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15.simulated anneling

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simulated anneling

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15.simulated anneling

  1. 1. Machine Learning Simulated Annealing
  2. 2. Intro ● Annealing – cooling temperature in metallargy ● An optimization algo inspired by Stastical Mechanics ● Combination of – 1) MCMC Algo 2) Metropilos Algo
  3. 3. MCMC Algo ● Marcov Chain Monte Carlo ● Involves a Stochastic element (random) ● This helps computer to take random decisions ● Depends on state and transition between 2 states in MM
  4. 4. Metropolis Algo ● Randomly generates perturbations of current state (approx soln) ● Accepts or rejects them based on how the probability of state is effected ● Like a schedule of lovering temperature
  5. 5. Example – Minimizing a function ● F = (x1.....xn) and f>=0 ● If f – represemtsenergy of a stastical mechanical system ● We have states S=(x1....xn) ● Hence the probability of state S at temperature T is given by ● p(S) = Boltzmann-gibbs distribution
  6. 6. ● If there are m states ● Limits P(S) = 1/m (is Sis at ground state) t->0 = 0 (if otherwise) ● Hence we could stimulate the system at temperature near 0, we get ground state
  7. 7. ● But MCMC and Metropolis fail to generate Minima ● Because, movement in state space is inhibited by regions of low probability and by high energy barriers ● Simulated Anneling overcomes this problem
  8. 8. ● Starts at high temp and progresses to lower temp ● Annealing Schedule is given By - ● ● ● Hence as algo proceeds – inc in energy is less likely ● And hence minima of energy could be acheived
  9. 9. Applications ● Molecular Dynamics ● PL docing ● Homology Modelling
  10. 10. Applications ● Molecular Dynamics ● PL docing ● Homology Modelling

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