Ceviche
Project description
ceviche
Electromagnetic Simulation Tools + Automatic Differentiation. Code for the arxiv preprint ForwardMode Differentiation of Maxwell's Equations.
(logo by @nagilmer)
What is ceviche?
ceviche
provides two core electromagnetic simulation tools for solving Maxwell's equations:

finitedifference frequencydomain (FDFD)

finitedifference timedomain (FDTD)
Both are written in numpy
/ scipy
and are compatible with the HIPS autograd package, supporting forwardmode and reversemode automatic differentiation.
This allows you to write code to solve your E&M problem, and then use automatic differentiation on your results.
As a result, you can do gradientbased optimization, sensitivity analysis, or plug your E&M solver into a machine learning model without the tedius process of deriving your derivatives analytically.
Tutorials
There is a comprehensive ceviche tutorial available at this link with several ipython notebook examples:
 Running FDFD simulations in ceviche.
 Performing inverse design of a mode converter.
 Adding fabrication constraints and device parameterizations.
 Inverse design of a wavelengthdivision multiplexer and advanced topics.
There are also a few examples in the examples/*
directory.
What can it do? An Example
Let's saw we have a simulation where we inject a current source at position source
and measure the electric field intensity at probe
.
Between these two points, there's a box at location pos_box
with permittivity eps
.
We're interested in computing how the intensity measured changes with respect to eps
.
With ceviche, we first write a simple function computing the measured intensity as a function of eps
using FDFD
import autograd.numpy as np # import the autograd wrapper for numpy
from ceviche import fdfd_ez as fdfd # import the FDFD solver
# make an FDFD simulation
f = fdfd(omega, dl, eps_box, npml=[10, 10])
def intensity(eps):
""" computes electric intensity at `probe` for a given box permittivity of `eps`
source  probe
.  eps  .
_____
"""
# set the permittivity in the box region to the input argument
fdfd.eps_r[box_pos] = eps
# solve the fields
Ex, Ey, Hz = f.solve(source)
# compute the intensity at `probe`
I = np.square(np.abs(Ex)) + np.square(np.abs(Ey))
return = np.sum(I * probe)
Then, we can easily take the derivative of the intensity with respect to eps
using a ceviche function
# use autograd to differentiate `intensity` function
grad_fn = ceviche.jacobian(intensity)
# then, evaluate it at the current value of `eps`
dI_deps = grad_fn(eps_curr)
The beauty is that ceviche lets you compute this derivative without having to do any calculations by hand! Using automatic differentiation, each step of the calculated is recorded and its derivative information is already known. This lets us take derivatives of arbitrary complex code, where the output depends in some way on the electromagnetic simulation.
Armed with this capability, we can now do things like performing gradientbased optimization (inverse design) to maximize the intensity.
for _ in range(10):
eps_current += step_size * dI_deps_fn(eps_current)
It's also worth noting that the mathematics behind this gradient implementation uses the 'adjoint method', which lets you take derivatives with several degrees of freedom. This is perfect for inverse design problems, or training of machine learning models that involve running an FDFD or FDTD simulation. If you're interested in the connection between adjoint methods and backpropagation in the context of photonics, check out our group's earlier work on the subject link.
Installation
There are many ways to install ceviche
.
The easiest is by
pip install ceviche
But to install from a local copy, one can instead do
git clone https://github.com/twhughes/ceviche.git
pip install e ceviche
pip install r ceviche/requirements.txt
from the main directory.
Alternatively, just download it:
git clone https://github.com/twhughes/ceviche.git
and then import the package from within your python script
import sys
sys.path.append('path/to/ceviche')
Package Structure
Ceviche
The ceviche
directory contains everything needed.
To get the FDFD and FDTD simulators, import directly from ceviche import fdtd, fdfd_ez, fdfd_hz, fdfd_ez_nl
To get the differentiation, import from ceviche import jacobian
.
constants.py
contains some constants EPSILON_0
, C_0
, ETA_0
, Q_E
, which are needed throughout the package
utils.py
contains a few useful functions for plotting, autogradding, and various other things.
Examples
There are many demos in the examples
directory, which will give you a good sense of how to use the package.
Tests
Tests are located in tests
. To run, cd
into tests
and
python m unittest
to run all or
python specific_test.py
to run a specific one. Some of these tests involve visual inspection of the field plots rather than error checking on values.
To run all of the gradient checking functions, run
chmod + test/test_all_gradients.sh
./tests/test_all_gradients.sh
Citation
If you use this for your research or work, please cite
@misc{1908.10507,
Author = {Tyler W Hughes and Ian A D Williamson and Momchil Minkov and Shanhui Fan},
Title = {ForwardMode Differentiation of Maxwell's Equations},
Year = {2019},
Eprint = {arXiv:1908.10507},
}
Project details
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