Activity Analysis for Operator Overloading Automatic Differentiation Automatic Differentiation of Leadership-Class Applications

Automatic Differentiation (AD) automatically performs the differentiation of models expressed in a high level programming language. Several DOE-sponsored tools implement AD in the source-to-source transformation approach and the operator overloading approach. Operator overloading AD exploits the operator overloading features of the programming language that the model is expressed in. Runtime libraries implement methods that overload operators such as +, −, ∗, / and mathematical functions such as sin and sqrt to compute derivative values along with elementary computation. Source-to-source transformation generates an output code that contains the original input code as well additional code to compute derivatives. It is typically faster than operator overloading AD as it can use compiler analysis such as activity analysis to optimize the generated code. Operator overloading AD is more robust as the tool does not have to handle esoteric syntactic and semantic programming language features itself. Often, AD users are interested in computing the derivatives of a subset of the output variables in the model with respect to a subset of the input variables (known as dependent and independent variables respectively). Depending on the role a temporary variable plays in the model sourc