I'm always suspicious of "breakthrough" announcements when it comes to fusion, especially ones that originate from a college's PR office. Can someone put this in context for us? Is it a big deal?
MIT did not overhype this. The MIT news office used the title "New finding may explain heat loss in fusion reactors".[1] The site from which this was taken added the clickbait title.
Now that the model is fine enough to explain the turbulences observed in the experiments one might hope that this will help suggest design changes to better deal with the turbulences. However the MIT article does not suggest any practical design modification yet.
But it is another thing entirely to take such a huge simulation and try to use many of them to do tokamak design optimization.
>> Now, researchers at General Atomics are taking these new results and using them to develop a simplified, streamlined simulation that could be run on an ordinary laptop computer
- 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.
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.
http://projecte-hermes.upc.edu/Optatives/B%20-%20Analysis%20...
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.
* 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.
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.
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=...
> The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1].
I will say this one more time: "As an equation". There is no equation that describes the system I described, there are only algorithms that cannot be expressed in closed form. The fact that they cannot be expressed or solved in closed form is revealed by the language of your reference: "by Numerical Process".
Numerical algorithms are used -- must be used -- for system that don't have a closed-form solution, i.e. an equation that describes the system. Weather and atmospheric physics are in that category. My specific example -- arctic temperature, rainfall and snow cover -- represents a system that we can't even model with any reliability, much less hope to express as an equation.
Another example, one that surprises many people, is the fact that there is no equation able to describe an orbital system with more than two masses. Those systems must also be solved numerically. (https://en.wikipedia.org/wiki/Three-body_problem)
> ... but that doesn't mean any QM result will ever improve weather prediction
So? I made the exact opposite claim -- that the effect of QM on weather systems may prevent accurate forecasts past a certain time duration.
>> 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.
Who cares what you wrote? You tried to say that 10,000 cells per processor is required for reasonable throughput. This is already false, and it will become more false in the future.
>> Quantum mechanics is thought to be the final obstacle to long-term weather forecasting
> [By whom?][Citation needed].
I didn't make an evidentiary claim, I expressed a commonly heard opinion, so I don't have to provide a citation.
> Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles?
The evidentiary burden is yours to try to support the idea that weather isn't affected by fundamental particles.
> You tried to say that 10,000 cells per processor is required for reasonable throughput. This is already false, and it will become more false in the future.
Can you show me a strong scaling plot for any PDE solver that shows good scaling significantly beyond 10k DOFs per processor?
> the effect of QM on weather systems may prevent accurate forecasts past a certain time duration.
No, and there are two reasons why, one practical and one fundamental. Practical first: The key here is that "exponential sensitivity to initial conditions" means you have to have precise measurements of the weather at close to the scale where QM is significant before QM can have an effect. To even think about approaching a description of that precision would require measurements of wind, temperature etc. at a grid resolution of much less than 1 mm. Leaving the huge practical problems with a measurement like that aside, if you were to measure with an (insufficient) 1 mm grid just air velocity and temperature for the Continental US, the data storage required would be 1 000 000 000 000 000 Terabytes of data for a single point in time. This is 1 000 000 000 times the total storage capacity of the largest supercomputer in the world. For a single second, and what you want is a time series spanning many days. And you're not even beginning to approach the regime where QM becomes important, that would require a storage capacity 10^18 times larger than this already absurd storage capacity. We're talking about 10^30 Terabytes of data at each instant in time!
The other and more fundamental objection to your assertion is the vast discrepancy between the Kolmogorov length scale, i.e. the smallest scale of variations in the flow, and the scale of QM. The Kolmogorov length scale for atmospheric motion lies in the range 0.1 to 10 mm. At scales much smaller than this, such as in QM, the flow is locally uniform everywhere.
There is no equation that describes that system. Which part of this is confusing you? A numerical algorithm is not an equation. My other example, easier to grasp, was the three-body problem -- the existence of a numerical solution doesn't mean there's an equation that describes a three- (or more) body orbit, quite the contrary (it has been proven that no such equation can exist) -- such orbits must be solved numerically, and there is no overarching equation, only an algorithm.
