Solving computer chess
The number of possible positions on a chess board is 1046. Several algorithms can be used to reduce this, but still, solving a game on a 1000 processor system takes 3*10**4 years. With a one million speed-up that would be 3*10**-2 or 11 days.
Playing the game still requires considerable software improvements too.
Turbulence modelling
Modelling a plane or a car, or even a golf ball flying or driving in the air, requires solving so-called Navier-Stokes equations with Direct Numerical Simulation. There is a Reynolds number influencing the calculations.
| golf ball | fast car | aircraft |
|
Re | 2*10**5 | 10**7 | 5*10**7
|
|
Grid | 10**9 | 10**13 | 10**15 |
|
Flops | 10**17 | 10**22 | 10**25 |
|
Speed (2 wks = 106 s) | 100 G | 10 P | 10 E |
|
Memory | 100 GByte | 1 PByte | 100 PByte |
According to Peter Michielse, we can solve the golf ball model today. For a fast car we have to wait 10 years. A full aircraft will only be possible in 2032 with the projected installed machine.
Climate research
In Climate research the main challenge is to take a grid that is as small as possible. A grid here means a grid in the atmosphere, for instance 10*10*10 km. The smaller the grid size the better the results. The goal is to have a calculation on a scale of about 1 km. This would allow to predict individual thunderstorms.
| | 1983 | 2007 | 2032 |
| Model | standalone | coupled coupled |
| Lat./Long. | 4 degrees | 0.1 degrees | 0.01 degrees |
| Layers | 12 | 45 | 45 |
| Grid | 5*10**4 | 5*10**8 | 5*10**12 |
| Period in years | 10-100 | 100 | 100 |
Software improvements
However, to achieve this type of performance gain in 2032, it will not be enough to rely completely on hardware improvements. Also in software developments. Also during the past 25 years, at least as much in application performance gain is due to algorthmic software improvement as to faster hardware.
In linear systems, multigrid and conjugate gradient methods were breakthroughs in solving partial differential equations.
Peter Michielse expects that in chess and other games, agent technology will play an important role. To really get 1 million times application performance improvement in 2032 in turbulence modelling and Climate research, probably a factor of 1000 will be required to come from software.
Peter Michilese collected the input from several Dutsch scientists:
- Prof. dr. ir. Henk Dijkstra (Climate Research)
- Prof. dr. Jaap van den Herik, dr. ir. Jos Uiterwijk (Gaming)
- Dr. ir. Herman te Riele (mathematics)
- Prof. dr. Arthur Veldman, dr. ir. Roel Verstappen (turbulent flow)
- Prof. dr. Henk van der Vorst (PDE solverw.)
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