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A Framework and Infrastructure for Uncertainty Quantification and Management in Materials Design
- 1. Changning Niu, Abhinav Saboo, Jiadong Gong, Greg Olson Work funded by August 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop Gaithersburg, MD Hosted by A Framework and Infrastructure for Uncertainty Quantification and Management in Materials Design
- 2. QuesTek Innovations LLC • A global leader in Integrated Computational Materials Engineering (ICME) • Many proprietary models to predict Process-Structure- Property-Performance relationships • Designing/deploying novel materials for government and industrial applications, including Energy, Aerospace, Automotive, Defense, etc. • Example: four commercially available Ferrium® steels licensed to Carpenter Technology • QuesTek is a partner of CHiMaD • Center for Hierarchical Materials Design, a NIST- sponsored center of excellence in Chicagoland Ferrium S53 flying on rockets Ferrium C61 rotor shaft for helicopters Ferrium M54 hook shank for T-45 aircraft Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 2
- 3. Outline Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 3 Overview MaGICMaT Uncertainty Management Cloud-Based Platform
- 4. Enhanced ICME with MGI and AI Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 4 ICME MGI AI 1. MaGICMaT 2. Uncertainty Management Materials Genome and Integrated Computational Materials Toolkit Uncertainty Quantification (UQ) & Propagation (UP) 3. Cloud-Based Platform QuesTek is exploring ways to incorporate MGI and AI into its ICME practice.
- 5. Motivation: MaGICMaT Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 5 Hierarchy of Present and Future Materials Genome Methods, Tools and Databases. Figure from: Olson, G. B., & Kuehmann, C. J. (2014). Materials genomics: From CALPHAD to flight. Scripta Materialia, 70, 25–30 MaGICMaT Build bridges between Materials Genome and ICME • Data retrieval from complex sources • Data & PSP linkages management • Interfaces with ICME & AI models ICME MGI AI 1. MaGICMaT
- 6. Motivation: Uncertainty Management Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 6 Hierarchy of Present and Future Materials Genome Methods, Tools and Databases. Figure from: Olson, G. B., & Kuehmann, C. J. (2014). Materials genomics: From CALPHAD to flight. Scripta Materialia, 70, 25–30 Uncertainty Management Build up uncertainty from fundamental thermodynamic data • Assess uncertainty within thermodynamic databases (TDBs) • Manage and apply the uncertainty in CALPHAD and ICME ICME MGI AI 2. Uncertainty Management
- 7. Motivation: Cloud-Based Platform Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 7 Hierarchy of Present and Future Materials Genome Methods, Tools and Databases. Figure from: Olson, G. B., & Kuehmann, C. J. (2014). Materials genomics: From CALPHAD to flight. Scripta Materialia, 70, 25–30 Cloud-Based Platform Unified platform with an HPC backend • Rapid development and deployment • User friendly on multiple levels ICME MGI AI 3. Cloud-Based Platform
- 8. Outline Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 8 Overview MaGICMaT Uncertainty Management Cloud-Based Platform
