deepxde.geometry

deepxde.geometry.csg module

class deepxde.geometry.csg.CSGDifference(geom1, geom2)

Bases: Geometry

Construct an object by CSG Difference.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component)

Compute the periodic image of x for periodic boundary condition.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

class deepxde.geometry.csg.CSGIntersection(geom1, geom2)

Bases: Geometry

Construct an object by CSG Intersection.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component)

Compute the periodic image of x for periodic boundary condition.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

class deepxde.geometry.csg.CSGUnion(geom1, geom2)

Bases: Geometry

Construct an object by CSG Union.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component)

Compute the periodic image of x for periodic boundary condition.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

deepxde.geometry.geometry module

class deepxde.geometry.geometry.Geometry(dim, bbox, diam)

Bases: ABC

background_points(x, dirn, dist2npt, shift)

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+')

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

difference(other)

CSG Difference.

distance2boundary(x, dirn)

abstract inside(x)

Check if x is inside the geometry (including the boundary).

intersection(other)

CSG Intersection.

mindist2boundary(x)

abstract on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component)

Compute the periodic image of x for periodic boundary condition.

abstract random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

abstract random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

uniform_points(n, boundary=True)

Compute the equispaced point locations in the geometry.

union(other)

CSG Union.

deepxde.geometry.geometry_1d module

class deepxde.geometry.geometry_1d.Interval(l, r)

Bases: Geometry

background_points(x, dirn, dist2npt, shift)

Parameters:

• dirn – -1 (left), or 1 (right), or 0 (both direction).

• dist2npt – A function which converts distance to the number of extra points (not including x).

• shift – The number of shift.

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+', where: None | Literal['left', 'right'] = None)

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

• where (string, optional) – A string to specify which part of the boundary to compute the distance, e.g., “left”, “right”. If None, compute the distance to the whole boundary. Default is None.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

distance2boundary(x, dirn)

inside(x)

Check if x is inside the geometry (including the boundary).

log_uniform_points(n, boundary=True)

mindist2boundary(x)

on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component=0)

Compute the periodic image of x for periodic boundary condition.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

uniform_points(n, boundary=True)

Compute the equispaced point locations in the geometry.

deepxde.geometry.geometry_2d module

class deepxde.geometry.geometry_2d.Disk(center, radius)

Bases: Hypersphere

background_points(x, dirn, dist2npt, shift)

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

distance2boundary(x, dirn)

distance2boundary_unitdirn(x, dirn)

inside(x)

Check if x is inside the geometry (including the boundary).

mindist2boundary(x)

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_2d.Ellipse(center, semimajor, semiminor, angle=0)

Bases: Geometry

Ellipse.

Parameters:

• center – Center of the ellipse.

• semimajor – Semimajor of the ellipse.

• semiminor – Semiminor of the ellipse.

• angle – Rotation angle of the ellipse. A positive angle rotates the ellipse clockwise about the center and a negative angle rotates the ellipse counterclockwise about the center.

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+')

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_2d.Polygon(vertices)

Bases: Geometry

Simple polygon.

Parameters:

vertices – The order of vertices can be in a clockwise or counterclockwise direction. The vertices will be re-ordered in counterclockwise (right hand rule).

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_2d.Rectangle(xmin, xmax)

Bases: Hypercube

Parameters:

• xmin – Coordinate of bottom left corner.

• xmax – Coordinate of top right corner.

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+', where: None | Literal['left', 'right', 'bottom', 'top'] = None, inside: bool = True)

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

• where (string, optional) – A string to specify which part of the boundary to compute the distance. “left”: x[0] = xmin[0], “right”: x[0] = xmax[0], “bottom”: x[1] = xmin[1], “top”: x[1] = xmax[1]. If None, compute the distance to the whole boundary. Default is None.

• inside (bool, optional) – The x is either inside or outside the geometry. The cases where there are both points inside and points outside the geometry are NOT allowed. Default is True.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

static is_valid(vertices)

Check if the geometry is a Rectangle.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_2d.StarShaped(center, radius, coeffs_cos, coeffs_sin)

Bases: Geometry

Star-shaped 2d domain, i.e., a geometry whose boundary is parametrized in polar coordinates as:

$$ r(theta) := r_0 + sum_{i = 1}^N [a_i cos( i theta) + b_i sin(i theta) ], theta in [0,2 pi]. $$

For more details, refer to: Hiptmair et al. Large deformation shape uncertainty quantification in acoustic scattering. Adv Comp Math, 2018.

Parameters:

• center – Center of the domain.

• radius – 0th-order term of the parametrization (r_0).

• coeffs_cos – i-th order coefficients for the i-th cos term (a_i).

• coeffs_sin – i-th order coefficients for the i-th sin term (b_i).

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_2d.Triangle(x1, x2, x3)

Bases: Geometry

Triangle.

The order of vertices can be in a clockwise or counterclockwise direction. The vertices will be re-ordered in counterclockwise (right hand rule).

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+', where: None | Literal['x1-x2', 'x1-x3', 'x2-x3'] = None)

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

• where (string, optional) – A string to specify which part of the boundary to compute the distance. If None, compute the distance to the whole boundary. “x1-x2” indicates the line segment with vertices x1 and x2 (after reordered). Default is None.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

deepxde.geometry.geometry_3d module

class deepxde.geometry.geometry_3d.Cuboid(xmin, xmax)

Bases: Hypercube

Parameters:

• xmin – Coordinate of bottom left corner.

• xmax – Coordinate of top right corner.

