[FRIAM] neural operators seem promising
Pieter Steenekamp
pieters at randcontrols.co.za
Thu Jul 17 15:03:28 EDT 2025
You’re right — I took a bit of a scenic route instead of sticking to your
actual point. Classic me: chasing the big picture and missing the turnoff!
I’ll pay closer attention next time.
Appreciate the nudge.
On Thu, 17 Jul 2025 at 20:41, glen <gepropella at gmail.com> wrote:
> Interesting. So here's how I saw it. My post was about whether or not NOs
> could help simulate the stack solving Hilbert's #6. And you respond saying
> that NOs are not human-like. You gotta admit that's at least a non sequitur.
>
> How is a simulation of the Hilbert #6 stack human-like or not human-like?
>
> On 7/17/25 11:19 AM, Pieter Steenekamp wrote:
> > It seems you didn’t like my reply — and that’s totally okay. Maybe you
> even think it’s complete nonsense. That’s fine too. Honestly, maybe it is
> nonsense!
> >
> > But the message is my own. I read the paper (no help from GROK or AI):
> > https://arxiv.org/pdf/2506.10973 <https://arxiv.org/pdf/2506.10973>
> > …and I also watched the YouTube talk:
> > https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI>
> >
> > Based on that — and my own experience — I shared my interpretation.
> >
> > Over the years, I’ve worked in related fields. I’ve written serious
> industrial code using convolution-style operators (back before
> convolutional neural networks became trendy) for model predictive control.
> I also built and shared an unlabelled image clustering tool using CNNs in
> PyTorch — it’s on Kaggle here:
> > https://www.kaggle.com/discussions/general/425317 <
> https://www.kaggle.com/discussions/general/425317>
> >
> > I even built a proof-of-concept Agent-Based Model (ABM) for a client,
> which I tied into an MPC setup.
> >
> > So yes — if it’s nonsense by your standards, I’ll take the hit.
> >
> > But if you’re suggesting the message is not mine… I’ll have to plead
> not guilty on that one, your honour.
> >
> > I have stated it before, my ability to express myself in the English
> language is limited, so yes - I do use (in this case ChatGPT) to help with
> the words. But I take responsibility for the all messages.
> >
> > By the way, my main message that I tried to communicate is that I am
> very serious about tools like CNNs and NOs are top down approaches and in
> my very humble opinion have very powerful but limited scope. I do think
> that unless a true bottom up approach is taken, the future of AI is
> limited. If you think it;s nonsense, again, that's fine with me, but that
> message comes from between my two ears and not from Grok or any AI or any
> other human but myself.
> >
> > On Thu, 17 Jul 2025 at 19:10, glen <gepropella at gmail.com <mailto:
> gepropella at gmail.com>> wrote:
> >
> > What is this? Do you simply feed posts directly to Grok and post the
> response, even if it's nonsense?
> >
> > On 7/17/25 9:39 AM, Pieter Steenekamp wrote:
> > > Yes... kind of.
> > >
> > > I know how NOs little siblings like CNNs have done cool stuff
> with images, and it makes sense to hope NOs (Neural Operators) might do
> similar things in "big boy" applications like fluid mechanics, weather
> modelling, and robotics control. I agree, that would be great!.
> > >
> > > But this is still a top-down approach. We're building tools that
> are smart in some ways, but they don’t really think like people. I don’t
> expect this to lead to true human-like intelligence.
> > >
> > > I wouldn’t be surprised if someone out there is quietly working
> on a bottom-up way to build AI—and I think that’s where big breakthroughs
> could happen.
> > >
> > > For now, NOs and similar models will keep giving us amazing
> results. But they're still just tools. Useful, potentially absolutely
> amazing. Human-like? No way, Jose.
> > >
> > > On Thu, 17 Jul 2025 at 16:50, glen <gepropella at gmail.com <mailto:
> gepropella at gmail.com> <mailto:gepropella at gmail.com <mailto:
> gepropella at gmail.com>>> wrote:
> > >
> > > I'm confident nobody but me cares. But just one more post, I
> promise. Perplexity is not normally my sycophant. She flat out rejected my
> extrapolation from Powell's "The Kraken" to the entirety of the Stop the
> Steal suits. And she flat out rejected my claim that the term "Scientific
> Materialism" is the best term to use for those of us who want to avoid
> teleo[logy|nomy]. But, here, she agrees with me that:
> > >
> > > "It is feasible and indeed a valuable research direction to
> use Neural Operators like those in the NNs-to-NOs repo to computationally
> approximate the full multi-scale stack from microscopic particle systems to
> macroscopic fluid equations that Deng et al. prove mathematically."
