modeling

[jagged palm]

This paper's fun https://arxiv.org/abs/2406.14427v3

[lean walrus]

I have two very offensive engineering moments

One was a few years ago, where I was running a simulation and my result was "off" on the order of 10^4

("Off" additively i.e. +- c*10^4)

But we were working on the order of 10^9

So I just said that was good enough and called it a day

One was more recent

I was running a numerical simulation and had to filter out values "near zero" and duplicate values

I would've tried to use like 10^(-12) \equiv 0 but my numbers were too big relative to that so I had to use 10^(-3) 💀 I said if the difference of two numbers was within a thousandth of each other (or if either number was less than a thousandth) it was "0"

That one felt pretty silly

But it worked 😁

[lean walrus]

@spice forge Do you remember this?

I tried looking for it in our DMs but it wasn't there, I don't remember where it happened. I just remember I was talking to you when it happened 😛

[spice forge]

Cooked

[lean walrus]

dawg what that even mean

[jagged palm]

Lol that doesn't seem so bad, you just gotta know your error tolerances

[lean walrus]

Ya you’re right, but I guess to the “average person” hearing that you’re 50,000 - 90,000 [units] off sounds like a lot 🤣 I was certainly not used to doing that at the time

[jagged palm]

It might be really bad haha

If you're making a bridge and your estimate of how many kilos it can take is off by that much, I'm scared

If you're estimating the number of kilometers to the middle of the Milky Way for general order of magnitude, I'm impressed if you nailed it down that far

[lean walrus]

LOL Yeah you’re right

[signal vault]

I have a real life engineering problem that I think math could help solve if anyone has any ideas:

there is wastewater going out to the city and the pH of this water is continuously monitored. If the pH drops below 5 then a valve upstream of the pH probe closes so that the water can be reprocessed.

The problem is that the pH probe occurs after the shutoff valve so by the time the pH is below 5 there is a lot of bad water that gets through even if the valve closes instantly.

I want to use mathematical tools on the pH signal to predict a below 5pH event before it happens so I can shut the valve early

My initial thoughts were to use autocorrelation but I’m not really sure what the best tools would be. I though that autocorrelation could tell me how much the signal correlates with itself over time

So maybe a better way to state the problem:

I have a continuous time signal which is mostly low frequency ‘noise’ (mostly stationary) but occasionally there will be a very sharp drop. I want to know what mathematical tools could help me predict the drop.

[upper stump]

Are you working with real data

Are there any signals in the data before a ph drop

[wide flame]

how fast is the drop wrt volume and valve deltas? are there probes/readings from upstream processes? you might not even need to "predict" also, unless rule based systems have already been evaluated

[signal vault]

Yes this is real data, here is an example of it falling out of range

And then this is the flow rate, pH signal, and derivative of pH signal over like 30 hours

[signal vault]

Okay so there are upstream pH probes but they are in pH buffer tanks that arnt mixed so sometimes they don’t read a low pH until 3 minutes after output pH is below 5

But regardless of the real world fixes of having more probes, I was more curious about what I could do given the information I have now

The system goes

Tank A (acid buffer) —> tank B (base buffer) —> shutoff valve —> flume pH probe (the main signal I am getting)

[wide flame]

personally, i would need more chemistry knowledge, but why can you not just directly calculate the expected ph if you have readings from both buffers?

[upper stump]

Do you know mechanistically why the pH drops

[signal vault]

Yea so this is for a factory where we do anodizing which takes aluminum parts and dips them in a bunch of chemicals to make them shiny chrome or shiny black. Depending on the levels of the tanks or how dirty the tanks ‘water is’ the tanks get sent to wastewater through A and B.

[signal vault]

What makes it hard is that the sensors on tanks A and B are not in a good spot so the entire tank doesn’t have a single pH. The area with the probe doesn’t actually see the pH change for awhile

Here are signals from one particular event

The red is what I am trying to prevent

The system works okay right now but the small red part is technically illegal so I want to fix it

[wide flame]

step 1 is to tell your manager to tell leadership to invest in better sensors + placement yesterday

i imagine that some ac model could do decent, esp given (from my understanding) you are really trying to determine when the water gets too "dirty"

[signal vault]

I know I’m gonna try that but they insist that the little spill to the city is not a big deal and so they arnt gonna spend any money. So my choices are throw them under the bus and lose my job or fix it without spending money by using an algorithm

But I’m also highly interested in the math that i could to fix this because it’s pretty cool to solve problems with an algorithm

[upper stump]

Wouldn’t this be illegal retaliation against a whistleblower

Anyways

Back to the math

[signal vault]

Most likely yes but it’s complicated which is why it’s hard to explain why I need to use math

Like maybe I wouldn’t get fired but then I would be bullied or never promoted or something idk

[wide flame]

actually, have you looked at the delta distribution for time between events? unless it is insane, there is a world where you can just say, if x above y, and > N hours since last event, pause the flow for t

not saying modeling isnt the "right" answer, but you usually want to avoid it if possible

(in corporate, ime)

[upper stump]

Do you know why there is the wiggliness in the third graph here

[signal vault]

It’s typically about a day between these events but it’s also pretty random. The problem is that after about 1 hour of closing the valve the system can’t hold anymore water and starts flooding the factory

[signal vault]

The flow rate one?

