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When models and data disagree: sparse resolutions to inconsistent datasets Arun Hegde Wenyu Li Jim Oreluk Andrew Packard Michael Frenklach This project is supported by the U.S. Department of Energy, National Nuclear Security Administration,

  1. When models and data disagree: sparse resolutions to inconsistent datasets Arun Hegde Wenyu Li Jim Oreluk Andrew Packard Michael Frenklach This project is supported by the U.S. Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002375 SIAM UQ18 APRIL 16-19, 2018

  2. Overview • Bound-to-Bound Data Collaboration (B2BDC) • models + data = dataset (model-data system) • Dataset Consistency – agreement between models and data • scalar consistency measure • vector consistency measure • Dataset examples • GRI-Mech 3.0 • DLR-SynG • Summary SIAM UQ18 APRIL 16-19, 2018

  3. Bound-to-Bound Data Collaboration UQ as constrained optimization: parameters constrained by models and data Models Data Dataset • Prior knowledge on “True” QOI models uncertain parameters Surrogate QOI models • QOI measurements (w/ uncertainty) Fitting error Feasible set ─ parameters for which the models and data agree. Prediction bounds the range of a model subject to the feasible set SIAM UQ18 APRIL 16-19, 2018

  4. Consistency as Model Validation • A dataset is consistent if it is feasible – Parameters exist for which model predictions match the experiments QOI space Parameter space • Consistency analysis provides measures of validation SIAM UQ18 APRIL 16-19, 2018

  5. Quantifying Consistency Scalar Consistency Measure (SCM)* Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) QOI space *Feeley, R.; Seiler, P.; Packard, A.; Frenklach., M.; J. Phys. Chem. A. 2004, 108 , 9573. SIAM UQ18 APRIL 16-19, 2018

  6. Quantifying Consistency Scalar Consistency Measure (SCM)* Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) If consistent , go to prediction *Feeley, R.; Seiler, P.; Packard, A.; Frenklach., M.; J. Phys. Chem. A. 2004, 108 , 9573. SIAM UQ18 APRIL 16-19, 2018

  7. Quantifying Consistency Scalar Consistency Measure (SCM)* Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) If inconsistent , … ??? *Feeley, R.; Seiler, P.; Packard, A.; Frenklach., M.; J. Phys. Chem. A. 2004, 108 , 9573. SIAM UQ18 APRIL 16-19, 2018

  8. Quantifying Consistency Scalar Consistency Measure (SCM)* Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) • Inconsistency  models and data disagree • Follow-up questions: • What are the sources of inconsistency? • Where do we begin to look? *Feeley, R.; Seiler, P.; Packard, A.; Frenklach., M.; J. Phys. Chem. A. 2004, 108 , 9573. SIAM UQ18 APRIL 16-19, 2018

  9. Quantifying Consistency Scalar Consistency Measure (SCM) Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) Lagrange multipliers from dual form Local: Sensitivities Global: Feeley, R.; Seiler, P.; Packard, A.; Frenklach., M.; J. Phys. Chem. A. 2004, 108 , 9573. SIAM UQ18 APRIL 16-19, 2018

  10. Quantifying Consistency Scalar Consistency Measure (SCM) Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) Q: New question: What is the fewest number of constraint relaxations required to render the dataset consistent? SIAM UQ18 APRIL 16-19, 2018

  11. Vector Consistency Scalar Consistency Measure (SCM) Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) If inconsistent, compute the Vector Consistency Measure (VCM) vector consistency measure ( VCM ) • Offers detailed analysis of inconsistency by allowing independent relaxations. • Can be used to flag constraints contributing to inconsistency SIAM UQ18 APRIL 16-19, 2018

  12. Vector Consistency Scalar Consistency Measure (SCM) Q: Does there exist a parameter vector for which the models and data agree, within uncertainty? A: Compute the scalar consistency measure ( SCM ) If inconsistent, compute the Vector Consistency Measure (VCM) vector consistency measure ( VCM ) heuristic for fewest # of nonzeros (sparsity) • Offers detailed analysis of inconsistency by allowing independent relaxations. • Can be used to flag constraints contributing to inconsistency SIAM UQ18 APRIL 16-19, 2018

  13. Examples * * Hegde, A.; Li, W.; Oreluk, J.; Packard, A.; Frenklach, M., SIAM/ASA J. Uncert. Quantif., 2018, 6(2), 429-456. SIAM UQ18 APRIL 16-19, 2018

  14. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • Procedure: apply SCM, use sensitivities to flag problems. SIAM UQ18 APRIL 16-19, 2018

  15. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • Procedure: apply SCM, use sensitivities to flag problems. • SCM < 0. Analyze ranked sensitivities SIAM UQ18 APRIL 16-19, 2018

  16. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • Procedure: apply SCM, use sensitivities to identify problems. • SCM < 0. Analyze ranked sensitivities SIAM UQ18 APRIL 16-19, 2018

  17. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • • Procedure: apply SCM, use Compute VCM. sensitivities to identify problems. • SCM < 0. Analyze ranked sensitivities SIAM UQ18 APRIL 16-19, 2018

  18. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • • Procedure: apply SCM, use Compute VCM. sensitivities to flag problems. • Two QOIs relaxed (same as in SCM), • dataset consistent. SCM < 0. Analyze ranked sensitivities • SCM > 0. Two QOIs removed, dataset consistent. SIAM UQ18 APRIL 16-19, 2018

  19. Example 1: GRI-Mech 3.0 GRI-Mech 3.0 dataset ( 77 QOIs, 102 uncertain parameters ) for natural gas combustion. Scalar Consistency Vector Consistency • • Procedure: apply SCM, use Compute VCM. sensitivities to flag problems. • Two QOIs relaxed (same as in SCM), • dataset consistent. SCM < 0. Analyze ranked sensitivities • SCM > 0. 2 QOIs removed, dataset consistent. Rapid and interpretable Rapid and interpretable resolution of inconsistency resolution of inconsistency SIAM UQ18 APRIL 16-19, 2018

  20. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR*. Scalar Consistency Vector Consistency * Slavinskaya, N.; et al. Energy & Fuels. 2017, 31, pp 2274 – 2297 SIAM UQ18 APRIL 16-19, 2018

  21. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. SIAM UQ18 APRIL 16-19, 2018

  22. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. Set aside the top most sensitive QOI Set aside the top two most sensitive QOIs Set aside the top n most sensitive QOIs Set aside the second most sensitive QOI (counter intuitive) . . . SIAM UQ18 APRIL 16-19, 2018

  23. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. Set aside the top most sensitive QOI Set aside the top two most sensitive QOIs Set aside the top n most sensitive QOIs Set aside the second most sensitive QOI (counter intuitive) . . . SIAM UQ18 APRIL 16-19, 2018

  24. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. – Remove QOI #104 from dataset. SIAM UQ18 APRIL 16-19, 2018

  25. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. – Remove QOI #104 from dataset. • SCM < 0. Analyze ranked sensitivities. SIAM UQ18 APRIL 16-19, 2018

  26. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. – Remove QOI #104 from dataset. • SCM < 0. Analyze ranked sensitivities. – Remove QOI # 109. SIAM UQ18 APRIL 16-19, 2018

  27. Example 2: DLR-SynG DLR-SynG dataset ( 159 QOIs, 55 uncertain parameters ) for syngas combustion developed at DLR. Scalar Consistency Vector Consistency • SCM < 0. Analyze ranked sensitivities. – Remove QOI #104 from dataset. • SCM < 0. Analyze ranked sensitivities. – Remove QOI # 109. Repeat until consistent SIAM UQ18 APRIL 16-19, 2018

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