Add antiderivative PI-DeepONet examples

Author: lululxvi

docs/demos/operator.rst

@@ -11,3 +11,9 @@ DeepONet
 
    operator/antiderivative_aligned
    operator/antiderivative_unaligned
+
+PI-DeepONet
+-----------
+
+- `Antiderivative operator with aligned data <https://github.com/lululxvi/deepxde/tree/master/examples/operator/antiderivative_aligned_pideeponet.py>`_
+- `Antiderivative operator with unaligned data <https://github.com/lululxvi/deepxde/tree/master/examples/operator/antiderivative_unaligned_pideeponet.py>`_

examples/operator/antiderivative_aligned_pideeponet.py

@@ -0,0 +1,59 @@
+"""Backend supported: tensorflow.compat.v1"""
+import deepxde as dde
+import matplotlib.pyplot as plt
+import numpy as np
+from deepxde.backend import tf
+
+
+dde.config.disable_xla_jit()
+
+# PDE
+geom = dde.geometry.TimeDomain(0, 1)
+
+
+def pde(x, u, v):
+    return dde.grad.jacobian(u, x) - v
+
+
+ic = dde.icbc.IC(geom, lambda _: 0, lambda _, on_initial: on_initial)
+pde = dde.data.PDE(geom, pde, ic, num_domain=20, num_boundary=2, num_test=40)
+
+# Function space
+func_space = dde.data.GRF(length_scale=0.2)
+
+# Data
+eval_pts = np.linspace(0, 1, num=50)[:, None]
+data = dde.data.PDEOperatorCartesianProd(
+    pde, func_space, eval_pts, 1000, num_test=100, batch_size=100
+)
+
+# Net
+net = dde.nn.DeepONetCartesianProd(
+    [50, 128, 128, 128],
+    [1, 128, 128, 128],
+    "tanh",
+    "Glorot normal",
+)
+
+# Hard constraint zero IC
+def zero_ic(inputs, outputs):
+    return outputs * tf.transpose(inputs[1])
+
+
+net.apply_output_transform(zero_ic)
+
+model = dde.Model(data, net)
+model.compile("adam", lr=0.0005)
+losshistory, train_state = model.train(epochs=40000)
+
+dde.utils.plot_loss_history(losshistory)
+
+v = np.sin(np.pi * eval_pts).T
+x = np.linspace(0, 1, num=50)
+u = np.ravel(model.predict((v, x[:, None])))
+u_true = 1 / np.pi - np.cos(np.pi * x) / np.pi
+print(dde.metrics.l2_relative_error(u_true, u))
+plt.figure()
+plt.plot(x, u_true, "k")
+plt.plot(x, u, "r")
+plt.show()

examples/operator/antiderivative_unaligned_pideeponet.py

@@ -0,0 +1,54 @@
+"""Backend supported: tensorflow.compat.v1"""
+import deepxde as dde
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# PDE
+geom = dde.geometry.TimeDomain(0, 1)
+
+
+def pde(x, u, v):
+    return dde.grad.jacobian(u, x) - v
+
+
+ic = dde.icbc.IC(geom, lambda _: 0, lambda _, on_initial: on_initial)
+pde = dde.data.PDE(geom, pde, ic, num_domain=20, num_boundary=2, num_test=40)
+
+# Function space
+func_space = dde.data.GRF(length_scale=0.2)
+
+# Data
+eval_pts = np.linspace(0, 1, num=50)[:, None]
+data = dde.data.PDEOperator(pde, func_space, eval_pts, 1000, num_test=1000)
+
+# Net
+net = dde.nn.DeepONet(
+    [50, 128, 128, 128],
+    [1, 128, 128, 128],
+    "tanh",
+    "Glorot normal",
+)
+
+# Hard constraint zero IC
+def zero_ic(inputs, outputs):
+    return outputs * inputs[1]
+
+
+net.apply_output_transform(zero_ic)
+
+model = dde.Model(data, net)
+model.compile("adam", lr=0.0005)
+losshistory, train_state = model.train(epochs=40000)
+
+dde.utils.plot_loss_history(losshistory)
+
+x = np.linspace(0, 1, num=50)
+v = np.sin(np.pi * x)
+u = np.ravel(model.predict((np.tile(v, (50, 1)), x[:, None])))
+u_true = 1 / np.pi - np.cos(np.pi * x) / np.pi
+print(dde.metrics.l2_relative_error(u_true, u))
+plt.figure()
+plt.plot(x, u_true, "k")
+plt.plot(x, u, "r")
+plt.show()