Efficient determination of soft spots in amorphous solids only using local structural information
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1 Efficient determination of soft spots in amorphous solids only using local structural information Ekin Dogus Cubuk Samuel Schoenholz, Jennifer Rieser, Brad Malone, Joerg Rottler, Doug Durian, Andrea J Liu, Efthimios Kaxiras
2 Introduction Soft spots are structurally different. These differences could not be used to identify soft spots*. *L. Manning & A. Liu, PRL 107, (2011)
3 Introduction Soft spots are structurally different. These differences could not be used to identify soft spots*. We propose a method that can efficiently predict regions vulnerable to rearrangement purely from local geometric quantities. *L. Manning & A. Liu, PRL 107, (2011)
4 Introduction Soft spots are structurally different. These differences could not be used to identify soft spots*. We propose a method that can efficiently predict regions vulnerable to rearrangement purely from local geometric quantities. We look at where rearrangements occur, and ask what was structurally different before the rearrangement. *L. Manning & A. Liu, PRL 107, (2011)
5 We propose to identify soft spots by supervised learning:
6 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
7 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
8 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
9 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
10 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
11 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
12 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
13 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment
14 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment observe the system and record plastic behavior
15 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment observe the system and record plastic behavior (use D 2 min )
16 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment observe the system and record plastic behavior learn (from examples) the structural quantities that make up a soft spot Descriptors (t 0 ) D 2 Min (t 0,ΔT) Rearranged? Particle 1 3.2,4.5, Yes Particle 2 1.3,5.6, No Particle 3 1.2,4.2, No
17 We propose to identify soft spots by supervised learning: calculate many descriptors for every particle s local environment observe the system and record plastic behavior learn (from examples) the structural quantities that make up a soft spot Potential advantages of this method: Extremely fast, O(N) scaling Does not need vibrational modes The system does not need to be quenched Does not require the Hamiltonian
18 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
19 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
20 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
21 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
22 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
23 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
24 The local descriptors Calculate descriptors for each particle i They are sums over neighbors j and k of i Constants μ, λ, ζ and ξ are varied G 1 (i; µ) = 1 p 2 2 X j e (R ij µ) 2 /2 2 G 2 (i;,, ) = X j,k e (R2 ij +R2 ik +R2 jk ) (1 + cos ijk )
25 Support Vector Machines A simple supervised learning model.
26 Support Vector Machines A simple supervised learning model. Find the hyper-plane that separates the two different classes for future predictions
27 Support Vector Machines A simple supervised learning model. Find the hyper-plane that separates the two different classes for future predictions?
28 Support Vector Machines A simple supervised learning model. Find the hyper-plane that separates the two different classes for future predictions
29 Sheared glass Simulation of a 2D glass being sheared (LJ temperatures 0.1 to 0.4). MD simulations done by Joerg Rottler.
30 Sheared glass Simulation of a 2D glass being sheared (LJ temperatures 0.1 to 0.4). MD simulations done by Joerg Rottler. Blue à machine learning soft spots Red à phonon method soft spots Our soft spots are very robust until rearrangement.
31 Results (sheared system) For the simulation of a sheared glass, (for T = 0.1, 0.2, 0.3 and 0.4) we correctly predict 78% of the rearrangements with a 24% soft spot coverage 20K training samples 20M test samples Tg = 0.33
32 Results (sheared system) For the simulation of a sheared glass, (for T = 0.1, 0.2, 0.3 and 0.4) we correctly predict 78% of the rearrangements with a 24% soft spot coverage P(So9 PHIn Soft Spot) SpotL K training samples 20M test samples Tg = D min ês 2 AA T
33 Results (sheared system) For the simulation of a sheared glass, (for T = 0.1, 0.2, 0.3 and 0.4) we correctly predict 78% of the rearrangements with a 24% soft spot coverage P(So9 Spot) PHIn Soft SpotL K training samples 20M test samples Tg = D min ês 2 AA T So& spots predict rearrangements just as well for T>Tg as for T<Tg!!!!
34 Results (sheared system) Results are transferable: train on T = 0.4, test on T = 0.1, 0.2, 0.3 and PHIn Soft SpotL P(So9 Spot) D min ês 2 AA T
35 Results (granular pillar) Cannot be analyzed with the phonon method! Jennifer Rieser Doug Durian
36 Results (granular pillar) Train on 10 pillars. For 10 test pillars, we correctly predict 80% of the rearrangements with a 22% soft spot coverage Jennifer Rieser Doug Durian
37 Results (granular pillar) Train on 10 pillars. For 10 test pillars, we correctly predict 80% of the rearrangements with a 22% soft spot coverage 1.0 PHIn Soft SpotL P(So9 Spot) D min ês AA Jennifer Rieser Doug Durian
38 Summary Very efficient method for identifying soft spots. Only requires observation of representative plastic behavior (training set). Can be applied to a large variety of systems (experimental/computational, quenched/thermal, 2D/3D). Ongoing work What in the structure determines if a spot is soft? Use the hyperplane to explore new physics. cubuk@fas.harvard.edu
39 Summary Very efficient method for identifying soft spots. Only requires observation of representative plastic behavior (training set). Can be applied to a large variety of systems (experimental/computational, quenched/thermal, 2D/3D). Ongoing work What in the structure determines if a spot is soft? Use the hyperplane to explore new physics. cubuk@fas.harvard.edu
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