1. Verification and Validation Using Code-Based Sensitivity Techniques
The LACSI Code-Based Sensitivity Project
Mike Fagan
Rice University
Dept. of Computational and Applied Mathematics

2. 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)

3. 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)

4. 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

5. 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

6. 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

7. Roadmap AD research Software Engineering and Construction
Sample Validation

8. 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

9. 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

10. 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)

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

12. 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

13. Laboratory Interactions
Visit summer Gave a talk
Visit summer 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 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

14. 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