> > >
> > > Whew! So I'm not crazy, right? Of course, I'm too lazy to
> actually do it ... or maybe I'll just blame it on "brain fog" ... another
> term I absolutely loathe. >8^D
> > >
> > > On 7/17/25 6:55 AM, glen wrote:
> > > > Sabina's recent defense of Weinstein [⛧] seems to follow
> in this vein. And I can't help but feel similarly when I try to understand
> Geometric Algebra. What is the value of these games over and above their
> binding to the world? Or, maybe more importantly, what's their value when
> they fail to bind well to the world? My favorite writer about Gödel was
> Torkel Franzén, who spent more time debunking the runaway [ab]use of the
> incompleteness theorems than he did inferring anything from them - or maybe
> I was simply more attracted to his debunking than I was to his in-theory
> work. I guess the same is true of Barwise's tinkering around with
> anti-foundations or Shapiro's foundations without foundationalism. Now that
> we have things like Isabelle/HOL, the "theory" seems to take on a life of
> its own. Inference tools like this help me play the games I could only
> imagine when I was a kid, even if my games are childish or of no use to
> anyone but me. Then again, I don't spew
> > grievance on
> > > > everyone I meet when *they* don't want to play the games I
> enjoy.
> > > >
> > > > Since we're still in the [F]NO thread, they do seem to
> fall directly in line with the way even the most banal of us are using AI.
> This result:
> > > >
> > > > Hilbert's sixth problem: derivation of fluid equations via
> Boltzmann's kinetic theory
> > > > https://arxiv.org/abs/2503.01800 <
> https://arxiv.org/abs/2503.01800> <https://arxiv.org/abs/2503.01800 <
> https://arxiv.org/abs/2503.01800>>
> > > >
> > > > is out of my reach. And even with
> https://github.com/neuraloperator/NNs-to-NOs <
> https://github.com/neuraloperator/NNs-to-NOs> <
> https://github.com/neuraloperator/NNs-to-NOs <
> https://github.com/neuraloperator/NNs-to-NOs>>, it's not clear to me
> whether I'd be able to understand enough to mimic the analyses Anandkumar
> presented in the talk. But like with Isabelle or Lean (plus tools like
> Claude) I can just barely *taste* it. I can just barely taste what it might
> be like to be a theorist - to have the cognitive power to think such things
> through in the way Eric describes Einstein. At the end of the day, though,
> Franzén's more my speed.
> > > >
> > > >
> > > > [⛧] Though her less recent discussion of Thiel and the
> relationship between Thiel and Weinstein smells like smoke. Of course
> Carroll is exactly the type of person the anti-establishment would accuse
> of Scientism. :face_with_rolling_eyes:
> > > >
> > > > On 7/16/25 9:30 PM, Pieter Steenekamp wrote:
> > > >> It reminds me of Gödel’s incompleteness theorems.
> > > >>
> > > >> Gödel’s incompleteness theorems show that any formal
> system powerful enough to describe arithmetic will always have true
> statements it can’t prove. This seems like a purely theoretical result, but
> the proof itself is highly constructive—Gödel uses very practical
> techniques like numbering symbols and mimicking logic inside arithmetic.
> > > >>
> > > >> In a way, it’s a perfect example of applied technique
> informing theory. A deep theoretical truth was uncovered not just by
> abstract thinking, but by rolling up sleeves and working with the system
> from the inside. Faraday/Maxwell, steam engines/thermodynamics all show how
> hands-on methods can push theory forward.
> > > >>
> > > >> On Thu, 17 Jul 2025 at 03:20, Santafe <
> desmith at santafe.edu <mailto:desmith at santafe.edu> <mailto:
> desmith at santafe.edu <mailto:desmith at santafe.edu>> <mailto:
> desmith at santafe.edu <mailto:desmith at santafe.edu> <mailto:
> desmith at santafe.edu <mailto:desmith at santafe.edu>>>> wrote:
> > > >>
> > > >> I _very often_ have the thought that, were the nature
> of people such that grievance and misanthropy simply didn’t do them any
> good, and so they simply never engaged in it, so many conversations would
> go on in such different ways, that we might have to adjust a bit to realize
> they started from the same query.
> > > >>
> > > >> One such query is whether the nature of anti-theory
> people is mainly an aesthetic style of thought (seems very possible), or
> mainly motivated by a dislike of people they met earlier who (whether with
> warrant or just to serve other needs of their own) they label as “theory
> people”. I would like it if it were mostly the former; that anti-theory
> people were “born this way”; it would give me a conversation that seems
> interesting in several dimensions and that I could navigate. Let’s suppose
> that such conversations are available somewhere, even if not everywhere.
