DualReal is the type underpinning all of MOOSE's automatic differentiation (AD) capabilities.

Overview AD-Related Timings


DualReal is a MOOSE typedef defined from the MetaPhysicL template class DualNumber. DualNumber takes two template arguments T and D; T represents the "value" type of the DualNumber, e.g. the type of , while D represents the derivative type of the DualNumber, e.g. the type of . MetaPhysicL offers several options for D types, including:

  1. NumberArray - C-array as underlying derivative vector storage for data - Fast because of static storage - Inflexible; no storage of indices so no sparse support. Essentially pick a maximum possible storage size and hope for the best. Doesn't work out for many 3D problems or problems with a lot of variables

  2. DynamicSparseNumberArray - std::vector as underlying storage for derivative data and indices - Maximum flexibility - Slow because of continual dynamic allocation of memory

  3. SemiDynamicSparseNumberArray - std::array as underlying storage for derivative data and indices - Fast because of static storage - Indice storage allows sparse operations and hence flexibility - Avoid looping over the whole size of the std::array by maintaining a dynamic size data member

The default configuration in MOOSE uses NumberArray for derivative storage because it is generally the fastest container (albeit inflexible). SemiDynamicSparseNumberArray can be selected as the derivative storage type by running ./configure --with-derivative-type=sparse in MOOSE's framework directory. The underlying derivative storage array size for both NumberArray and SemiDynamicSparseNumberArray can be modified by running configure with the option --with-derivative-size=<n> where <n> is the desired size of the container. By default, MOOSE is configured --with-derivative-size=50.

AD-Related Timings

Stabilized Incompressible Navier Stokes

Stabilized Incompressible Navier Stokes

Test specs

  • Navier-Stokes test directory input file: ad_lid_driven_stabilized.i

  • 200x200 mesh

  • default backing array size of 50

  • Computer specs: - MacBook Pro running Mojave 10.14.5 - 2.4 GHz Intel Core i9 - 32 GB 2400 MHz DDR4

SNESComputeJacobian timing

  • MOOSE non-sparse config: 9.61 seconds

  • MOOSE sparse config: 9.22 seconds