Modulus Utilities

Defines helper Plotter class for adding plots to tensorboard summaries

class modulus.utils.io.plotter.DeepONetValidatorPlotter(n_examples: int = 1)[source]

Bases: _Plotter

DeepONet validation plotter for structured data

class modulus.utils.io.plotter.GridValidatorPlotter(n_examples: int = 1)[source]

Bases: _Plotter

Grid validation plotter for structured data

class modulus.utils.io.plotter.InferencerPlotter[source]

Bases: _Plotter

Default plotter class for inferencer

class modulus.utils.io.plotter.ValidatorPlotter[source]

Bases: _Plotter

Default plotter class for validator

Helper functions for generating vtk files

class modulus.utils.io.vtk.VTKFromFile(file_path: str, export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', force_legacy: bool = False)[source]

Bases: object

Reads VTK file into memory and constructs corresponding VTK object

Parameters

• file_path (str) – File directory/name of input vtk file

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• force_legacy (bool, optional) – Force a legacy only read, by default False

class modulus.utils.io.vtk.VTKPolyData(points: array, line_index: Optional[array] = None, poly_index: Optional[Tuple[array, array]] = None, export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', init_vtk: bool = True)[source]

Bases: VTKBase

vtkPolyData wrapper class

Parameters

• points (np.array) – Array of point locations [npoints, (1,2 or 3)]

• line_index (np.array, optional) – Array of line connections [nedges, 2], by default None

• poly_index (Tuple[poly_offsets, poly_connectivity]) – Tuple of polygon offsets and polygon connectivity arrays. Polygon offsets is a 1D array denoting how many points make up a face for each polygon. Polygon connectivity is a 1D array that contains verticies of each polygon face in order, by default None

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• init_vtk (bool, optional) – Initialize new VTK object from parameters (used by VTKFromFile), by default True

class modulus.utils.io.vtk.VTKRectilinearGrid(axis_coords: List[array], export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', init_vtk: bool = True)[source]

Bases: VTKBase

vtkRectilinearGrid wrapper class

Parameters

• axis_coords (List[np.array]) – List of arrays that define points on each axis

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• init_vtk (bool, optional) – Initialize new VTK object from parameters (used by VTKFromFile), by default True

class modulus.utils.io.vtk.VTKStructuredGrid(points: array, dims: List[int], export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', init_vtk: bool = True)[source]

Bases: VTKBase

vtkStructuredGrid wrapper class

Parameters

• points (np.array) – Mesh grid of points in ‘ij’ format

• dims (List[int]) – Number of points in each dimension

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• init_vtk (bool, optional) – Initialize new VTK object from parameters (used by VTKFromFile), by default True

class modulus.utils.io.vtk.VTKUniformGrid(bounds: List[List[int]], npoints: List[int], export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', init_vtk: bool = True)[source]

Bases: VTKBase

vtkUniformGrid wrapper class

Parameters

• bounds (List[List[int]]) – Domain bounds of each dimension

• npoints (List[int]) – List of number of points in each dimension

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• init_vtk (bool, optional) – Initialize new VTK object from parameters (used by VTKFromFile), by default True

class modulus.utils.io.vtk.VTKUnstructuredGrid(points: array, cell_index: Tuple[array, array], cell_types: array, export_map: Dict[str, List[str]] = {}, file_name: str = 'vtk_output', file_dir: str = '.', init_vtk: bool = True)[source]

Bases: VTKBase

vtkUnstructuredGrid wrapper class

Parameters

• points (np.array) – Array of point locations [npoints, (1,2 or 3)]

• cell_index (Tuple[ np.array, np.array ]) – Tuple of (cell_offsets, cell_connectivity) arrays. Cell offsets is a 1D array denoting how many points make up a face for each cell. Cell connectivity is a 1D array that contains verticies of each cell face in order

• cell_types (np.array) – Array of cell vtk types: https://vtk.org/doc/nightly/html/vtkCellType_8h_source.html

• export_map (Dict[str, List[str]], optional) – Export map dictionary with keys that are VTK variables names and values that are lists of output variables. Will use 1 to 1 mapping if none is provided, by default {}

• file_name (str, optional) – File name of output vtk file, by default “vtk_output”

• file_dir (str, optional) – File directory of output vtk file, by default “.”

• init_vtk (bool, optional) – Initialize new VTK object from parameters (used by VTKFromFile), by default True

modulus.utils.io.vtk.grid_to_vtk(var_dict: Dict[str, array], file_path: str, batch_index: int = 0)[source]

Helper method for nodes to export image/grid data to vtkUniformData file. Arrays should be in the numpy ‘ij’ layout (element [0,0] is origin)

Parameters

• var_dict (Dict[str, np.array]) – Dictionary of variables in the array format [batch, dim, xdim, ydim, zdim]

• file_path (str) – File directory/name of output vtk file

• batch_index (int, optional) – Batch index to write to file, by default 0

modulus.utils.io.vtk.var_to_polyvtk(var_dict: Dict[str, array], file_path: str, coordinates=['x', 'y', 'z'])[source]

Helper method for nodes to export thier variables to a vtkPolyData file Should be avoided when possible as other VTK formats can save on memory.

