2.4.7 Custom noise

This example solves a diffusion equation with a custom noise.

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import numpy as np

from pde import DiffusionPDE, ScalarField, UnitGrid


class DiffusionCustomNoisePDE(DiffusionPDE):
    """Diffusion PDE with custom noise implementation."""

    def noise_realization(self, state, t):
        """Numpy implementation of spatially dependent noise."""
        noise_field = ScalarField.random_uniform(state.grid, -self.noise, self.noise)
        return state.grid.cell_coords[..., 0] * noise_field

    def make_noise_realization(self, state, backend):
        """Compilable implementation of spatially dependent noise."""
        noise = float(self.noise)
        x_values = state.grid.cell_coords[..., 0]

        def noise_realization(state_data, t):
            return x_values * np.random.uniform(-noise, noise, size=state_data.shape)

        return noise_realization


eq = DiffusionCustomNoisePDE(diffusivity=0.1, noise=0.1)  # define the pde
state = ScalarField.random_uniform(UnitGrid([64, 64]))  # generate initial condition
result = eq.solve(state, t_range=10, dt=0.01)
result.plot()