> > > >>
> > > >> The start of this went something along the lines of
> “Faraday locked in electromagnetism by its empirical evidences, and Maxwell
> put some pretty symbols onto it.” (The original wasn’t exactly as I just
> wrote it, and I am over-drawing here to take the direction to its
> cartoon-simplified limit. I am also _sure_ I can find some truly
> anti-theory people who believe this is the absolutely right take on it.
> Within Chemistry, where I have the counterpart to this conversation fairly
> often, I have a good list of names, because it is still the prevalent
> aesthetic of the field.)
> > > >>
> > > >> The sort of mind that believes that the former take
> on Maxwellian electromagnetism is indeed the only real-man’s hard-headed
> take, is likely (to the extent that it has any patience with formal logical
> analysis at all as not a priestly self-indulgent waste of time) inclined to
> think that Popper has a good description of the criteria for scientific
> meaningfulness and truthfulness.
> > > >>
> > > >> But then we can do it recursively all the way down.
> Is Newtonian gravity just one among an infinitude of data-compressions of
> Keplerian orbits (since, at the end, everything moving under gravity and
> approximating away other effects such as friction is on a Keplerian orbit,
> including apples, so there “isn’t” really anything else).
> > > >>
> > > >> Let’s not answer, but simply add attested
> observations:
> > > >>
> > > >> It was studying Maxwell’s field equations in school
> that led Einstein to try to construct general relativity within similar
> concepts. And presumably the very geometric flux-sphere picture that comes
> with Newtonian gravity that causes geometry to be retained as the
> phenomenon for Einstein’s gravitational field theory to be about.
> > > >>
> > > >> One can go through such idea-chains across the
> sciences. In some, people don’t leave pithy accounts of why they believed
> it occurred to them to do things one way rather than another; in other
> cases they do leave such trails, at least about their beliefs. Or
> philosophers come along later and do forensics and argue that their work
> shows their reasons to be such-and-such.
> > > >>
> > > >> A compact representation of the latter collection of
> asserted-observations is that there is some kind of work that theory is
> doing as itself, not as a proxy for something else (like description-length
> shortening for a pile of data-instances). I remember how it seemed an
> insightful turn for me when my graduate advisor commented that the particle
> physicists had felt a sense of liberation when they could throw away the
> Particle Data Book, with the advent of first Murray’s symmetry
> classification and eventually the settling in of QCD as a theory in which
> one could stably compute things, and then the whole symmetry-grouping of
> all the elementary particles by a few terms.
> > > >>
> > > >>
> > > >> Circling back to thermodynamics, Harold’s “Emergence
> of Everything”, and what is or isn’t substantial in the world of
> observations and states of mind that we take on in relation to them:
> > > >>
> > > >> Harold was happy invoking Popper, and didn’t want to
> sweat a lot over how much Popper was trying to take over a dichotomy from
> first-order logic, and the asymmetry between there-exists and for-all, and
> how much it doesn’t work to press that into service as a formalization for
> empiricist reasoning. Harold was, generally, an easy-going guy, and
> willing for things to be rough, or half-wrong, supposing that if he could
> intuitively get them half-right, that would be much better than nothing,
> and there would be time to come back and fix whatever parts may have been
> wrong. So he could like Popper as one of his half-right positions, even
> though it was the inability to deal with being half-right where Popper
> ultimately undermined himself. btw., that’s where a very useful study of
> metaphor in science, along the lines that DaveW gave a definition of it
> from Quine, can get built up.
> > > >>
> > > >> Probably likewise with thermo and steam engines. For
> the purpose of making a certain point — that theory doesn’t arise in a
> vacuum or from direct access to the Mind of God — Harold would be happy to
> overstate the simplicity of this position, and to evangelize for empiricism.
> > > >>
> > > >> But of course, in the world we live in — and
> especially the world where I live, which is almost-all thermodynamics
> almost-all the time, and almost-none of it about steam engines, or even
> anything having to do with mechanics or energy — we have learned much, much
> more about nearly-everything, from thermodynamics, than there even was of
> thermodynamics, to have learned from steam engines. At the end of the day,
> the lessons of thermodynamics, when properly understood, constitute the
> explanation for why there even are stable macro-worlds. Of more-or-less
> anything. In other working conversations, with other aims, Harold would of
> course have seen that too, and been happy with the statement putting it on
> record. Even though that statement would have seemed, to a debaterly-type
> mind, to have contradicted the earlier one.