Parameters

• var_dict (Dict[str, np.array]) – Dictionary of variables in the array format [nstates, dim]

• file_path (str) – File directory/name of output vtk file

• coordinates (list, optional) – Variable names that corresponds to point positions, by default [“x”, “y”, “z”]

simple helper functions for reading and saving CSV files

modulus.utils.io.csv_rw.csv_to_dict(filename, mapping=None, delimiter=',')[source]

reads a csv file to a dictionary of columns

Parameters

• filename (str) – The file name to load from

• mapping (None, dict) – If None load entire csv file and store every column as a key in the dict. If mapping is not none use this to map keys from CSV to keys in dict.

• delimiter (str) – The string used for separating values.

Returns

data – numpy arrays have shape [N, 1].

Return type

dict of numpy arrays

modulus.utils.io.csv_rw.dict_to_csv(dictonary, filename)[source]

saves a dict of numpy arrays to csv file

Parameters

• dictionary (dict) – dictionary of numpy arrays. The numpy arrays have a shape of [N, 1].

• filename (str) – The file name to save too

simple Sympy helper functions

modulus.utils.sympy.functions.line(x, point_x_1, point_y_1, point_x_2, point_y_2)[source]

line function from point intercepts

Parameters

• x (Sympy Symbol/Exp) – the x in equation y=a*x+b

• point_x_1 (Sympy Symbol/Exp, float, int) – first intercept x position

• point_y_1 (Sympy Symbol/Exp, float, int) – first intercept y position

• point_x_2 (Sympy Symbol/Exp, float, int) – second intercept x position

• point_y_2 (Sympy Symbol/Exp, float, int) – second intercept y position

Returns

y – y=slope*x+intercept

Return type

Sympy Expr

modulus.utils.sympy.functions.parabola(x, inter_1, inter_2, height)[source]

parabola from point intercepts

Parameters

• x (Sympy Symbol/Exp) – the x in equation y=a*x*2+b*x+c

• inter_1 (Sympy Symbol/Exp, float, int) – first intercept such that y=0 when x=inter_1

• inter_2 (Sympy Symbol/Exp, float, int) – second intercept such that y=0 when x=inter_1

• height (Sympy Symbol/Exp, float, int) – max height of parabola

Returns

y – y=factor*(x-inter_1)*(x-+inter_2)

Return type

Sympy Expr

modulus.utils.sympy.functions.parabola2D(x, y, inter_1_x, inter_2_x, inter_1_y, inter_2_y, height)[source]

square parabola from point intercepts

Parameters

• x (Sympy Symbol/Exp) – the x in equation z=parabola(x)*parabola(y)

• y (Sympy Symbol/Exp) – the y in equation z=a*x**2+b*y**2+c*xy+d*y+e*x+f

• inter_1_x (Sympy Symbol/Exp, float, int) – first intercept such that z=0 when x=inter_1_x

• inter_2_x (Sympy Symbol/Exp, float, int) – second intercept such that z=0 when x=inter_2_x

• inter_1_y (Sympy Symbol/Exp, float, int) – first intercept such that z=0 when y=inter_1_y

• inter_2_y (Sympy Symbol/Exp, float, int) – second intercept such that z=0 when y=inter_2_y

• height (Sympy Symbol/Exp, float, int) – max height of parabola

Returns

y – y=factor*(x-inter_1)*(x-+inter_2)

Return type

Sympy Expr

Helper functions for converting sympy equations to numpy

modulus.utils.sympy.numpy_printer.np_lambdify(f, r)[source]

generates a numpy function from a sympy equation

Parameters

• f (Sympy Exp, float, int, bool or list of the previous) – the equation to convert to a numpy function. If float, int, or bool this gets converted to a constant function of value f. If f is a list then output for each element in list is is concatenated on axis -1.

• r (list, dict) – A list of the arguments for f. If dict then the keys of the dict are used.

Returns

np_f

Return type

numpy function

Helper functions for converting sympy equations to pytorch

class modulus.utils.sympy.torch_printer.CustomDerivativePrinter(settings=None)[source]

Bases: StrPrinter

class modulus.utils.sympy.torch_printer.SympyToTorch(sympy_expr, name: str, freeze_terms: List[int] = [], detach_names: List[str] = [])[source]

Bases: Module

forward(var: Dict[str, Tensor]) → Dict[str, Tensor][source]

Defines the computation performed at every call.

Should be overridden by all subclasses.

modulus.utils.sympy.torch_printer.torch_lambdify(f, r, separable=False)[source]

generates a PyTorch function from a sympy equation

Parameters

• f (Sympy Exp, float, int, bool) – the equation to convert to torch. If float, int, or bool this gets converted to a constant function of value f.

• r (list, dict) – A list of the arguments for f. If dict then the keys of the dict are used.

Returns

torch_f

Return type

PyTorch function

Helper functions and classes for integration

class modulus.utils.vpinn.integral.Quad_Rect(v, n, region_type=True, scheme_fcn=quadpy.c2.get_good_scheme)[source]

Bases: Quadrature

The points are specified in an array of shape (2, 2, …) such that arr[0][0] is the lower left corner, arr[1][1] the upper right, and set region_type=False. If your c2 has its sides aligned with the coordinate axes, you can use v=[[x0, x1], [y0, y1]], and set region_type=True (default).

Helper functions for and classes for making test functions used in VPINNs