Improve point sampling

deepxde/data/func_constraint.py

@@ -43,14 +43,14 @@ def losses(self, targets, outputs, loss_fn, inputs, model, aux=None):
 
     @run_if_any_none("train_x", "train_y")
     def train_next_batch(self, batch_size=None):
-        if self.dist_train == "log uniform":
+        if self.dist_train == "uniform":
+            self.train_x = self.geom.uniform_points(self.num_train, False)
+        elif self.dist_train == "log uniform":
             self.train_x = self.geom.log_uniform_points(self.num_train, False)
-        elif self.dist_train == "random":
+        else:
             self.train_x = self.geom.random_points(
                 self.num_train, random=self.dist_train
             )
-        else:
-            self.train_x = self.geom.uniform_points(self.num_train, False)
         if self.anchors is not None:
             self.train_x = np.vstack((self.anchors, self.train_x))
         self.train_y = self.func(self.train_x)

deepxde/geometry/geometry_nd.py

@@ -118,7 +118,7 @@ def on_boundary(self, x):
         return np.isclose(np.linalg.norm(x - self.center, axis=-1), self.radius)
 
     def distance2boundary_unitdirn(self, x, dirn):
-        """https://en.wikipedia.org/wiki/Line%E2%80%93sphere_intersection"""
+        # https://en.wikipedia.org/wiki/Line%E2%80%93sphere_intersection
         xc = x - self.center
         ad = np.dot(xc, dirn)
         return -ad + (ad ** 2 - np.sum(xc * xc, axis=-1) + self._r2) ** 0.5
@@ -136,24 +136,24 @@ def boundary_normal(self, x):
         return _n
 
     def random_points(self, n, random="pseudo"):
-        """https://math.stackexchange.com/questions/87230/picking-random-points-in-the-volume-of-sphere-with-uniform-probability"""
+        # https://math.stackexchange.com/questions/87230/picking-random-points-in-the-volume-of-sphere-with-uniform-probability
         if random == "pseudo":
             U = np.random.rand(n, 1)
             X = np.random.normal(size=(n, self.dim))
         else:
             rng = sample(n, self.dim + 1, random)
-            U, X = rng[:, 0:1], rng[:, 1:]
+            U, X = rng[:, 0:1], rng[:, 1:]  # Error if X = [0, 0, ...]
             X = stats.norm.ppf(X)
         X = preprocessing.normalize(X)
         X = U ** (1 / self.dim) * X
         return self.radius * X + self.center
 
     def random_boundary_points(self, n, random="pseudo"):
-        """http://mathworld.wolfram.com/HyperspherePointPicking.html"""
+        # http://mathworld.wolfram.com/HyperspherePointPicking.html
         if random == "pseudo":
             X = np.random.normal(size=(n, self.dim)).astype(config.real(np))
         else:
-            U = sample(n, self.dim, random)
+            U = sample(n, self.dim, random)  # Error for [0, 0, ...] or [0.5, 0.5, ...]
             X = stats.norm.ppf(U)
         X = preprocessing.normalize(X)
         return self.radius * X + self.center

deepxde/geometry/sampler.py

@@ -1,7 +1,5 @@
 __all__ = ["sample"]
 
-from distutils.version import LooseVersion
-
 import numpy as np
 import skopt
 
@@ -35,24 +33,31 @@ def pseudorandom(n_samples, dimension):
 
 
 def quasirandom(n_samples, dimension, sampler):
+    # Certain points should be removed:
+    # - Boundary points such as [..., 0, ...]
+    # - Special points [0, 0, 0, ...] and [0.5, 0.5, 0.5, ...], which cause error in
+    #   Hypersphere.random_points() and Hypersphere.random_boundary_points()
+    skip = 0
     if sampler == "LHS":
-        sampler = skopt.sampler.Lhs(
-            lhs_type="centered", criterion="maximin", iterations=1000
-        )
+        sampler = skopt.sampler.Lhs()
     elif sampler == "Halton":
-        sampler = skopt.sampler.Halton(min_skip=-1, max_skip=-1)
+        # 1st point: [0, 0, ...]
+        sampler = skopt.sampler.Halton(min_skip=1, max_skip=1)
     elif sampler == "Hammersley":
-        sampler = skopt.sampler.Hammersly(min_skip=-1, max_skip=-1)
+        # 1st point: [0, 0, ...]
+        if dimension == 1:
+            sampler = skopt.sampler.Hammersly(min_skip=1, max_skip=1)
+        else:
+            sampler = skopt.sampler.Hammersly()
+            skip = 1
     elif sampler == "Sobol":
-        # Remove the first point [0, 0, ...] and the second point [0.5, 0.5, ...], which
-        # are too special and may cause some error.
-        if LooseVersion(skopt.__version__) < LooseVersion("0.9"):
-            sampler = skopt.sampler.Sobol(min_skip=2, max_skip=2, randomize=False)
+        # 1st point: [0, 0, ...], 2nd point: [0.5, 0.5, ...]
+        sampler = skopt.sampler.Sobol(randomize=False)
+        if dimension < 3:
+            skip = 1
         else:
-            sampler = skopt.sampler.Sobol(skip=0, randomize=False)
-            space = [(0.0, 1.0)] * dimension
-            return np.asarray(
-                sampler.generate(space, n_samples + 2)[2:], dtype=config.real(np)
-            )
+            skip = 2
     space = [(0.0, 1.0)] * dimension
-    return np.asarray(sampler.generate(space, n_samples), dtype=config.real(np))
+    return np.asarray(
+        sampler.generate(space, n_samples + skip)[skip:], dtype=config.real(np)
+    )

docs/requirements.txt

@@ -1,7 +1,7 @@
 matplotlib
 numpy
 scikit-learn
-scikit-optimize
+scikit-optimize>=0.9.0
 scipy
 docutils<0.18  # https://github.com/readthedocs/readthedocs.org/issues/8616
 

requirements.txt

@@ -1,5 +1,5 @@
 matplotlib
 numpy
 scikit-learn
-scikit-optimize
+scikit-optimize>=0.9.0
 scipy