1 / 25

CS 351/ IT 351 Modeling and Simulation Technologies

This article explains various sources of errors in models, including input values, machine inaccuracies, and algorithm inaccuracies, and discusses how to characterize and interpret these errors. It also explores the implications of errors in models and provides strategies for controlling and predicting their effects.

suethompson
Download Presentation

CS 351/ IT 351 Modeling and Simulation Technologies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Errors In Models Dr. Jim Holten CS 351/ IT 351 Modeling and SimulationTechnologies

  2. CS 351/ IT 351 Errors in Models • Sources of Errors • Characterizing Errors • Using Error Bounds • Interpreting Error Implications

  3. CS 351/ IT 351 Sources of Errors • Input Values (measurements) • Machine Inaccuracies • Algorithm Inaccuracies • Bad models

  4. CS 351/ IT 351 Measurement Errors • Measurement granularity • Granularity accuracy ==> Error intervals • Types of measurements

  5. CS 351/ IT 351 Machine Errors: Representation • Float: 7 decimal places, E+/-38, or subnormal E-45 (fewer digits of precision) • Double – 16 decimal places, E +/-308, or subnormal E-324 (fewer digits of precision)

  6. CS 351/ IT 351 Machine Errors: Representation • Equality comparisons (does 0.0F == 0.0D?) • Overflow (too big an exponent) • Underflow (too small an exponent) • Mismatch (1.000E19D + 47.3D = ?)

  7. CS 351/ IT 351 Machine Errors • Divide by zero (+/- Inf), or divide zero by zero (NaN) • Propagate “bad” values • Worst-case scenarios, not seen as errors • Near zero results of add or subtract • Near zero denominator

  8. CS 351/ IT 351 Algorithm Sources of Errors • Inaccurate representation of real world • Inaccurate representation of ideal world • Computational errors

  9. CS 351/ IT 351 Real World to Ideal Model • Math Models are Idealistic • Real world has many perturbations • Statistical estimates are only “best fit” to observed measurements • Results in an inaccurate ideal model

  10. CS 351/ IT 351 Ideal Model to Implementation • Machine errors in number representations • Machine errors in arithmetic calculations • Results in even worse implementation model values

  11. CS 351/ IT 351 Computational Errors • Numerical calculation to approximate math functions • Numerical Integration • Numerical differentiation • Techniques used determine the error behaviors

  12. CS 351/ IT 351 Controllable Errors • Understanding sources and behavior of errors empowers you to control them and predict their effects on the results. • Identifying sources and effects of errors allows you to better judge the quality of models.

  13. CS 351/ IT 351 What Gives Bad Models? • Wrong equations • Wrong numerical methods • Details gone awry • All irrationally affect results.

  14. CS 351/ IT 351 Characterizing Errors • Error Forms (Probability Distributions?) • Error propagation effects on error forms • Limitations versus needs

  15. CS 351/ IT 351 Error Characterizationss • Error probability distributions • The normal distribution • Zoo of common other distributions • Arbitrary distributions • Error bounds • Generalized error estimation functions • Enumerated values and “false negatives”

  16. CS 351/ IT 351 Error Probability Distributions • Measurement error characteristics • Calculation error characteristics • Introduced algorithmic error terms

  17. CS 351/ IT 351 Measurement ErrorCharacteristics • Discrete sample on a number line • Spacing determines “range” for each measurement point • Actual value may be anywhere in that range

  18. CS 351/ IT 351 Calculation ErrorCharacteristics • Round-off • Divide by near-zero • Divide by zero • Algorithm inaccuracies

  19. CS 351/ IT 351 Algorithmic ErrorCharacteristics • Depends on the algorithms/solvers used • Depends on the problem size • Depends on inter-submodel data sharing patterns and volume

  20. CS 351/ IT 351 Errors: Normal Distributions • Easy to characterize • Propagates nicely through linear stages • Useless for nonlinearities, special conditions • Not always a good fit

  21. CS 351/ IT 351 Errors:Generalized Distributions • Not commonly used • Easy to represent (histograms into PDFs) • Propagate through nonlinear calculations? • Awkward: histograms, PDFs, CDFs for each variable

  22. CS 351/ IT 351 Errors: Bounded • Not commonly used • Easy to represent (+/-error magnitude) • Can be propagated through nonlinear calculations • Still awkward for some calculations

  23. CS 351/ IT 351 Errors: Propagating a Distribution • Highly dependent on the distribution and the calculations being performed. • Generally only linear operations give easily predictable algebraic results. • Others require piecewise approximations

  24. CS 351/ IT 351 Error Bounds • Expected value, +/-error magnitude, or min/max • Propagates through calculations? • More complex forms may be needed after propagation – bounded piecewise linear distributions

  25. CS 351/ IT 351 Errors: Unhandled Implications • Misinterpretation of results • Misplaced confidences • “Chicken Little”, “The Boy Who Cried 'Wolf'”, and ignored real consequences

More Related