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EDA among Sci & Eng fields EDA among Sci & Eng fields CS CS EDA EDA EE EE From Computability  to Simulation Optimization to Simulation, Optimization,  and back Biology Physics Igor Markov University of Michigan What can be Computed ? What can be Computed ? “Computation is Physical” Computation is Physical • Casting practical problems in formal terms • Non-traditional physics & technolgies may offer additional computational powers (or not) p p ( ) – AI, EDA: simulation, layout, verification … , , y , – S. Aaronson, J. Watrous: “Closed Timelike Curves Make • Computability in principle (e.g., decidability ) Quantum & Classical Computing Equivalent,” 2008 • Efficient computation at large scale ff • Key questions from last slide apply, suggest – NP, PSPACE… , comparisons: classical vs non-classical comp comparisons: classical vs non-classical comp • Optimization algorithms & heuristics – Full spectrum from theoretical to practical – Approximation schemes, ILP… A i ti h ILP • Can non-traditional computing be faster ? • Practical software ( empirical algorithmics, SWE ) – Most answers will be negative – that’s OK Most answers will be negative that s OK • Cross-pollination between EDA & other CS – How does one arrive at a negative answer ?

Simulation as a Tool of Scientific Discovery • Basic idea • Basic idea – Develop a simulator of a new physical effect or technology on conventional computers – The more efficient the simulation, the less helpful the new effect / technology (otherwise, simulation can be useful in the lab) • Many types of simulation possible – Monte-Carlo simulation of Probabilistic CMOS – Monte-Carlo simulation of Probabilistic CMOS – Numerical solution of Schrodinger’s equation – Symbolic simulation of quantum states – Logic simulation of memristors EDA + Physics = Synergies EDA + Physics = Synergies CS CS EDA EDA EE EE  Physics

Principle of Energy Min’zation Principle of Energy Min zation Principle of Energy Min’zation Principle of Energy Min zation • Physical systems naturally find least-energy states y y y gy • Idea: exploit natural energy-minimization • S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi to solve hard combinatorial problems p “ Optimization by Simulated Annealing ” p y g Science , May 1983 – Encode problem instance into sys. configuration – Applied to VLSI placement with great success Applied to VLSI placement with great success – Launch the system, let it settle into ground state Launch the system let it settle into ground state (interconnect length ~ total energy) – Read out the answers • Modern placement algorithms • Modern placement algorithms • Energy minimization + quantum tunneling also use other physics metaphors – e.g., adiabatic quantum computing (AQC) e.g., adiabatic quantum computing (AQC) – Force-directed modeling; electrostatic repulsion • Sample app: number-factoring • In many cases, simulation is optimization In many cases, simulation is optimization minimize f(x,y)=(N-xy) 2 ) 2 i i i f( ) (N • Vice versa : adapt EDA algos to physics & CS (zero out leading bits of x and y) Ising Model Ising Model Ising Model Ising Model ising  G ( V , E ) bonds spins • Captures atomic interactions • Captures atomic interactions  V set of spins (vertices) : S ,..., S in physical systems 0 n   E E set set of of bonds bonds (edges) (edges) : : ( ( i i , j j ) ) using binary variables i bi i bl    1, spin is • Represents total energy in p gy     S S  i 2 -dim graph  - 1, spin is terms of spin configurations     J J bond bond weight weight : : i.i.d i i d (Gaussian (Gaussian or or 1 1 bimodal) bimodal) • Fundamental analysis tool Fundamental analysis tool i , j  h magnetizat ion : i.i.d (Gaussian) – Magnetism i   spin configurat ion – Phase transitions PrAu 2 Si 2     (  (        Energy Energy ) ) J J S S S S h h S S [ScienceNewsDaily.com, 4/09] [ y , ] i , j i j i i  11 12 ( i , j ) E i

From Computability to Simulation, Finding Ground States Finding Ground States Optimization, and back • Idea: observe computational similarities • Idea: observe computational similarities • EDA research offers many answers EDA h ff with hypergraph partitioning algorithms as to what is computable – Binary variables Bi i bl • EDA adapted key concepts from Physics – Edge-based total cost function – simulation ~ optimization simulation ~ optimization – Sparse connectivity • EDA provided several key computational techniques to Physics, can do more • Develop move-based algorithms for • When exploring new comp technologies When exploring new comp. technologies, finding ground states in Ising spin-glasses fi di d t t i I i i l expect many negative answers – Empirical results: outperform state of the art p p • Use (new types of) simulation for scientific U ( t f) i l ti f i tifi in physics literature discovery, and also in engineering tools