example of ODE

examples/first_order_ode.py

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+import argparse
+import torch
+
+from torch.nn import ReLU, Tanh, Softplus, PReLU
+
+from pina.problem import SpatialProblem, ParametricProblem
+from pina.operators import nabla, grad, div
+from pina.model import FeedForward, DeepONet
+from pina import Condition, Span, LabelTensor, Plotter, PINN
+
+import matplotlib
+matplotlib.use('Qt5Agg')
+
+
+class FirstOrderODE(SpatialProblem):
+
+    x_rng = [0, 5]
+    output_variables = ['y']
+    spatial_domain = Span({'x': x_rng})
+
+    def ode(input_, output_):
+        y = output_
+        x = input_
+        return grad(y, x) + y - x
+
+    def fixed(input_, output_):
+        exp_value = 1.
+        return output_ - exp_value
+
+    def solution(self, input_):
+        x = input_
+        return x - 1.0 + 2*torch.exp(-x)
+
+    conditions = {
+        'bc': Condition(Span({'x': x_rng[0]}), fixed),
+        'dd': Condition(Span({'x': x_rng}), ode),
+    }
+    truth_solution = solution
+
+
+if __name__ == "__main__":
+
+    parser = argparse.ArgumentParser(description="Run PINA")
+    group = parser.add_mutually_exclusive_group(required=True)
+    group.add_argument("-s", "-save", action="store_true")
+    group.add_argument("-l", "-load", action="store_true")
+    parser.add_argument("id_run", help="number of run", type=int)
+    args = parser.parse_args()
+
+    problem = FirstOrderODE()
+    model = FeedForward(
+        layers=[4]*2,
+        output_variables=problem.output_variables,
+        input_variables=problem.input_variables,
+        func=Softplus,
+    )
+
+    pinn = PINN(problem, model, lr=0.03, error_norm='mse', regularizer=0)
+
+    if args.s:
+
+        pinn.span_pts(
+            {'variables': ['x'], 'mode': 'grid', 'n': 1}, locations=['bc'])
+        pinn.span_pts(
+            {'variables': ['x'], 'mode': 'grid', 'n': 30}, locations=['dd'])
+        Plotter().plot_samples(pinn, ['x'])
+        pinn.train(1200, 50)
+        pinn.save_state('pina.ode')
+
+    else:
+        pinn.load_state('pina.ode')
+        plotter = Plotter()
+        plotter.plot(pinn, components=['y'])