Verification and Validation Using Code-Based Sensitivity Techniques The LACSI Code-Based Sensitivity Project Mike Fagan Rice University Dept. of Computational and Applied Mathematics http://lacsi.rice.edu/review/slides/Fagan_LACSI_review.ppt

The Problem Development of computer models of physical phenomena requires a “reality” check. If the computer model output matches the real data, then all is well If the model output does not match, then ??? Underlying mathematics/physics is inadequate to capture the salient features of the phenomena under study. VALIDATION problem. Program implementing the model is incorrect. VERIFICATION problem Together, referred to as V&V (alternative spelling VnV)

V&V Techniques Validation Verification Obtain “best” fit with (some portion of) the data Evaluate if “best” is good enough Evaluate tuned simulation on other data, see if fit is adequate Best fits may be obtained with Newton’s Method Verification For now, this means testing. If simulation model is a differential equation, then Method of Manufactured Solutions (MMS) Roundoff error estimation: run-time error bounds (Wilkinson)

A Common Subproblem Newton’s method  compute derivatives MMS  compute derivatives Runtime error bounds  compute derivatives Some additional uses of derivatives (optimal) design Taylor series techniques for DEs Newton-Krylov iterations

Finite Differences Hand Coding Research Overview Purpose : Efficiently,accurately, and with minimal human intervention compute sensitivities of computer codes. “Sensitivity” means ( calculus ) derivative Accomplish this through Automatic Differentiation (AD) 3 Ways to Compute Derivatives: Finite Differences Hand Coding Automatic Differentiation Finite Differences Hand Coding

State of the Art in AD Fortran 77 Fortran 90 C,C++ Adifor 3.0 First to use compiler technology 1995 Wilkinson prize to Adifor 2 Price/Distribution model fits well TAF (TAMC), TAPENADE Fortran 90 Adifor 3.0, TAF, TAPENADE all support a little C,C++ ADIC, ADOL-C, FADBAD

Roadmap AD research Software Engineering and Construction Sample Validation

AD Research Areas of inquiry Memory usage for adjoint methods Improved derivative methods for simple assignment statements Techniques for advanced language features Array slices, structured data Pointers, dynamic memory allocation Operator overloading Multiple data representations Association-by-name or Association-by-address Activity Analysis for advanced programming languages AD for MPI programs

Software Engineering and Development Develop a framework for multi-language AD. Component Model: separating language knowledge from differentiation. Leverage other work (Open64) Develop a Fortran 90 AD tool (with Unit Tests) 80 Unit tests, all pass Ubiksolve, a component of the Truchas system Good Truchas Surrogate (Brian Lally) Linear solvers, so differentiation is easy to check 50% run and verified

AD and V & V at Los Alamos Rudy Henninger: Ralph Nelson: Mesa 1D, 2D anti-armor codes Caravana lagrangian test code (hydro methods from FLAG code) Truchas 1d (metal casting code) Ralph Nelson: TRAC (reactor safety code)

Detonation Shock Dynamics (DSD) Curvature Equation How could one tune these 6 parameters??

DSD - better fit of 6 parameters - SNL DAKOTA package drives the optimization process - Gradients provided by AD of DSD solver - ~40 passes improves the fit

Laboratory Interactions Visit summer 2001 -- Gave a talk Visit summer 2002 -- visit w Rudy to work on explosion code SIAM Session on Validation of Metal Flow Simulations, talk on verification of DEs LACSI Symposium session on Verification and Validation talk on verification of DEs Visit summer 2003 -- gave a talk Methods conference 2004 Truchas conference 2004, talk on Adifor90 6 Registered Adifor users at LANL T-10,T-11,EES-5,XMH, CCS-2,X5

Runtime Error Analysis Doug Kothe indicated at the LACSI Priorities and Strategies meeting in 2004 that the V&V groups at LANL are concerned about roundoff error Can get estimated linearized forward error analysis by computing For each statement executed in the program. Approximate dx by machine epsilon * x