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20:16
@JMac Thanks for asking/remembering :)
Hi all, I got a question regarding this expression for a quantum mechanical electronic current density:
I do not understand the units of this.
"normally" j has units of m$^{-2}$s$^{-1}$, right?
possibly times charge (C) or something
But here I have this e^2/(12 mc) prefactor, that I do not get.
Yes, this has units of $\mathrm{C}\mathrm{m}^{-2}\mathrm{s}^{-1}$
And what about that $c$?
My currents "normally" look like
Hm, the expression on the r.h.s. has units of $\mathrm{C}\mathrm{m}^{-2}$, unless I'm missing something.
20:26
It would indeed seem there's a $\mathrm{s}^{-1}$ "missing"
@ACuriousMind it confirm my suspicion, that here is something wrong.
Yeah since the speed of light thing is only a question on how you define B right?
I mean its different in cgs or SI/atomic units, right?
Maybe it's in cgs units and correct there. I'm not good at cgs :P
(just to be sure $n$ is the (electron) density for you as well, right?)
Whatever it is, it better be dimensionless otherwise the 2/3 exponent messes up the units entirely
no that fine
20:29
Although...
because [n] = /m^3
then [\nabla n] = m$^{-4}$
then [\nabla n/n] = m$^{-2}$
but then everything works out if $B/c$ has units of Tesla (i.e. we're in cgs), no?
s$^{-1}$ would be still missing, no?
$\mathrm{C}\mathrm{T} = \mathrm{kg}\mathrm{s}^{-1}$, right?
you're right
OK then it looks fine
So big question: How would that j(r) transform to SI units?
20:37
My completely naive guess would be to just strike the $c$, but as said I'm out of my depth here
me too, I am scared about the $\pi$ and stuff ...
20:49
$\pi$ and stuff
It is scary, I agree. You can't ever fully know what it's up to
for real
I bet it's hiding something really deep in its digits.
if it's a normal number then I think every possible sequence is somewhere in there?
so...some encoding of Moby Dick is in there somewhere
Also the Bible
@enumaris I was thinking the same thing as I wrote that. Is there like a moneys writing shakespeare thing going on with pi?
20:54
I'm not sure, but I think that has to do with whether $\pi$ is a normal number or not
it hasn't been proven to be
It is not known whether $\pi$ is such a number, see math.stackexchange.com/q/216343/143136
Maybe it just contains all the terrible books
Ah right, digits of pi isn't exactly like monkeys typing randomly for infinite time, it might be more similar to actual monkeys typing where there's no guarantee they will actually type random patterns.
Normal-ness is the property that describes this afaik
Normality?
Normalcy?
20:57
Normalhood?
Normaliciousness?
Yes, that one wins
:D
Someone should write a paper "On the Normaliciousness of Pi, E, and other Well Known Constants"
While $\pi e$ might be even rational ...
[image of Homer Simpson drooling] Hmmm, normalicious...
21:00
who knows
@enumaris $\pi$ knows!
no, $\pi$ doesn't know $e$
And then $e^{i\pi}$ is an integer...hmmm
So it seems one has to muliply j(r) by "10 c" to arrive at the SI expression.
21:37
seems legit
21:50
I'm at a workshop for machine learning in transport phenomena... my conclusion: it's a mess.
The word "transport" has been forever ruined for me by ABAP's equivalent to git commits being called "transport".
Machine learning, I mean. Not the workshop
I've never heard of ABAP
(googling it)
@tpg2114 It's SAP's proprietary language that I write analyzer tools for for a living :P
Yeah, doesn't sound very fun
Well, I suppose you enjoy it :)
And I write Fortran, so I guess I might be a poor judge of fun
I do! But I've always had a bit of a masochistic streak, I guess ;P
21:54
machine learning is a beautiful mess :)
Beautiful is subjective... heh.
It's pretty powerful
but there's a lot of rough edges that need to be straightened
Well, for some things it is. The main drive here is that for engineering applications and for predictions of physics, it may not be the right tool and it probably shouldn't be used alone
@tpg2114 Can fortran even do machine learning? All I know is that it's quite old. My numerical methods textbook always mentioned it, but we never actually used fortran.
Like, 90% of the time it can identify a dog. But we need airplanes to work 99.999999999% of the time
@JMac Well, Fortran is a (mostly) general purpose language, so it can do anything C or Python or whatever can do. And old Fortran, like F66 or F77, is horrendous and I can't read it.
21:57
well you probably shouldn't have a ML algorithm fly a plane by itself or something...
You need to deploy it to the right use case lol
They are still releasing new standards and it's a pretty good language for numerical calculations
@enumaris We're talking about it for predicting flow fields or modeling flow fields.
@tpg2114 Ah okay. I knew it was like the standard for numerical at one point. I think my professor was biased against it because she wasn't great with it.
It is still the standard for numerical
Or maybe just used really old annoying versions and so was biased that way
Yeah we ended up doing all our numerical with matlab even though the book always talked about fortran
The supercomputer folks got confused when I asked for Boost to be installed on their systems 5 years ago -- they said they didn't know anybody using their machines that used anything other than Fortran
I can't read old Fortran. It's like trying to read Chaucer or Shakespeare in their contemporary English.
