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We present a new software system PETSc TSAdjoint for first-order andsecond-order adjoint sensitivity analysis of time-dependent nonlineardifferential equations. The derivative calculation in PETSc TSAdjoint isessentially a high-level algorithmic differentiation process. The adjointmodels are derived by differentiating the timestepping algorithms andimplemented based on the parallel infrastructure in PETSc. Full differentiationof the library code including MPI routines thus is avoided, and users do notneed to derive their own adjoint models for their specific applications. PETScTSAdjoint can compute the first-order derivative, that is, the gradient of ascalar functional, and the Hessian-vector product that carries second-orderderivative information, while requiring minimal input (a few callbacks) fromthe users. Optimal checkpointing schemes are employed by the adjoint model in amanner that is transparent to users. Usability, efficiency, and scalability aredemonstrated through examples from a variety of applications.

PETSc TSAdjoint: a discrete adjoint ODE solver for first-order and second-order sensitivity analysis