: False, using: 0 IPUs
|
||||
HPU available: False, using: 0 HPUs
|
||||
|
||||
| Name | Type | Params
|
||||
----------------------------------------
|
||||
0 | _loss | MSELoss | 0
|
||||
1 | _neural_net | Network | 4
|
||||
----------------------------------------
|
||||
4 Trainable params
|
||||
0 Non-trainable params
|
||||
4 Total params
|
||||
0.000 Total estimated model params size (MB)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Epoch 999: : 1it [00:00, 149.45it/s, v_num=48, mean_loss=1.34e-16, gamma1_loss=6.66e-16, gamma2_loss=2.6e-18, gamma3_loss=4.84e-19, gamma4_loss=2.59e-18, D_loss=4.84e-19]
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
`Trainer.fit` stopped: `max_epochs=1000` reached.
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Epoch 999: : 1it [00:00, 117.81it/s, v_num=48, mean_loss=1.34e-16, gamma1_loss=6.66e-16, gamma2_loss=2.6e-18, gamma3_loss=4.84e-19, gamma4_loss=2.59e-18, D_loss=4.84e-19]
|
||||
|
||||
|
||||
In such a way, the model is able to reach a very high accuracy! Of
|
||||
@@ -384,11 +409,11 @@ features.
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
plotter.plot(pinn_learn)
|
||||
plotter.plot(trainer_learn)
|
||||
|
||||
|
||||
|
||||
.. image:: tutorial_files/tutorial_25_0.png
|
||||
.. image:: tutorial_files/tutorial_23_0.png
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
@@ -396,9 +421,9 @@ features.
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
plt.figure(figsize=(16, 6))
|
||||
plotter.plot_loss(pinn, label='Standard')
|
||||
plotter.plot_loss(pinn_feat, label='Static Features')
|
||||
plotter.plot_loss(pinn_learn, label='Learnable Features')
|
||||
plotter.plot_loss(trainer, label='Standard')
|
||||
plotter.plot_loss(trainer_feat, label='Static Features')
|
||||
plotter.plot_loss(trainer_learn, label='Learnable Features')
|
||||
|
||||
plt.grid()
|
||||
plt.legend()
|
||||
@@ -406,5 +431,5 @@ features.
|
||||
|
||||
|
||||
|
||||
.. image:: tutorial_files/tutorial_26_0.png
|
||||
.. image:: tutorial_files/tutorial_24_0.png
|
||||
|
||||
|
||||
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Reference in New Issue
Block a user