Multiscale Materials Design Using Informatics. S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan AFOSR-FA

Transcription

1 Multiscale Materials Design Using Informatics S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan AFOSR-FA

2 Hierarchical Material Structure Kalidindi and DeGraef, ARMS, 2015

3 Main Challenges in Multiscale Materials Design Statistical Quantification of Hierarchical Structure (including chemistry) Templated Workflows for Mining Core Knowledge (PSP Linkages) New Multiscale Design Approaches Cross-Disciplinary e-collaboration 3

4 Structure Quantification: Conventional Approaches Conventional microstructure descriptors are devised based on observation, intuition or expertise: Phase Volume Fraction or Porosity Average Grain/Pore/Particle/Fiber Size Connectivity/Percolation/Tortuosity Average Grain/Particle Coordination Number Main Challenges: The important features or their relative importance change from expert to expert. Takes years of experience and knowhow to obtain a PSP linkage. 4

5 Comprehensive & Systematic Structure Quantification n-point Correlation Functions as a Microstructure Descriptors Utilizes a statistical framework that inherently captures variance and uncertainty Provides a natural origin in registering structure Generates a vast pool of microstructure features Accounts/quantifies anisotropy in the structure Appears naturally in the best known composite theories C = C C ΓC + C ΓC ΓC C ΓC = C ΓC = f 2 h, h r C h Γ r C h dhdh dr H H Ψ(r Probability of finding h and h at the head and tail of a vector r 2-point Statistics n th term needs n-point statistics of structure Broadly applicable to many properties 5

6 2-Point Statistics: Definition and Visualization Not Allowed %50 0 Solid f r hh = # Trials Successful # Trials Attempted 1 Pore Complete Set of f r hh for all possible r. %0 Produces a very large number of microstructure descriptors! 6

7 Main Benefit of 2-Point Statistics Provides a natural origin for registering structure %50 %10 7

8 Feature Extraction Using PCA Objective and hierarchical identification of most characteristic features. Features are independent and uninformed of process and property. Original Axes Principal Axes Reduced Axis y p1 p1 p1 p2 x p2 Obtain the first handful dimensions (out of possibly thousands or millions) that show the highest variation within the dataset

9 Tracking Microstructure Evolution Initial Microstructure 2-Point Statistics Principal Component Analysis (PCA) Final Microstructure 9

10 Project Product: Extensible Framework for Spatial Correlations Diverse boundary assumptions Irregular regions Diverse length/structure scales (atomistic to mesoscales Diverse local state descriptors Examples will be presented in follow-up talks 10

11 New Computational Algorithms for Large Datasets Efficient Resource Utilization in Computing Spatial Correlations Memory (GBs) Time (minutes) Full Sweep Minimal for Laptop for Desktop 11

12 Process-Structure-Property (PSP) Linkages Conventional Approaches 1. Experimentation Time-consuming and expensive Hard to generalize the result 2. Physics-based simulations (e.g., FE) High computational cost Scale-bridging is a major challenge Large uncertainty in model forms and parameters 3. First principle methods Numerous gaps in known physics, especially for mechanical properties High computational cost Need a framework to capture uncertain (or incomplete) knowledge into computationally efficient and easily accessible databases Express the core knowledge in invertible metamodels (i.e., surrogate models) Harmoniously blend known physics with data science tools in formulating and expressing high value, low computational cost, PSP linkages

13 Templated Workflows for Mining PSP Linkages Allow automation, efficient large scale exploration Allow sharing and facilitate productive e-collaborations Meta-Model Learning Multivariate Polynomial Regression Decision Table Instance Based KNN KStar (Entropy KNN) Support Vector Machines Linear Regression (Line) Robust Regression (Line) Pace Regression (Clustering) Artificial Neural Networks M5 Model Tree Leave One Out Cross Validation Choose a model the has low average error, while minimizing the effect of individual data points on the final model.

14 Multiscale Design and Optimization Conventional Approaches 1. Mathematical methods Linear, nonlinear and dynamic programming These methods represent a limited approach, and no single method is completely efficient and robust for all types of optimization problems. 2. Exhaustive searches (e.g., gradient search) Subject to local optima Sensitive to initial values; solutions usually end up in the neighborhood of the starting point. Complexity of calculating derivatives Large amount of enumeration memory required Mostly intractable in high dimensional searches Material selection is currently approached with repetitive and inefficient trials that rely largely on serendipity 14

15 Nonlinear and Multi-Objective Optimization Motivation is to explore microstructure property relationship in the design of magnetoelastic Fe-Ga alloy. Objective is to obtain accurate, complete ODF microstructures with desired optimized property in an effective manner. Techniques developed include data mining enhanced combinatory search within a large space. Microstructure Statistical descriptor (ODF) Properties Sampling reconstruction Homogenization Optimization Elastic Modulus Yield Strength Magnetostrictive Strain The orientation distribution function (ODF) is applied for the quantification of crystallographic texture. Theoretically computing properties given microstructure are known but inversion of relationships is challenging. 15

16 Screening for New Materials in Composition Space Construc on of FE predic on database Predic ve Modeling Consists of compounds with known forma on energy (FE) Empiric periodic table informa on added (e.g. electro nega vity, mass, atomic radii, # valence s, p, d, f electrons) Model Evalua on Construct data mining models to predict forma on energy using chemical formula and derivable empirical informa on Test model on unseen data 10-fold cross valida on (data divided into 10 segments, model built on 9 segments and tested on remaining 1 segment; process repeated 10 mes with different test segment) (a) Run combinatorial list of compounds through the FE model Combinatorial list of ternary compounds Valida on Screening Large scale FE predic on FE model Thermodynamic stability and heuris cs List of predic ons Shortlisted highpoten al candidates Structure predic on Quantum mechanical modeling Fingerprint of entire unexplored ternary composition space! Stable discovered structures (b) Interesting insights: Highest ranked ternary: SiYb3F5 Si acts as an anion Validated with structure and DFT calculations pnictides, chalcogenides, halides Pt-X-Y Pm12S19Se a missing binary Pm2S3? B. Meredig*, A. Agrawal*, S. Kirklin, J. E. Saal, J. W. Doak, A. Thompson, K. Zhang, A. Choudhary, and C. Wolverton, Combinatorial screening for new materials in unconstrained composition space with machine learning, Phys. Rev. B, 89, , March 2014.

17 Process-Fatigue Linkages R 2 > 0.98 A. Agrawal, P. D. Deshpande, A. Cecen, G. P. Basavarsu, A. N. Choudhary, and S. R. Kalidindi, Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters, Integrating Materials and Manufacturing Innovation, 3 (8): 1 19,

18 Project Outcomes Microstructure Statistical descriptor (ODF) Properties Sampling Elastic Modulus Homogenization Yield Strength reconstruction Optimization Magnetostrictive Strain New Machine learning approach for multiscale materials design Meta-heuristics developed to expedite the search in large dimensional spaces Allows for incorporation of legacy domain knowledge Able to find better solution than traditional searches Able to find multiple design candidates that fit the stipulated criterion; these choices can then be downselected based on real-world constraints 18

19 Cross-Disciplinary Collaboration Engage and exploit cross-disciplinary expertise to create high value information for multiscale materials design Simulations Domain Expertise Experiments Data Science Reliable PSP Linkages Multiscale Materials Design Uncertainty Quantification Cross-disciplinary Integration demands e-collaboration 19

20 Cross-Disciplinary Collaboration Nucleation of a core community Development and curation of tools that facilitate intermediate publishing and sharing of information Materials Informatics Course: 9 teams used this for diverse research projects Current Users 20