22:00
@tpg2114 I think a very different problem for engineering/science applications is that we usually want to understand how a result follows from the inputs, in the sense that a human can at least in principle explain the reasoning. That's not really possible for most types of machine learning.
@ACuriousMind Yeah, they are arguing about that now -- the counter point is that for a general, turbulent flow over an arbitrary body, we can't reason that very well either
With the machine learning transport phenomenon, are they able to use it to search for weird optimizations?
And so maybe expecting ML to be interpretable is unfair, because we can't intepret the problem either
@tpg2114 I find that difficult to believe considering that e.g. SPEC benchmarks 15 yers ago had went from something like no C++ to half C++ or so.
@JMac Well, some are using it to generate reduced order models -- so get a similar answer, much faster. Some are using it to add resolution to low-order solutions. Others are using it to generate models for unused/unknown terms in things like RANS or LES
22:02
@tpg2114 Yeah, that problem exists for numerical solutions in general, that's true
@alarge SPEC had it, but that doesn't mean the users were running codes in it. Our flow solver is part of SPEC, but it isn't the flow solver we actually use -- it's a toy version extracted to show great scaling
I'm just thinking of all the weird FEM mechanical designs they can come up with, like strangely organic shaped rims and stuff that look more like bone structures than traditional structures that they get by optimizing FEM for minimum mass or whatever. It seems like ML could help that process quite a bit.
But it isn't what we actually use
@ACuriousMind I think part of the problem is that the gurus like to think they know what will happen based on X+10 years of experience, but that may not be true
@JMac Yeah, that's more ML for exploring design spaces -- you would use some ML algorithm to find some optimal solution, but you still have to use your FEM or whatever tool to evaluate the design generated by the ML algorithm
To riff off von Neumann's quote about maths: They don't understand it, they just got used to it
We're working on that for jet engine combustors -- use ML to determine which designs should be evaluated by the RANS model
I need to find people to work for me to take on these kinds of problems... there's too many cool ideas and not enough time to do them all
22:11
@tpg2114 Are you doing this in academia or industry?
@alarge Government lab -- so kind of both?
We're publishing parts of it, not publishing other parts of it
Well, not publishing other parts in the open. We're putting it into export controlled journals/meetings
We're doing method development with academics so we can figure out the tools/techniques and designs, then transfer those to industry
We presented some of the work at AIAA SciTech in January, and I think there will be presentations of it at ASME TurboExpo in London this summer
Cool. Have your designs been used for building something physical (full scale - I assume scaled down versions you'd build ~often)?
We're doing that now -- we had an engineer design a baseline combustor the "old" way to use as the starting point, then we found the Pareto front based on our inputs/outputs and are currently building the baseline, an optimal, and a non-optimal so we can test them
And see how well the tools work
If interested, that gives how it's being done and what kinds of things they are looking at
We're doing the design for small jet engines, so no need to scale down, we're doing the full problem
@tpg2114 Not that I really understand what's going on, but I guess that does kind of look amenable to machine learning to an extent. To sample the solution space somehow and thus make the optimizing faster. But I guess that's kind of what you were saying earlier.
Yeah -- that's how we're using it now. I want to replace and/or augment the RANS simulations with another ML algorithm to do faster estimates of the flow field
22:27
@tpg2114 you ever see this paper on Super Slo-Mo? It uses optic flow to create interpolation frames to convert regular video into super slow-motion video :D
something about flows in there :)
@enumaris I haven't seen that specifically, but my summer intern last summer used some convolutional neural networks to in-fill frames in time from experimental data. I guess it's basically the same idea, we had 10 kHz movie and we upscaled it to 1 MHz
I guess that turns a super slo-mo to a hyper slo-mo :)
@ACuriousMind actually explainable AI is much harder for neural-types of ML. Traditional ML algorithms tend to be surprisingly explainable... e.g. linear regression is pretty easy to explain
Trees also tend to tell you exactly how their nodes are split
which can basically reduce them to a bunch of if-else statements
To me, all ML is explainable -- "Glorified curve fitting"
:)
Neural networks are somewhat harder to "explain"
The results from Super Slo-mo are actually quite good :D
you should check it out
Did you see the folks who upscaled the first movie from 189<something> to 4k?
22:31
yeah..that's mostly a resolution up-scaling which is a different set of techniques I would guess
I would probably try first by building an auto-encoder to do it :D
Yeah. Although, that's the key to turbulence if we can do it right. Large-eddy simulation (LES) coarse-grains the solution and then models the small scale turbulent effects on the coarse-grained solution. One of the assumptions that comes from Kolmogorov's hypothesis is that the small scales are universal
So if we could upscale our coarse-grained solution, we can get much better answers (in theory)
ymmv
But, upscaling a train image is one thing... upscaling an infinite dimensional space that is highly correlated in space and time is another
I would guess that if you just think of Neural Networks as powerful function approximators capable of modeling quite non-linear functions, you might be able to find some nice applications.
That's one of my interests in it
Ideally, I'd like to use it to find the best functional form for models that I can plug into my existing solvers
22:35
go approximate away!
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