Download presentation

Presentation is loading. Please wait.

Published byDoreen Ward Modified over 2 years ago

1
Constraint Reasoning and Kernel Clustering for Pattern Decomposition With Scaling Ronan LeBrasComputer Science Theodoros DamoulasComputer Science Ashish SabharwalComputer Science Carla P. GomesComputer Science John M. GregoireMaterials Science / Physics Bruce van DoverMaterials Science / Physics Sept 15, 2011CP’11

2
Motivation Ronan Le Bras - CP’11, Sept 15, 20112 Cornell Fuel Cell Institute Mission: develop new materials for fuel cells. An Electrocatalyst must: 1) Be electronically conducting 2) Facilitate both reactions Platinum is the best known metal to fulfill that role, but: 1) The reaction rate is still considered slow (causing energy loss) 2) Platinum is fairly costly, intolerant to fuel contaminants, and has a short lifetime. Goal: Find an intermetallic compound that is a better catalyst than Pt.

3
Motivation 3 Recipe for finding alternatives to Platinum 1)In a vacuum chamber, place a silicon wafer. 2)Add three metals. 3)Mix until smooth, using three sputter guns. 4)Bake for 2 hours at 650ºC Ta Rh Pd (38% Ta, 45% Rh, 17% Pd) Deliberately inhomogeneous composition on Si wafer Atoms are intimately mixed [Source: Pyrotope, Sebastien Merkel] Ronan Le Bras - CP’11, Sept 15, 2011

4
Motivation 4 Identifying crystal structure using X-Ray Diffraction at CHESS XRD pattern characterizes the underlying crystal fairly well Expensive experimentations: Bruce van Dover’s research team has access to the facility one week every year. Ta Rh Pd (38% Ta, 45% Rh, 17% Pd) [Source: Pyrotope, Sebastien Merkel] Ronan Le Bras - CP’11, Sept 15, 2011

5
Motivation 5 Ta Rh Pd α β δ γ Ronan Le Bras - CP’11, Sept 15, 2011

6
Motivation 6 Ta Rh Pd α β α+βα+β δ γ γ+δγ+δ Ronan Le Bras - CP’11, Sept 15, 2011

7
Motivation 7 Ta Rh Pd α β δ γ Ronan Le Bras - CP’11, Sept 15, 2011

8
Motivation 8 Ta Rh Pd α β δ γ α+βα+β Ronan Le Bras - CP’11, Sept 15, 2011 PiPi PjPj

9
Motivation 9 Ta Rh Pd α β α+βα+β δ γ Ronan Le Bras - CP’11, Sept 15, 2011 PiPi PkPk PjPj

10
Motivation Fe Al Si INPUT: pure phase region Fe Al Si m phase regions k pure regions m-k mixed regions XRD pattern characterizing pure phases Mixed phase region OUTPUT: Additional Physical characteristics: Peaks shift by 15% within a region Phase Connectivity Mixtures of 3 phases Small peaks might be discriminative Peak locations matter, more than peak intensities 10Ronan Le Bras - CP’11, Sept 15, 2011

11
Motivation 11 Ta Rh Pd Figure 1: Phase regions of Ta-Rh-PdFigure 2: Fluorescence activity of Ta-Rh-Pd Ronan Le Bras - CP’11, Sept 15, 2011

12
Outline 12 Motivation Problem Definition Abstraction Hardness CP Model Kernel-based Clustering Bridging CP and Machine learning Conclusion and Future work Ronan Le Bras - CP’11, Sept 15, 2011

13
Problem Abstraction: Pattern Decomposition with Scaling 13 Input Output Ronan Le Bras - CP’11, Sept 15, 2011

14
Problem Abstraction: Pattern Decomposition with Scaling 14 Input Output v1v1 v2v2 v3v3 v4v4 v5v5 Ronan Le Bras - CP’11, Sept 15, 2011

15
Problem Abstraction: Pattern Decomposition with Scaling 15 Input Output v1v1 v2v2 v3v3 v4v4 v5v5 P1P1 P2P2 P3P3 P4P4 P5P5 Ronan Le Bras - CP’11, Sept 15, 2011

16
Problem Abstraction: Pattern Decomposition with Scaling 16 Input Output v1v1 v2v2 v3v3 v4v4 v5v5 P1P1 P2P2 P3P3 P4P4 P5P5 M= K = 2, δ = 1.5 Ronan Le Bras - CP’11, Sept 15, 2011

17
Problem Abstraction: Pattern Decomposition with Scaling 17 Input Output v1v1 v2v2 v3v3 v4v4 v5v5 P1P1 P2P2 P3P3 P4P4 P5P5 M= K = 2, δ = 1.5 B2B2 B1B1 Ronan Le Bras - CP’11, Sept 15, 2011

18
Problem Abstraction: Pattern Decomposition with Scaling 18 Input Output v1v1 v2v2 v3v3 v4v4 v5v5 P1P1 P2P2 P3P3 P4P4 P5P5 M= K = 2, δ = 1.5 B2B2 B1B1 s 11 =1.00 s 12 =0.95 s 13 =0.88 s 14 =0.84 s 15 =0 s 21 =0.68 s 22 =0.78 s 23 =0.85 s 24 =0.96 s 25 =1.00 Ronan Le Bras - CP’11, Sept 15, 2011

19
Problem Hardness 19 Assumptions: Each B k appears by itself in some v i / No experimental noise The problem can be solved* in polynomial time. Assumption: No experimental noise The problem becomes NP-hard (reduction from the “Set Basis” problem) Assumption used in this work: Experimental noise in the form of missing elements in P i v1v1 v2v2 v3v3 v4v4 v5v5 P1P1 P2P2 P3P3 P4P4 P5P5 M= K = 2, δ = 1.5 B2B2 B1B1 s 11 =1.00 s 12 =0.95 s 13 =0.88 s 14 =0.84 s 15 =0 s 21 =0.68 s 22 =0.78 s 23 =0.85 s 24 =0.96 s 25 =1.00 Ronan Le Bras - CP’11, Sept 15, 2011 P0=P0=

