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Neurodiffeq Conditions

This library extends the neurodiffeq library by providing more initial / boundary conditions.

The APIs are NOT finalized until incorporated into the main neurodiffeq library. USE WITH CAUTION.

Install

To simply install/update to latest version

pip install -U git+https://github.com/NeuroDiffGym/neurodiffeq-conditions

Alternatively, to edit and develop this library

git clone https://github.com/NeuroDiffGym/neurodiffeq-conditions
cd neurodiffeq-conditions && pip install -e .
git checkout <COMMIT-OR-BRANCH-OR-TAG>

Conditions

Dirichlet-Neumann Mixed 3D

A boundary condition imposed on a rectangular region in R^3. To construct such a condition, first decompose the condition into several components.

Imposing condition on a 2-D plane perpendicular to x-axis

import torch
from neurodiffeq_conditions import ConditionComponent3D

# Just Dirichlet: u(x=0.0, y, z) = f(y,z) = sin(y) + cos(z) 
f = lambda x, y, z: torch.sin(y) + torch.cos(z)
comp_x0 = ConditionComponent3D(0.0, f_dirichlet=f, coord_name='x')

# Just Neumann: u'_x(x=1.0, y, z) = g(y,z) = 2*y + 3*z
g = lambda x, y, z: 2*x + 3*z
comp_x1 = ConditionComponent3D(1.0, f_neumann=g, coord_name='x')

# Dirichlet: u(x=2.0, y, z) = f(y,z) = sin(y) + cos(z) 
# Neumann: u'_x(x=2.0, y, z) = g(y,z) = 2*y + 3*z
f = lambda x, y, z: torch.sin(y) + torch.cos(z)
g = lambda x, y, z: 2*x + 3*z
comp_x2 = ConditionComponent3D(2.0, f_dirichlet=f, f_neumann=g, coord_name='x')

Imposing condition on a 2-D plane perpendicular to y- or z-axis

# similar to above, just change `coord_name='x'` to `coord_name='y'`
comp_y0 = ConditionComponent3D(..., coord_name='y')
comp_y1 = ConditionComponent3D(..., coord_name='y')
# or change it to 'z'
comp_z0 = ConditionComponent3D(..., coord_name='z')
comp_z1 = ConditionComponent3D(..., coord_name='z')

Putting Them Together

from neurodiffeq_conditions import Condition3D

# You can put in arbitraily many components, in any order
condition = Condition3D(components=[comp_x0, comp_x1, comp_x2, comp_y0, comp_y1, comp_z0, comp_z1, ...])

The constructed condition can now be used for neurodiffeq.

Note: The condition depends on limits when evaluating on points exactly on the boudary. Since PyTorch is a numerical package and cannot take limits, you need to make sure that points on the boundary are never sampled. Use points close to boundaries instead. Say, add an EPS=10^-6 to points exactly on the boundary.