Verification and Validation Using CodeBased Sensitivity Techniques

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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/rev
iew/slides/Fagan_LACSI_review.ppt
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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 VV (alternative
  spelling VnV)

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VV Techniques

• Validation
• 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 Newtons 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)

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A Common Subproblem

• Newtons 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

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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 DifferencesHand Coding
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State of the Art in AD

• Fortran 77
• 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

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Roadmap

• AD research
• Software Engineering and Construction
• Sample Validation

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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

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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

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AD and V V at Los Alamos

• Rudy Henninger
• 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)

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

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Runtime Error Analysis

• Doug Kothe indicated at the LACSI Priorities and
  Strategies meeting in 2004 that the VV 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