The presence of an algorithm doesn't suggest that there's an equation behind it. Here's another example -- the integral of the error function used in statistics. It's central to statistical calculations, there is no closed form (i.e. no equation), consequently it must be, and is, solved numerically everywhere. This is just one of hundreds of practical problems in many disciplines for which there is no equation, only an algorithm. Reference:
https://en.wikipedia.org/wiki/Error_function
We can locate/identify prime numbers with reasonable efficiency. Does this mean there's an equation to locate prime numbers? Well, no, there isn't -- there's an algorithm (several, actually).
We can compute square roots with reasonable efficiency. Does this mean there's an equation that produces a square root for a given argument? As Isaac Newton (and many others) discovered, no, there isn't -- there's an algorithm, a sequential process that ends when a suitable level of accuracy has been attained.
I could give hundreds of examples, but perhaps you will think a bit harder and arrive at this fact for yourself.
> To even think about approaching a description of that precision would require measurements of wind, temperature etc. at a grid resolution of much less than 1 mm.
Your argument is that, because we can't measure the atmosphere to the degree necessary to associate changes with the quantum realm, we therefore can rule it out as a cause. Science doesn't work that way. Remember that I didn't say it was so, I said it was a matter of active discussion among professionals, as it certainly is.
> At scales much smaller than this, such as in QM, the flow is locally uniform everywhere.
What an argument. It says that, even though at larger length scales, there is turbulence that prevents closed-form solutions (and in this connection everyone is waiting for a solution to the Navier-Stokes equations, which may ultimately be a pipe dream), but as the length scale decreases, things smooth out and become uniform (I would have added "predictable" but you had the good sense not to make that claim). This contradicts everything we know about nature in modern times, and contradicts the single most important property of QM.
> Can you show me a strong scaling plot for any PDE solver that shows good scaling significantly beyond 10k DOFs per processor?
Would you like to make the argument that, as time passes and as processors become less expensive, faster and more numerous, any such argument isn't undermined by changing circumstances?
This paper (PDF warning):
http://www.shodor.org/media/content/petascale/materials/UPMo...
Makes the unsurprising argument that, as time passes and as processor costs fall, matrices are broken into more and more, smaller, parallel subsets in the name of rapid throughput (with appropriate graphics to demonstrate the point). The end result of that process should be obvious, and at the present time, 10,000 serial computations per processor is absurd -- this is not a realistic exploitation of a modern supercomputer. In reality, more processors would each be assigned fewer cells, because that produces a faster result. This is not a difficult concept to grasp.
This is beyond any HPC that I have ever witnessed before. Maybe CERN does more, but I don't quite know the details of it.
Eg. saying that "switch to Heliocentric worldview was a major breakthrough for Geocentric theory" sounds really weird to me.
The heliocentric theory was a breakthrough for a variety of technologies. We certainly would have found going into space much more difficult if we still followed the geocentric theory.
Another way to put it is that they improved the model.
That _does_ bring us closer to improving actual reactors.
1) The reactors have been failing to generate sustained plasma due to specific failures.
2) The simulation models of the reactors did not correctly predict those failures.
3) The new model correctly predicts those failures.
4) Now you can iterate designs using the model with the expectation that these particular failures can be identified before building a full reactor.
5) Breakthrough.
All told, the mainstream scientific community has been very responsible lately in what claims they make about fusion. It's the contractors and startups who think career scientists don't know what they're doing that are over-hyping their pet schemes.
I honestly wish them the best of luck, but what I resent is the credibility gap that fusion scientists work under due to their broken promises.
If you can simulate a design hypothesis instead of having to build an actual reactor, you can make a lot more progress. Understanding the phenomena should also inform the design process.
It seems to be a step toward making our models agree with actual observations, which in general is a very good thing. As to whether it's a big deal WRT actual fusion, that will have to wait until someone thinks of a way to apply this result to present tokamak designs.