- 9. Current Data & PSP Linkage Management Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 9 StructureProcessing Properties Alloy Composition Rapid Hot Pressing Anneal Matrix Phase Charge Carrier Doping Band Engineering 2nd-Phase Nanostructures Interface Engineering Grain Refinement Grain Boundary Engineering Thermal Cond. k Electronic Th. Con. ke Electrical Conductivity s Seebeck Coefficient S Carrier Con. n Effective Mass m* Degeneracy Nv Interface Res. ri Scattering t zT Lattice Thermal Cond. kL Int. Th. Res. 1/ki Grain Lat. TC kL,g Mobility m Getting data from public databases A storage tool for collected data Management of PSP linkages • Matminer • Web APIs • etc. • MDCS • etc. • iCMD • Pymatgen • Jupyter Notebook? MaGICMaT to fill these gaps
- 10. Ability to Manage & Generate Design Charts Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 10 Experimental approach using literature High-throughput approach using DFT data Fast exploration of ICME design methods Calibration of high-throughput approach using experimental data data data Proprietary Information Proprietary Information
- 11. Outline Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 11 Overview MaGICMaT Uncertainty Management Cloud-Based Platform
- 12. Uncertainty from Bayesian Inference 𝑃 𝜃 𝐷 = 𝐷 𝜃 ( ) ( ) , 𝜃 is vector in parameter space e.g. (a,b) • 𝑃(𝜃) prior probability, probability before considering data D • 𝑃 𝐷 𝜃 likelihood • How likely this data is to be measured if the (true) model has parameters 𝜃 • 𝑃 𝜃 𝐷 posterior probability, probability after considering data D • 𝑃(𝐷), normalizing factor (complex integral) Classical (least-squre) Model 𝑦 = 𝑎𝑥 + 𝑏 Result 𝑎 = 2, 𝑏 = 1 Bayesian 𝑎 = 𝑏 = Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 12
- 13. CALPHAD Theory • Unary: • 𝐺 = 𝑎 + 𝑏𝑇 + 𝑐𝑇ln 𝑇 + Σ 𝑑 𝑇 • Binary/higher order: • 𝐺 𝑥 = ∑ 𝑥 𝐺 , + ∑ 𝑅𝑇𝑥 ln 𝑥 + ∑ 𝑥 𝑥 𝐿 , (𝑥 − 𝑥 ) , 𝐿 , = 𝑎 , 𝑇 + 𝑏 , • Measurable quantities can be derived from the Gibbs energy, e.g.: • Enthalpy: 𝐻 = 𝐺 − 𝑇 • Heat capacity: 𝐶 (𝑇, 𝜃) = −𝑇 𝐺 • Activity: 𝑎 = 𝑒 ∅ , 𝜇 = • Phase boundaries: 𝐺 𝑥 , 𝑇 = 𝐺 𝑥 , 𝑇 Unary energy Ideal mixing energy Excess mixing energy It is possible to assess these quantities analytically. In this study, we use the ThermoCalc engine, which is regarded as a black box. Generalized for common TDB files Good performance from ThermoCalc Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 13
- 14. CALPHAD UQ Steps Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 14 TDB file Synthetic Data UQ Calc TDB + UQ Same? + noiseThermo-Calc Thermo-Calc 1. Algorithm Validation 2. UQ Assessment Real Data UQ Calc TDB + UQ Thermo-Calc 3. UQ Calculation TDB + UQ HT Calc UQ Results Thermo-Calc
- 15. System to Start with: Ni-Cr 𝐺 𝑥 = 𝑥 𝐺 , + 𝑅𝑇𝑙𝑛 𝑥 +𝑥 𝑥 𝑳 𝑨,𝟎(𝑥 − 𝑥 ) + 𝑥 𝑥 𝑳 𝑨,𝟏(𝑥 − 𝑥 ) 𝐿0(𝐵𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐵𝐶𝐶 ∗ 𝑇 + 𝑏0, 𝐵𝐶𝐶 𝐿1(𝐵𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐵𝐶𝐶 ∗ 𝑇 + 𝑏1, 𝐵𝐶𝐶 𝐿0(𝐹𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐹𝐶𝐶 ∗ 𝑇 + 𝑏0, 𝐹𝐶𝐶 𝐿1(𝐹𝐶𝐶, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐹𝐶𝐶 ∗ 𝑇 + 𝑏1, 𝐹𝐶𝐶 𝐿0(𝐿𝐼𝑄𝑈𝐼𝐷, 𝐶𝑟, 𝑁𝑖) = 𝑎0, 𝐿𝐼𝑄 ∗ 𝑇 + 𝑏0, 𝐿𝐼𝑄 𝐿1(𝐿𝐼𝑄𝑈𝐼𝐷, 𝐶𝑟, 𝑁𝑖) = 𝑎1, 𝐿𝐼𝑄 ∗ 𝑇 + 𝑏1, 𝐿𝐼𝑄 Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 15 First study was on Ni-Cr system because of: • Availability of raw data for CALPHAD assessment • Simplicity of phase diagram • 12 parameters were assessed
- 16. Synthetic Data: Ground Truth vs. Prediction No. of steps Parametervalue Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 16 Algorithm is validated by the synthetic data results.
