Overview

ADCME is suitable for conducting inverse modeling in scientific computing. The purpose of the package is to: (1) provide differentiable programming framework for scientific computing based on TensorFlow automatic differentiation (AD) backend; (2) adapt syntax to facilitate implementing scientific computing, particularly for numerical PDE discretization schemes; (3) supply missing functionalities in the backend (TensorFlow) that are important for engineering, such as sparse linear algebra, constrained optimization, etc. Applications include

coupled hydrological and full waveform inversion
constitutive modeling in solid mechanics
learning hidden geophysical dynamics
physics informed machine learning (scientific machine learning)
parameter estimation in stochastic processes

The package inherents the scalability and efficiency from the well-optimized backend TensorFlow. Meanwhile, it provides access to incooperate existing C/C++ codes via the custom operators. For example, some functionalities for sparse matrices are implemented in this way and serve as extendable "plugins" for ADCME.

ADCME is open-sourced with an MIT license. You can find the source codes at

https://github.com/kailaix/ADCME.jl

Read more about methodology, philosophy, and insights about ADCME: slides. Start with tutorial to solve your own inverse modeling problems!

Installation

If you use Windows OS, you need to install Microsoft Visual Studio 15 (2017) first. If you do not have the compiler yet, you can download and install the compiler from here. A free community version is available.

It is recommended to install ADCME via

using Pkg
Pkg.add("ADCME")

However, in some cases, you may want to install the package and configure the environment manually.

Step 1: Install ADCME on a computer with Internet access and zip all files from the following paths

julia> using Pkg
julia> Pkg.depots()

The files will contain all the dependencies.

Step 2: Build ADCME mannually.

using Pkg;
ENV["manual"] = 1
Pkg.build("ADCME")

However, in this case you are responsible for configuring the environment by modifying the file

using ADCME; 
print(joinpath(splitdir(pathof(ADCME))[1], "deps/deps.jl"))

Quick Overview

Let's consider a simple problem: we want to solve the unconstrained optimization problem

\[f(\mathbf{x}) = \sum_{i=1}^{n-1}\left[ 100(x_{i+1}-x_i^2) + (1-x_i)^2 \right]\]

where $x_i\in [-10,10]$ and $n=100$.

We solve the problem using the L-BFGS-B method.

using ADCME
n = 100
x = Variable(rand(n)) # Use `Variable` to mark the quantity that gets updated in optimization
f = sum(100((x[2:end]-x[1:end-1])^2 + (1-x[1:end-1])^2)) # Use typical Julia syntax 
sess = Session(); init(sess) # Create and initialize a session is mandatory for activating the computational graph
BFGS!(sess, f, var_to_bounds = Dict(x=>[-10.,10.]))

To get the value of $\mathbf{x}$, we use run to extract the values

run(sess, x)

The above command will return a value close to the optimal values $\mathbf{x} = [1\ 1\ \ldots\ 1]$.

Do you know...

You can also use ADCME to do typical machine learning tasks and leverage the Julia machine learning ecosystem! Here is an example of training a ResNet for digital number recognition.

using MLDatasets
using ADCME

# load data 
train_x, train_y = MNIST.traindata()
train_x = reshape(Float64.(train_x), :, size(train_x,3))'|>Array
test_x, test_y = MNIST.testdata()
test_x = reshape(Float64.(test_x), :, size(test_x,3))'|>Array

# construct loss function 
ADCME.options.training.training = placeholder(true)
x = placeholder(rand(64, 784))
l = placeholder(rand(Int64, 64))
resnet = Resnet1D(10, num_blocks=10)
y = resnet(x)
loss = mean(sparse_softmax_cross_entropy_with_logits(labels=l, logits=y))

# train the neural network 
opt = AdamOptimizer().minimize(loss)
sess = Session(); init(sess)
for i = 1:10000
    idx = rand(1:60000, 64)
    _, loss_ = run(sess, [opt, loss], feed_dict=Dict(l=>train_y[idx], x=>train_x[idx,:]))
    @info i, loss_
end

# test 
for i = 1:10
    idx = rand(1:10000,100)
    y0 = resnet(test_x[idx,:])
    y0 = run(sess, y0, ADCME.options.training.training=>false)
    pred = [x[2]-1 for x in argmax(y0, dims=2)]
    @info "Accuracy = ", sum(pred .== test_y[idx])/100
end

Contributing

Contribution and suggestions are always welcome. In addition, we are also looking for research collaborations. You can submit issues for suggestions, questions, bugs, and feature requests, or submit pull requests to contribute directly. You can also contact the authors for research collaboration.