1*46696af2SBarry Smith# Sensitivity Analysis for ODE and DAE 2*46696af2SBarry Smith 3*46696af2SBarry Smith 4*46696af2SBarry SmithThe `TS` library provides discrete adjoint models (`TSAdjoint`) and tangent linear models (`TSForward`) for sensitivity analysis for ODEs and DAEs. Users guide section: [](section_sa). 5*46696af2SBarry Smith 6*46696af2SBarry SmithThe adjoint solvers support gradient calculation for multiple cost functions, and the tangent linear solvers support gradient calculation with respect to multiple parameters. 7*46696af2SBarry SmithAdjoint is particularly efficient when the number of cost functions is much less than the number of parameters. 8*46696af2SBarry SmithNote that the parameters can be initial states or system parameters as used in the calculation of ODE/DAE right-hand sides. 9*46696af2SBarry Smith 10*46696af2SBarry SmithTypical cost functions of interest may depend on the final solution to the ODE/DAE or on the whole trajectory (taking an integral form). 11*46696af2SBarry SmithThe integral can be evaluated together with the time integration. 12*46696af2SBarry Smith 13*46696af2SBarry Smith<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/index.html">Examples</A><BR> 14*46696af2SBarry Smith 15*46696af2SBarry Smith 16