4 ms·
> I would be curious to know the process for even modeling this sort of thing. How do they know they got it right? It helps that the model creates the same out
by lutusp 11y ago
> I would be curious to know the process for even modeling this sort of thing. How do they know they got it right?
It helps that the model creates the same outcomes as the actual observations (and the old model didn't). This isn't an ironclad guarantee that the model reflects reality, but it suggests that we're moving toward a more accurate reflection of nature.
> I've always wondered how modeling these types of complex systems works.
To explain I will use a simpler example -- weather forecasting. In weather forecasting, we need to model the atmosphere. It's not possible to model the entire atmosphere directly, instead we break the atmosphere into a bunch of cubes, each with an initial temperature and humidity and a few other things.
Then we process the cubes in a supercomputer consisting of many processors running in parallel -- one processor per cube. The actual computation consists of seeing what effect a cube's neighbor's pressures, temperatures, etc. have on the tested cube, for a brief interval of time. Then we repeat the process for another slice of time. Ad infinitum.
This is obviously a numerical process, with no overarching equation that explains it all, but with some basic first principles at work (a theme in modern physics). Such a process becomes more accurate if we can create more, smaller cubes, and for that we need more and faster processors. So most of modern supercomputer design involves thinking of ways to acquire more and faster parallel processors.
The kind of model that led to the discussed result follows the same basic pattern. The irony is that the most often cited reason for having supercomoputers -- to be able to say whether it will rain 72 hours from now -- is also the least likely to succeed, because of the role played by quantum mechanics (i.e. by chance processes) in earth's atmosphere.
- semi-extrinsic 11y agoSome corrections/nitpicks on your weather forecasting example: * there are most definitely some overarching equations that explain it all. We just can't solve them analytically. But we use them to write the code. * when you say "one processor per cube": if you mean cube = grid cell you're way off. You want to have at least ~ 10 000 grid cells per processor to have any level of performance. * it is definitely not quantum mechanics that makes weather hard to predict. It's what's popularly called "chaos", or mathematically, "exponential sensitivity to variations in initial data". * getting more performance for this type of application is not about getting more cores, it's about getting more memory bandwidth. That's why e.g. GPUs are useless for speeding up weather forecasting. * funfact: weather simulations today are not running any faster than in 1994; it's at about 15 minutes per simulation. The increases in computing power are used to a) increase grid resolution and b) run more replicas. * The last point is what makes modern weather simulations tick. You don't run one simulation, you run 1000, each with slightly different initial data, and you analyse the ensemble results.
- lutusp 11y ago> * there are most definitely some overarching equations that explain it all. Not so, not for Earth's atmosphere, the topic I was discussing. There are first principles, but no overarching equations, analytically expressible or not. Prove me wrong -- show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. > * when you say "one processor per cube": if you mean cube = grid cell you're way off. You want to have at least ~ 10 000 grid cells per processor to have any level of performance. It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. I say this on a day when the Raspberry Pi Zero is so much in demand that I can't find one for sale. > * it is definitely not quantum mechanics that makes weather hard to predict. It's what's popularly called "chaos", or mathematically, "exponential sensitivity to variations in initial data". Both play a part. Quantum mechanics is thought to be the final obstacle to long-term weather forecasting, and chaos theory (extreme sensitivity to initial conditions) is the mechanism by which small initial causes lead to large effects. Your last three point weren't corrections, so no need for comment.
- semi-extrinsic 11y ago> show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1]. > It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. No. You didn't read what I wrote. Unless some radical paradigm shift occurs in both hardware and algorithm design, strong scaling is never going to pay off once you get less than about 10 000 grid cells per CPU. Core cost is not tge issue, power usage over the cluster lifetime is already a huge cost. Memory bandwidth is the issue, Linpack (peak float) performance is so irrelevant even management has started to ignore it. > Quantum mechanics is thought to be the final obstacle to long-term weather forecasting [By whom?][Citation needed]. Of course QM is behind how atoms and molecules behave, but that doesn't mean any QM result will ever improve weather prediction. And, why stop at quantum mechanics? Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles? [1] https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=fnd&pg=PA3&dq=equations#v=onepage&q&f=false https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=...