Automatic Differentiation
Automatic Differentiation (AD) is a set of techniques based on the
mechanical application of the chain rule to obtain derivatives of
a function given as a computer program. AD exploits the fact that every
computer program, no matter how complicated, executes a
sequence of elementary arithmetic operations such as additions or
elementary functions such as exp().
By applying the chain rule of derivative calculus repeatedly
to these operations, derivatives of arbitrary
order can be computed automatically, and accurate to working precision.
Conceptually, AD is different from symbolic differentiation
and approximations by divided differences.
AD is used in the following areas:
- Numerical Methods
- Sensitivity Analysis
- Design Optimization
- Data Assimilation & Inverse Problems
You can find more information on AD via the
web portal on automatic differentiation,
www.autodiff.org.