DiffSL

A compiler for a domain-specific language for ordinary differential equations (ODEs) of the following form:

$$ M(t) \frac{d\mathbf{u}}{dt} = F(\mathbf{u}, t) $$

As an example, the following code defines a classic DAE testcase, the Robertson (1966) problem, which models the kinetics of an autocatalytic reaction, given by the following set of equations:

$$ \begin{align} \frac{dx}{dt} &= -0.04x + 10^4 y z \ \frac{dy}{dt} &= 0.04x - 10^4 y z - 3 \cdot 10^7 y^2 \ 0 &= x + y + z - 1 \end{align} $$

The DiffSL code for this problem is as follows:

in = [k1, k2, k3]
k1 { 0.04 }
k2 { 10000 }
k3 { 30000000 }
u_i {
  x = 1,
  y = 0,
  z = 0,
}
dudt_i {
  dxdt = 1,
  dydt = 0,
  dzdt = 0,
}
M_i {
  dxdt,
  dydt,
  0,
}
F_i {
  -k1 * x + k2 * y * z,
  k1 * x - k2 * y * z - k3 * y * y,
  1 - x - y - z,
}
out_i {
  x,
  y,
  z,
}

DiffSL Language Features

See the DiffSL Language section for a full description.

• Input parameters
• Define arbitrary intermediate variables:
  • Scalars (double precision floating point numbers)
  • Vectors (1D arrays of scalars)
  • N-dimensional tensor of scalars
  • Sparse tensors
• Tensor operations:
  • Elementwise operations
  • Tensor contractions/matmul/translation etc via index notation
• Stop the simulation when a condition is met

Dependencies

You will need to install the LLVM project. The easiest way to install this is to use the package manager for your operating system. For example, on Ubuntu you can install these with the following command:

sudo apt-get install llvm

Installing DiffSL

You can install DiffSL using cargo. You will need to indicate the llvm version you have installed using a feature flag. For example, for llvm 14:

cargo add diffsl --features llvm14-0

Other versions of llvm are also supported given by the features llvm4-0, llvm5-0, llvm6-0, llvm7-0, llvm8-0, llvm9-0, llvm10-0, llvm11-0, llvm12-0, llvm13-0, llvm14-0, llvm15-0, llvm16-0, llvm17-0.