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+', where: None | Literal['back', 'front', 'left', 'right', 'bottom', 'top'] = None, inside: bool = True)

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

• where (string, optional) – A string to specify which part of the boundary to compute the distance. “back”: x[0] = xmin[0], “front”: x[0] = xmax[0], “left”: x[1] = xmin[1], “right”: x[1] = xmax[1], “bottom”: x[2] = xmin[2], “top”: x[2] = xmax[2]. If None, compute the distance to the whole boundary. Default is None.

• inside (bool, optional) – The x is either inside or outside the geometry. The cases where there are both points inside and points outside the geometry are NOT allowed. NOTE: currently only support inside=True.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

class deepxde.geometry.geometry_3d.Sphere(center, radius)

Bases: Hypersphere

Parameters:

• center – Center of the sphere.

• radius – Radius of the sphere.

deepxde.geometry.geometry_nd module

class deepxde.geometry.geometry_nd.Hypercube(xmin, xmax)

Bases: Geometry

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0', where: None = None, inside: bool = True)

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

  • WARNING

  In current implementation, numerical underflow may happen for high dimensionalities when smoothness=”C0+” or smoothness=”Cinf”.

• where (string, optional) – This option is currently not supported for Hypercube.

• inside (bool, optional) – The x is either inside or outside the geometry. The cases where there are both points inside and points outside the geometry are NOT allowed. NOTE: currently only support inside=True.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

periodic_point(x, component)

Compute the periodic image of x for periodic boundary condition.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

uniform_boundary_points(n)

Compute the equispaced point locations on the boundary.

uniform_points(n, boundary=True)

Compute the equispaced point locations in the geometry.

class deepxde.geometry.geometry_nd.Hypersphere(center, radius)

Bases: Geometry

background_points(x, dirn, dist2npt, shift)

boundary_constraint_factor(x, smoothness: Literal['C0', 'C0+', 'Cinf'] = 'C0+')

Compute the hard constraint factor at x for the boundary.

This function is used for the hard-constraint methods in Physics-Informed Neural Networks (PINNs). The hard constraint factor satisfies the following properties:

• The function is zero on the boundary and positive elsewhere.

• The function is at least continuous.

In the ansatz boundary_constraint_factor(x) * NN(x) + boundary_condition(x), when x is on the boundary, boundary_constraint_factor(x) will be zero, making the ansatz be the boundary condition, which in turn makes the boundary condition a “hard constraint”.

Parameters:

• x – A 2D array of shape (n, dim), where n is the number of points and dim is the dimension of the geometry. Note that x should be a tensor type of backend (e.g., tf.Tensor or torch.Tensor), not a numpy array.

• smoothness (string, optional) –

  A string to specify the smoothness of the distance function, e.g., “C0”, “C0+”, “Cinf”. “C0” is the least smooth, “Cinf” is the most smooth. Default is “C0+”.

  • C0

  The distance function is continuous but may not be non-differentiable. But the set of non-differentiable points should have measure zero, which makes the probability of the collocation point falling in this set be zero.

  • C0+

  The distance function is continuous and differentiable almost everywhere. The non-differentiable points can only appear on boundaries. If the points in x are all inside or outside the geometry, the distance function is smooth.

  • Cinf

  The distance function is continuous and differentiable at any order on any points. This option may result in a polynomial of HIGH order.

Returns:

A tensor of a type determined by the backend, which will have a shape of (n, 1). Each element in the tensor corresponds to the computed distance value for the respective point in x.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

distance2boundary(x, dirn)

distance2boundary_unitdirn(x, dirn)

inside(x)

Check if x is inside the geometry (including the boundary).

mindist2boundary(x)

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

deepxde.geometry.pointcloud module

class deepxde.geometry.pointcloud.PointCloud(points, boundary_points=None, boundary_normals=None)

Bases: Geometry

A geometry represented by a point cloud, i.e., a set of points in space.

Parameters:

• points – A 2-D NumPy array. If boundary_points is not provided, points can include points both inside the geometry or on the boundary; if boundary_points is provided, points includes only points inside the geometry.

• boundary_points – A 2-D NumPy array.

• boundary_normals – A 2-D NumPy array.

boundary_normal(x)

Compute the unit normal at x for Neumann or Robin boundary conditions.

inside(x)

Check if x is inside the geometry (including the boundary).

on_boundary(x)

Check if x is on the geometry boundary.

random_boundary_points(n, random='pseudo')

Compute the random point locations on the boundary.

random_points(n, random='pseudo')

Compute the random point locations in the geometry.

deepxde.geometry.sampler module

deepxde.geometry.sampler.sample(n_samples, dimension, sampler='pseudo')

Generate pseudorandom or quasirandom samples in [0, 1]^dimension.

Parameters:

• n_samples (int) – The number of samples.

• dimension (int) – Space dimension.

• sampler (string) – One of the following: “pseudo” (pseudorandom), “LHS” (Latin hypercube sampling), “Halton” (Halton sequence), “Hammersley” (Hammersley sequence), or “Sobol” (Sobol sequence).

deepxde.geometry.timedomain module

class deepxde.geometry.timedomain.GeometryXTime(geometry, timedomain)

Bases: object

boundary_normal(x)

on_boundary(x)

on_initial(x)

periodic_point(x, component)

random_boundary_points(n, random='pseudo')

random_initial_points(n, random='pseudo')

random_points(n, random='pseudo')

uniform_boundary_points(n)

Uniform boundary points on the spatio-temporal domain.

Geometry surface area ~ bbox. Time surface area ~ diam.

uniform_initial_points(n)

uniform_points(n, boundary=True)

Uniform points on the spatio-temporal domain.

Geometry volume ~ bbox. Time volume ~ diam.

class deepxde.geometry.timedomain.TimeDomain(t0, t1)

Bases: Interval

on_initial(t)