5 ms·

I would be curious to know the process for even modeling this sort of thing. How do they know they got it right? How accurately does this model existing experim

by S_A_P 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? How accurately does this model existing experiments? Im also wondering if they model to a result vs modeling to what should actually be happening. Would anyone learned on this subject please chime in? I've always wondered how modeling these types of complex systems works.

tfgg 11y ago
I think the answer is "with great difficulty". When you're developing something like this, you might have an issue with: - Experiment - Model - Approximation to the model - Numerics - Code (- Compiler & hardware) So, your answer might not match experiment. Maybe the experiment is wrong. Maybe it's an expected effect due to an approximation you used. Maybe your integration grid isn't sufficiently converged. You just have to systematically eliminate these, often by comparing to more expensive but verified simulations, or analytic solutions on simplified models.
evanb 11y ago
I don't do plasma physics but other sorts of HPC numerical physics. The answer is a myriad of ways: Check small numerical cases on an already-validated code. Check problems for which you have an analytic solution (in this case, maybe many laminar flow scenarios). Check problems where the 'weird part' (ie the turbulence in this case) is limited to one small part of the simulation. Compare only moderately complicated simulations to experiments that are already entirely understood.
semi-extrinsic 11y ago
In addition to the points mentioned by others, for PDE based codes like this we have the very powerful "method of manufactured solutions". http://projecte-hermes.upc.edu/Optatives/B%20-%20Analysis%20of%20thermal%20and%20fluid%20dynamic%20issues%20in%20industrial%20and%20aeronautical%20systems%20and%20equipment/MMS.pdf http://projecte-hermes.upc.edu/Optatives/B%20-%20Analysis%20...
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 ago
  Some 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.

by S_A_P 11y ago

tfgg 11y ago

I think the answer is "with great difficulty". When you're developing something like this, you might have an issue with: - Experiment - Model - Approximation to the model - Numerics - Code (- Compiler & hardware) So, your answer might not match experiment. Maybe the experiment is wrong. Maybe it's an expected effect due to an approximation you used. Maybe your integration grid isn't sufficiently converged. You just have to systematically eliminate these, often by comparing to more expensive but verified simulations, or analytic solutions on simplified models.

evanb 11y ago

I don't do plasma physics but other sorts of HPC numerical physics. The answer is a myriad of ways: Check small numerical cases on an already-validated code. Check problems for which you have an analytic solution (in this case, maybe many laminar flow scenarios). Check problems where the 'weird part' (ie the turbulence in this case) is limited to one small part of the simulation. Compare only moderately complicated simulations to experiments that are already entirely understood.

semi-extrinsic 11y ago

In addition to the points mentioned by others, for PDE based codes like this we have the very powerful "method of manufactured solutions". http://projecte-hermes.upc.edu/Optatives/B%20-%20Analysis%20of%20thermal%20and%20fluid%20dynamic%20issues%20in%20industrial%20and%20aeronautical%20systems%20and%20equipment/MMS.pdf http://projecte-hermes.upc.edu/Optatives/B%20-%20Analysis%20...

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 ago
Some 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.