Weather Forecasting Problem (One Trillion Operations per Second?) Predict the weather over United States and Canada for the next two days: Model the atmosphere from sea level to an altitude of 20 kilometers., and predict the weather at each hour for the next two days. Standard Approach: Cover the region of interest with a grid and then predict the weather at each vertex of the grid Cubical grid with each cube measuring 0.1 kilometer on each side Area of United States and Canada = 20 million square kilometers

Weather Forecasting Problem (One Trillion Operations per Second?) Number of grid points = 2.0 * 10 ^7 * 20 * 10 ^3 = 4 * 10 ^11 No of calculations per grid point = 100 Predicting weather for each hour for 48 hours Total number of calculations = 4 * 10 ^13 * 48 = 2 * 10^15 calculations

Weather Forecasting Problem (One Trillion Operations per Second?) Number of instructions per second for an existing computer = 1 billion (10^9) Time needed = 2 * 10 ^15 /10^9 = 2 * 10^6 seconds = 23 days Problem with Von Neumann Computer Let us assume that we have a computer that can execute the following code in one second: For (I = 0; I < ONE_TRILLION; I++) z[I] = x [I] + y[I] Fetch x[I] and y[I] from memory Store the result z[I] into memory 3 * 10 ^12 copies between memory and CPU per second

Weather Forecasting Problem (One Trillion Operations per Second?) Speed of light = 3 * 10 ^8 m/sec R is the average distance between memory and CPU 3 * 10^12 *R = 3 * 10^8 R = 10 ^-4 Use a square grid for memory and connect the CPU to the center of the square S/2 = r = 10^-4 S= 2*10^-4 Capacity of memory = 3 * 10^12 “Row” of memory words will contain (3 * 10 ^12) = (3) * 10^6 words Word length = (2 * 10 ^-4) /  (3) * 10 ^6 = 10 ^-10 meters This is approximately size of an atom. How do you represent 32/64 bits using the size of an atom? END