The ADCME library (Automatic Differentiation Library for Computational and Mathematical Engineering) aims at general and scalable inverse modeling in scientific computing with gradient-based optimization techniques. It is built on the deep learning framework TensorFlow, which provides the automatic differentiation and parallel computing backend. The dataflow model adopted by the framework makes it suitable for high performance computing and inverse modeling in scientific computing. The design principles and methodologies are summarized in the slides.

Several features of the library are

MATLAB-style syntax. Write A*B for matrix production instead of tf.matmul(A,B).
Custom operators. Implement operators in C/C++ for bottleneck parts; incorporate legacy code or specially designed C/C++ code in ADCME; differentiate implicit schemes.
Numerical Scheme. Easy to implement numerical schemes for solving PDEs.
Static graphs. Compilation time computational graph optimization; automatic parallelism for your simulation codes.
Custom optimizers. Large scale constrained optimization? Use CustomOptimizer to integrate your favorite optimizer.
Sparse linear algebra. Sparse linear algebra library tailored for scientific computing.

Start building your forward and inverse modeling using ADCME today!

Documentation	Tutorial	Research

Installation

⚠️ The latest version only supports Julia≧1.3.

⚠️ PyCall is forced to use the default interpreter by ADCME. Do not try to reset the interpreter by rebuilding PyCall.

Install Julia
Install ADCME

julia> ]
pkg> add ADCME

(Optional) Test ADCME.jl

julia> ]
pkg> test ADCME

(Optional) Enable GPU Support To enable GPU support, first, make sure nvcc is available from your environment (e.g., type nvcc in your shell and you should get the location of the executable binary file).

ENV["GPU"] = 1
Pkg.build("ADCME")

For manual installation without access to the internet, see here.

Tutorial

For a detailed tutorial, click here. Consider solving the following problem

-bu''(x)+u(x) = f(x), x∈[0,1], u(0)=u(1)=0

where

f(x) = 8 + 4x - 4x²

Assume that we have observed u(0.5)=1, we want to estimate b. The true value, in this case, should be b=1.

using LinearAlgebra
using ADCME

n = 101 # number of grid nodes in [0,1]
h = 1/(n-1)
x = LinRange(0,1,n)[2:end-1]

b = Variable(10.0) # we use Variable keyword to mark the unknowns
A = diagm(0=>2/h^2*ones(n-2), -1=>-1/h^2*ones(n-3), 1=>-1/h^2*ones(n-3)) 
B = b*A + I  # I stands for the identity matrix
f = @. 4*(2 + x - x^2) 
u = B\f # solve the equation using built-in linear solver
ue = u[div(n+1,2)] # extract values at x=0.5

loss = (ue-1.0)^2 

# Optimization
sess = Session(); init(sess) 
BFGS!(sess, loss)

println("Estimated b = ", run(sess, b))

Expected output

Estimated b = 0.9995582304494237

The gradients can be obtained very easily. For example, if we want the gradients of loss with respect to b, the following code will create a Tensor for the gradient

julia> gradients(loss, b)
PyObject

Under the hood, a computational graph is created for gradients back-propagation.

For more documentation, see here.

Featured Applications

Constitutive Modeling	Seismic Inversion	Coupled Two-Phase Flow and Time-lapse FWI	Calibrating Jump Diffusion

LICENSE

ADCME.jl is released under MIT License. See License for details.