Mimicking Natural Ways of Computing N. Shukla 1 , A. Parihar 2 , A. - - PowerPoint PPT Presentation

Mimicking Natural Ways of Computing

• N. Shukla1, A. Parihar2,
• A. Raychowdhury2, and Suman Datta1

1University of Notre Dame, Notre Dame, IN, USA 2Georgia Tech, Atlanta, GA, USA

1

Dagstuhl Seminar, Feb 2017

Natural Ways of Computing

Natural Ways of Computing

Prediction

EXCEL (sponsored by NSF/NRI)

Notre Dame, Georgia Tech, Penn St, U Chicago, UC San Diego

Computational Paradigms

Many body analog computing with both feedback and feedforward dynamics Potential super-Turing capabilities (debatable) Compatible with CMOS Room temperature

• peration

Coupled Dynamical Systems

Vertex Coloring of Graphs

time evolution of the dynamical system created by the coupled oscillator circuit correspond to an approximate vertex color sorting algorithm

Parihar, Shukla et a “Vertex coloring of graphs via phase dynamics of coupled oscillatory networks“ (submitted to Nature Scientific Reports)

Coupled Oscillatory Systems

Synchronization of Metronomes Spin Torque Nano Oscillators CMOS PLLs

Zhang, Mian, et al. "Synchronization of micromechanical oscillators using light." Physical review letters 109.23 (2012): 233906.

Opto-mechanical Oscillators

8

https://www.youtube.com/watch?v=JWToUATLGzs; (Ikelguchi Lab)

Kaka, Shehzaad, Matthew R. Pufall, William H. Rippard, Thomas J. Silva, Stephen E. Russek, and Jordan A. Katine. "Mutual phase-locking of microwave spin torque nano-oscillators." Nature 437, no. 7057 (2005): 389-392. Shibata, Tadashi, et al. "CMOS supporting circuitries for nano-oscillator-based associative memories.“ CNNA, 2012 13th International Workshop on. IEEE, 2012.

Fixed layer Free layer

9

Thermally driven Insulator-metal phase transition in VO2

Abrupt change in VO2 resistivity through electron correlation dynamics in ultra-thin VO2 films.

240 270 300 330 10

• 4

10

• 3

10

• 2

10

• 1

10

Temperature (K)

Resistivity (Ω.cm)

insulator metal

• M. Huefner, R. Ghosh, E. Freeman, N. Shulka, H. Paik, D. G. Schlom, and S. Datta "Hubbard Gap Modulation in Vanadium Dioxide Nanoscale Tunnel Junctions", Nano

Letters, October 2014.

monoclinic

Insulating VO2 Metallic VO2

rutile

Abrupt, hysteretic phase transition can be electrically triggered

Electrically induced “abrupt”, “reversible” and “hysteretic” phase transition 20 40 0.0 0.5 1.0 1.5 2.0

Current (mA)

Electric Field (kV/cm)

insulator

metal

10

VDC

VO2 based Relaxation Oscillators

Negative feedback by series resistor (RS) enable oscillations

V1 VDC RS

V1 t

VDC t

V1

IM

VO2 C

VDC

V1

MI

VO2 C

VDC

RS RS

V1 V1 t t

11

50 100 150 6 8 10 12

V1 (V)

Time (µs)

experiment

VGS D S V1 VDC

Si substrate

0.0 0.2 0.4 0.6 0.8 20 40 60 80 100

Frequency (kHz) VGS (V)

Hybrid VO2-MOSFET (HVFET) oscillator

50 100 150 5 10 15

Time (µs)

V1 (V)

Voltage controlled VO2 oscillator realized by replacing RS with a MOSFET (HVFET Oscillator)

VDC t

V1 t

12

VGS,1 VGS,2

Si substrate

VDC VDC

V2 (output) V1 (output)

S D D S

CC

Pairwise Coupled HVFET Oscillators

Capacitively coupled oscillators show frequency synchronization

10 20 30

• 50
• 40
• 30
• 20
• 10

Frequency (kHz) Power (dB)

Resonant frequency

V1 V2

CC= 2.2nF

VDC

t

V2

t

V1

t

13

Equivalent Circuit for coupled HVFET Oscillators

Equivalent circuit to analyze synchronization dynamics of pairwise coupled HVFET oscillators

14

MOSFET

VMOS RVO

g0

gmVgs

C1

+

g0

gmVgs

C2

+

MOSFET

VMOS

VGS,1 VGS,2

CC

2 1

• RVO2

2

Locked Locked Unlocked Unlocked

Phase Space Diagram (locking / unlocking)

VO2

VDC

Vgs1

VO2

VDC

Vgs2

CC Gate Input voltage difference decides synchronization

ΔVGS=VGS,2-VGS,1

ΔVGS=-0.2 V ΔVGS=-0.02 V ΔVGS=0.2 V ΔVGS=0.02 V

15

Experiments vs Simulation

16

Degree of Locking (Locked Case)

Part of steady state periodic orbit in the XOR=0 region

• f the phase space depends on ΔVGS = VGS,2 - VGS,1

0.6 0.7 0.8 0.6 0.7 0.8

P

0.6 0.7 0.8 0.6 0.7 0.8 0.6 0.7 0.8 0.6 0.7 0.8

V1 (V) V2 (V)

VGS,1 = 0.3V VGS,2 = 0.3V VGS,1 = 0.3V VGS,2 = 0.32V VGS,1 = 0.3V VGS,2 = 0.35V

XOR=0

17

Phase Difference measurement

Coupled Oscillator Output Output Threshold

XOR

Time Average

V1 V2

18

System implementation to measure steady state periodic orbit of the HVFET oscillators

Graph Coloring Experiments

Net phase of any oscillator is the aggregate of the ‘repelling effect’ of all the adjacent oscillators

19

Connectivity of Graphs

Tradeoff between settling time and # of colors detected (as a function of average connectivity)

20

Heuristics vs Dynamical System

Dynamical systems can outperform heuristic algorithms in some cases

21 DIMACS implementation challenge

22

Connection between Phase Dynamics of coupled oscillator system and spectral techniques of solving graph coloring problems provides a new way to think about next generation computing systems Perhaps we can finally realize the true potential of beyond-CMOS devices by matching the “physics” of emerging nanodevices to the “mathematics” of the computing”