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Report on Sensitivity Analysis

Report on Sensitivity Analysis. TOPS SciDAC Project All-hands Meeting. Radu Serban Keith Grant, Alan Hindmarsh, Steven Lee, Carol Woodward Center for Applied Scientific Computing, LLNL. Work performed under the auspices of the U.S. Department of Energy

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Report on Sensitivity Analysis

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  1. Report on Sensitivity Analysis TOPS SciDAC Project All-hands Meeting Radu Serban Keith Grant, Alan Hindmarsh, Steven Lee, Carol Woodward Center for Applied Scientific Computing, LLNL Work performed under the auspices of the U.S. Department of Energy By Lawrence Livermore National Laboratory under Contract W-7405-Eng-48

  2. User main routine User problem-defining function User preconditioner function Vector Kernels CVODE ODE Integrator IDA DAE Integrator KINSOL Nonlinear Solver Band Linear Solver Dense Linear Solver Preconditioned GMRES Linear Solver General Preconditioner Modules Differential and Nonlinear Solvers @ CASC • CVODE – explicit ODE solver • IDA – implicit DAE solver • KINSOL – Krylov Inexact Newton solver

  3. Sensitivity Analysis: What for? • Model evaluation • Most and/or least influential parameters • Model reduction • Uncertainty quantification • Optimization • design optimization • optimal control • parameter estimation • … • …

  4. Computational effort: Forward Sensitivity Analysis Remarks: • Sensitivity r.h.s. can be user-defined, AD-generated, or FD-approximated • Sensitivity equations are independent of g! • Explicit ODE (CVODE) • i-th sensitivity equation • Gradient of a derived function

  5. Computational effort: Adjoint Sensitivity Analysis Remarks: • Formulation can be extended to find gradients of g(tf,y,p) • No FD approximation of the adjoint r.h.s. • Adjoint equations are independent of p! • Explicit ODE (CVODE) • For a derived function • Adjoint ODE • Gradient of derived function

  6. Options • sensitivity approach (simultaneous or staggered) • user-defined, FD, or AD-generated sensitivity r.h.s. • error control on sensitivity variables • user-defined tolerances for sensitivity variables User main routine Specification of problem parameters Activation of sensitivity computation User problem-defining function User preconditioner function Vector Kernels CVODES ODE Integrator IDAS DAE Integrator KINSOLS Nonlinear Solver Band Linear Solver Dense Linear Solver Preconditioned GMRES Linear Solver General Preconditioner Modules Forward Sensitivity Variants of CASC Solvers • CVODES currently available

  7. Implementation • check point approach; total cost is 2 forward solutions + 1 backward solution • integrate any system backwards in time • may require modifications to some user-defined vector kernels User main routine Activation of sensitivity computation User problem-defining function User reverse function User preconditioner function User reverse preconditioner function CVODEA ODE Integrator IDAA DAE Integrator KINSOLA Nonlinear Solver Band Linear Solver Dense Linear Solver Preconditioned GMRES Linear Solver General Preconditioner Modules Modified Vector Kernels Adjoint Sensitivity Variants of CASC Solvers • CVODEA currently available

  8. Effects of Aerosols on Cloud Properties* Problem description • Condensation-evaporation eqs. coupled with eqs. of parcel motion and properties  Implicit ODEs Sensitivity of cloud liquid water to temperature and water vapor profiles Problem dimensions • Ny 300 • Np=2 *K. Grant, C. Chuang, S. Lee, C. Woodward

  9. Groundwater Flow Problem description • Variably saturated flow nonlinear elliptic PDEs  Nonlinear eqs. • Study influence of permeability field on solution (pressure) • Quantify uncertainty in solution due to uncertainty in relative permeability and saturation curves Problem dimensions • Ny=19000 • Np=3 *C. Woodward, K. Grant, R. Maxwell

  10. 2-D Advection-Diffusion u0 l dG for du0=d(x-x’,y-y’) Problem description • 2-D time-dependent PDEs with homogeneous Dirichlet B.C.  Explicit ODEs Problem dimensions • Nu=800 • Np=800

  11. CVD of Superconducting Thin Films (YBaCuO)* Problem description • Compressible, chemically reacting, stagnation-flow equations • 1-D time-varying PDEs  Hessenberg index-2 DAEs • Control film stoichiometry through inlet composition Problem dimensions • Ny 500 • Np=24 *L. Raja, R. Kee, R. Serban, L. Petzold

  12. Future Developments • Code development: • IDAS and IDAA • KINSOLA • SciDAC collaboration: • Terrascale Supernova Initiative: Sensitivity analysis for radiation hydrodynamics (CVODES/IDAS) • Other? • TOPS collaborations? • Time-dependent DE constrained optimization • Other?

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