- 17. Real Data: Prediction vs. Original TDB Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 17 Parametervalue No. of steps • Good results from UQ calculations • Deviation of parameters from original TDB due to weights on datasets
- 18. Phase Diagram with Uncertainty from Real Data Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 18 TDB File UQ Trace TDB * 1000 QT Cloud Thermo-Calc • We have developed a package to combine TDB with UQ traces for automatic CALPHAD calculations using Thermo-Calc on HPC. • Unlike regular CALPHAD assessment, CALPHAD UQ can continuously “grow” as we collect new data without using old data.
- 19. Outlier Sensitivity: Theory 𝑓 𝑥 𝜇, 𝑏 = 1 2𝑏 exp − 𝑥 − 𝜇 𝑏 𝑓 𝑥 𝜇, 𝜎 = 1 2𝜋𝜎 exp − 𝑥 − 𝜇 2𝜎 Gaussian Distribution Laplace Distribution Images from Wikipedia The Laplace distribution has heavier tails (than the Gaussian distribution). The Laplace distribution often leads to median regression, which is more robust to outliers than mean regression.” Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 19
- 20. Outlier Sensitivity: Performance Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 20 With outliers, Gaussian With outliers, Laplace No outliers, Gaussian No outliers, Laplace When outliers exist, Laplace distribution performs much better than Gaussian distribution. • This doesn’t mean Laplace is always better than Gaussian. • Choosing correct distribution requires domain knowledge. Parameter value Probability (Synthetic data)
- 21. Outlier Sensitivity: Performance Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 21
- 22. Weighting Datasets Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 22 Weighted, Gaussian Not weighted, Laplace Weighted, Gaussian Not weighted, Laplace When we add proper weights to datasets, we get good results regardless of the distribution. • The proper weights on each dataset requires domain knowledge. (Synthetic data)
- 23. Weighting Datasets Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 23
- 24. Outline Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 24 Overview MaGICMaT Uncertainty Management Cloud-Based Platform
- 25. Architecture of Cloud-Based Platform Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 25 (demo available upon request) • Middleware between frontend and calculations • Central storage of relevant data Middleware • QuesTek’s Proprietary Packages • CALPHAD results from Thermo-Calc & TC-Python • Uncertainty data Calculations • Web apps to run basic CALPHAD calculations • Extra features for CALPHAD UQ Frontend Regular Users Experts APIs APIs
- 26. Acknowledgements MaGICMaT QuesTek (Intern) • Ramya Gurunathan Northwestern University • Prof. Jeff Snyder Argonne National Lab • Logan Ward, Ph.D. U Chicago & Argonne Nat. Lab • Ben Blaiszik, Ph.D. Funded by Department of Energy • SBIR Phase I (DE-SC0019679) CALPHAD in the Cloud QuesTek (Intern) • Ramon Frey Rice University • Prof. Meng Li Thermo-Calc Software • Johan Jeppsson, Ph.D. • Adam Hope, Ph.D. Funded by Department of Energy • SBIR Phase II (DE-SC0017234) Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 26
- 27. Summary & Future Work Summary MaGICMaT • Materials Genome and ICME Toolkit • Data & PSP linkage management Uncertainty Management • A framework for CALPHAD UQ • Outlier tolerance • Weight on data sets • A toolkit for application of CALPHAD UQ • User friendly frontend Cloud-Based Platform • Web apps with an HPC backend Future Work Contribute to CHiMaD Phase II • Thermoelectrics • Uncertainty Quantification of Phase Equilibria and Thermodynamics (UQPET) More opportunities of MGI & AI for enhanced ICME • Current cloud platform can be an enabler for many more technologies embedded for ICME Aug 1, 2019 Artificial Intelligence for Materials Science (AIMS) Workshop 2019 27 ICME MGI AI More Opportunities More Opportunities Contact: Changning Niu cniu@questek.com