20
Outline 20 Motivation Problem Definition CP Model Model Experimental Results Kernel-based Clustering Bridging CP and Machine learning Conclusion and Future work Ronan Le Bras - CP’11, Sept 15, 2011

21
CP Model 21 Advantage: Captures physical properties and relies on peak location rather than height. Drawback: Does not scale to realistic instances; poor propagation if experimental noise. Ronan Le Bras - CP’11, Sept 15, 2011

22
CP Model (continued) 22 Advantage: Captures physical properties and relies on peak location rather than height. Drawback: Does not scale to realistic instances; poor propagation if experimental noise. Advantage: Captures physical properties and relies on peak location rather than height. Drawback: Does not scale to realistic instances; poor propagation if experimental noise. Ronan Le Bras - CP’11, Sept 15, 2011

23
CP Model – Experimental Results 23 Advantage: Captures physical properties and relies on peak location rather than height. Drawback: Does not scale to realistic instances; poor propagation if experimental noise. For realistic instances, K’ = 6 and N ≈ 218... Ronan Le Bras - CP’11, Sept 15, 2011

24
Outline 24 Motivation Problem Definition CP Model Kernel-based Clustering Bridging CP and Machine learning Conclusion and Future work Ronan Le Bras - CP’11, Sept 15, 2011

25
Kernel-based Clustering Advantage: Captures physical properties and relies on peak location rather than height. Drawback: Does not scale to realistic instances; poor propagation if experimental noise. 25 Set of features: X = Similarity matrices: [X.X T ] Method: K-means on Dynamic Time-Warping kernel Goal: Select groups of samples that belong to the same phase region to feed the CP model, in order to extract the underlying phases of these sub-problems. Better approach: take shifts into account Red: similar Blue: dissimilar ++ ++ ++ Ronan Le Bras - CP’11, Sept 15, 2011

26
Bridging CP and ML 26 Goal: a robust, physically meaningful, scalable, automated solution method that combines: Similarity “Kernels” & Clustering Machine Learning for a “global data-driven view” Underlying Physics A language for Constraints enforcing “local details” Constraint Programming model Ronan Le Bras - CP’11, Sept 15, 2011

27
Bridging Constraint Reasoning and Machine Learning: Overview of the Methodology 27 Fe Al Si INPUT: Peak detection Machine Learning: Kernel methods, Dynamic Time Wrapping Machine Learning: Partial “Clustering” Fe Al Si CP Model & Solver on sub-problems , + , only only Full CP Model guided by partial solutions OUTPUT Fix errors in data Ronan Le Bras - CP’11, Sept 15, 2011

28
Experimental Validation 28 Al-Li-Fe instance with 6 phases: Ground truth (known) Our CP + ML hybrid approach is much more robust Previous work (NMF) violates many physical requirements

29
Conclusion 29 Hybrid approach to clustering under constraints More robust than data-driven “global” ML approaches More scalable than a pure CP model “locally” enforcing constraints An exciting application in close collaboration with physicists Best inference out of expensive experiments Towards the design of better fuel cell technology Ronan Le Bras - CP’11, Sept 15, 2011

30
Future work Ongoing work: Spatial Clustering, to further enhance cluster quality Bayesian Approach, to better exploit prior knowledge about local smoothness and available inorganic libraries Active learning: Where to sample next, assuming we can interfere with the sampling process? When to stop sampling if sufficient information has been obtained? Correlating catalytic properties across many thin-films: In order to understand the underlying physical mechanism of catalysis and to find promising intermettalic compounds 30Ronan Le Bras - CP’11, Sept 15, 2011

31
The end Thank you! 31Ronan Le Bras - CP’11, Sept 15, 2011

32
Extra slides 32Ronan Le Bras - CP’11, Sept 15, 2011

33
Experimental Sample 33 Example on Al-Li-Fe diagram: Ronan Le Bras - CP’11, Sept 15, 2011

34
Applications with similar structure 34 Flight Calls / Bird conservation Identifying bird population from sound recordings at night. Analogy: basis pattern = species samples = recordings physical constraints = spatial constraints, species and season specificities… Fire Detection Detecting/Locating fires. Analogy: basis pattern = warmth sources samples = temperature recordings physical constraints = gradient of temperatures, material properties… Ronan Le Bras - CP’11, Sept 15, 2011

35
Previous Work 1: Cluster Analysis (Long et al., 2007) 35 x i = (Feature vector)(Pearson correlation coefficients)(Distance matrix) (PCA – 3 dimensional approx)(Hierarchical Agglomerative Clustering) Drawback: Requires sampling of pure phases, detects phase regions (not phases), overlooks peak shifts, may violate physical constraints (phase continuity, etc.). Ronan Le Bras - CP’11, Sept 15, 2011

36
Previous Work 2: NMF (Long et al., 2009) 36 x i = (Feature vector)(Linear positive combination (A) of basis patterns (S)) (Minimizing squared Frobenius norm X = A.S + EMin ║E║ Drawback: Overlooks peak shifts (linear combination only), may violate physical constraints (phase continuity, etc.). Ronan Le Bras - CP’11, Sept 15, 2011

Similar presentations

OK

Kernelized Value Function Approximation for Reinforcement Learning Gavin Taylor and Ronald Parr Duke University.

Kernelized Value Function Approximation for Reinforcement Learning Gavin Taylor and Ronald Parr Duke University.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google