> > > >>
> > > >>
> > > >> I have seen a lot of chat over the years about what
> is “the nature” of theory as something that can do work that deserves to be
> called different-in-kind, and not just different-in-cost, than listing data
> instances, thus making theory particular among data compressions (the
> latter, as a kind of generic category; obviously theories are, as one of
> their aspects, compressions of data instances; the question here is whether
> to say that is “all” they are is as good or as useful an account as we can
> give). But at the end, I just hear the same positions reiterated, some of
> them more rhetorically elegantly (Cris Moore did a very nice job in a tiny
> soliloquy in one of the SFI public lectures), or more tritely and
> conventionally. But I haven’t heard somebody with something really
> original to say on the question, that makes me stop and think I see things
> better, for a long time now. I think the Philosophers of Science (I’ll
> capitalize both for DaveW) put a lot of
> > time into
> > > this.
> > > >> If I had more time I would probably try to listen to
> them, and I might find they have interesting things to say.
> > > >>
> > > >> Eric
> > > >>
> > > >>
> > > >>
> > > >>
> > > >>
> > > >>> On Jul 17, 2025, at 2:19, Steve Smith <
> sasmyth at swcp.com <mailto:sasmyth at swcp.com> <mailto:sasmyth at swcp.com
> <mailto:sasmyth at swcp.com>> <mailto:sasmyth at swcp.com <mailto:
> sasmyth at swcp.com> <mailto:sasmyth at swcp.com <mailto:sasmyth at swcp.com>>>>
> wrote:
> > > >>>
> > > >>> * Anima's presentation reminded me quite nicely of
> the Numenta/Redwood work of Jeff Hawkins et al? Cortical columns, etc.
> > > >>> * Did Harold Morowitz make a strong assertion to
> the tune: "we learned more about thermodynamics from steam-engines than
> vice-versa"? EricS or StephenG might have first-hand knowledge?
> > > >>> * Is this theory/practice dichotomy just another
> form of meta-scaffolding in evolution (of any system) with the cut-and-try
> providing the mutation/selection and the theory/formalism binding the
> "lessons learned" into well... "lessons learned"?
> > > >>>
> > > >>> On 7/16/2025 2:12 AM, Pieter Steenekamp wrote:
> > > >>>> Both the video of Anima Anandkumar’s Stanford
> seminar and her scientific paper on Neural Operators really got me
> excited—the ideas feel fresh and powerful.
> > > >>>>
> > > >>>> The paper is quite technical and digs into the math
> behind Neural Operators, without talking much about robotics. In her talk,
> though, she clearly links the work to robots, and it sounds as if robotics
> is a big focus for her team.
> > > >>>>
> > > >>>> What jumped out at me is how different her style is
> from Elon Musk’s approach with Tesla’s Optimus robot. Anandkumar begins
> with deep theory, building firm mathematical foundations first. Musk takes
> a “just build it” path—make it, test it, break it, fix it, and keep going.
> > > >>>>
> > > >>>> This contrast reminds me of engineering school and
> the Faraday‑Maxwell story. Faraday was the hands‑on experimenter who
> uncovered the basics of electricity and magnetism through careful tests.
> Maxwell came later and wrote the elegant equations that explained what
> Faraday had already shown.
> > > >>>>
> > > >>>> So I wonder: will the roles flip this time? Will
> deep theory from researchers like Anandkumar guide the breakthroughs first,
> with practice following? Or will practical builders like Musk sprint ahead
> and let theory catch up afterward?
> > > >>>>
> > > >>>> Either way, watching these two paths unfold side by
> side is thrilling. It feels like we’re standing on the edge of something
> big.
> > > >>>>
> > > >>>> On Wed, 16 Jul 2025 at 04:11, Jon Zingale <
> jonzingale at gmail.com <mailto:jonzingale at gmail.com> <mailto:
> jonzingale at gmail.com <mailto:jonzingale at gmail.com>> <mailto:
> jonzingale at gmail.com <mailto:jonzingale at gmail.com> <mailto:
> jonzingale at gmail.com <mailto:jonzingale at gmail.com>>>> wrote:
> > > >>>>
> > > >>>> Even if just for the freedom of scale, learning
> infinite dimensional function spaces, etc...
> > > >>>>
> > > >>>> https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI> <
> https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI>> <
> https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI> <
> https://www.youtube.com/watch?v=caZyFlSSKtI <
> https://www.youtube.com/watch?v=caZyFlSSKtI>>>
> > > >>>> https://arxiv.org/pdf/2506.10973 <
> https://arxiv.org/pdf/2506.10973> <https://arxiv.org/pdf/2506.10973 <
> https://arxiv.org/pdf/2506.10973>> <https://arxiv.org/pdf/2506.10973 <
> https://arxiv.org/pdf/2506.10973> <https://arxiv.org/pdf/2506.10973 <
> https://arxiv.org/pdf/2506.10973>>>
> > > >>>>
> > --
> --
> ¡sıɹƎ ןıɐH ⊥ ɐןןǝdoɹ ǝ uǝןƃ
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