Because if I had to guess about that it’s because the electrical sensor is not always submerged and is being hit by waves within the pipe

And also electrical noise from the chemicals being used or something

And also tanks A and B are ‘automatically controlled’ so if they detect high or low pH they dump acid or base into the tanks respectively.

[wide flame]

do you have data for those processes?

that seems rather significant

i would hope that the control system is logging events

[signal vault]

I just started recording the flow rate and pH of this system. Everything else is relay logic so at best it’s “if tank A pH is above X for Y seconds, dump acid for Z seconds” all completely fixed

This system was on the dinosaur level and i started logging the pH signals and flow rate to a database and that’s when I realized we were dumping out bad water

And now my systems data is being fudged and then sent to the city …

[wide flame]

this is likely still important info for whichever model/system you go with

[terse adder]

can I ask questions in this channel about linear regression and time series?

[lean walrus]

I think that fits, yeah!

[jagged palm]

Go ahead and ask

[lean walrus]

me when the intersection of two domains is donated by the + operator (idk just reads easier to me)

[jagged palm]

That is confusing to me lol I would have expected that + means union

in the context of that picture it makes sense tho

[upper stump]

<@&268886789983436800> spammed in multiple channels

[sand onyx]

Please don’t advertise here or cross post your messages.

[golden saddle]

Okay 👍

[lean walrus]

Silly question but how would you model the following phenomenon?

Say a mother is 29 when she gives birth, and take her child to be 1 year old at birth (very common in Asia)

Her age is 29x the child's age

Let one year pass; the child is now 2, and the mother is now 30, making her 15x the child's age

3 and 31 make her (10 + 1/3)x the age, and you get the idea

How can I plot/study the ratio of the mother's age to the child's age as a function of time?

[upper stump]

(29+t)/(1+t)

[lean walrus]

Something something (mother + x*t)/(son + x*t) I assume?

Okay

Yes

LOL

Thank you

I feel silly

[graceful kindle]

What modeling is about?

I'm new to it

[jagged palm]

Anything applying math to understand phenomena in the real world, really

[graceful kindle]

Example?

[grizzled turret]

Pretty much all of physics

[graceful kindle]

What resource is recommended to learn modeling?

[upper stump]

Why do you want to learn about mathematical modeling

[jagged palm]

Mathematical modeling is as much about learning math as it is about learning the subject area that you want to apply the math to

Do you have something in particular you're trying to gain understanding about via mathematical modeling?

[graceful kindle]

Because I know some linear algebra but idk how to use it

[graceful kindle]

I want to know how to model real life problems and situations

[grizzled turret]

How much physics(or engineering) have you taken? Since lots of the classic modeling examples are solved/discusses in those kinds of classes

Also models often (but not always) arise from differential equations, so you may wanna have at least an introductory understanding of that area of math as well

[upper stump]

What real life problems and situations do you want to model

[graceful kindle]

Idk anything much about physics, and in engineering, I don't think I've ever modeled a thing 🤔

[graceful kindle]

Got it, so am gonna learn calculus first

[graceful kindle]

Idk, cause idk what modeling is

[lean walrus]

This will be a bit vague because I'm learning about it as I go, but I can demonstrate an example of modeling that I am currently doing now. Perhaps that may give you an idea of what modeling "looks like" and how it can be applied

So I'm working on a "personal finance simulator" in Excel, where the idea is that I input in a few numbers and it shows me how my balances and expenditures evolve over time

There is already a very simple model of this

The idea is that you start off with an initial balance P, define a rate of return r, then define a timespan t and a compounding frequency n within that timespan (how often your rate of return applies to your balance)

Then, the final balance F after t number of timespans is given by

[wanton ravine]

feather
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[lean walrus]

So this models that situation because you take your rate and divide it by the number of times it compounds per year, giving you the effective rate at which it compounds on each compounding period (this is the 1 + r/n). Then you take this over the number of compounding periods across the timespan (this is the exponent nt), and since that's all compounding on your principal, you scale it by P

So there's a simple and effective example of a model right there

But we can make this even more detailed

Consider the stock market; while you can form averages of the rate of return over a year (this is 10% afaik), the actual number changes depending on the economic situation

You might get 4% returns one year and 16% another and -9% the next

[lean walrus]

Furthermore, with retirement funds, you typically make a contribution every so often. Like, a 401k you make a contribution on with each paycheck, for a Roth you make a contribution (however frequently you do), etc

So your principal also grows with time now

[lean walrus]

You see how this model is no longer sufficient to model the more complex situation I described? It assumes a constant rate of return and no contributions

Let's step it up another level

[lean walrus]

The amount you can actually contribute every time you contribute depends a lot on your economic situation!

I'll give you the context of mine, as an example

I currently live with my parents; they pay the mortgage, they pay for food, they pay utility bills. They take care of all the "big stuff", so I really don't spend much money outside of personal expenses

So right now I can afford to throw a lot of my savings into my retirement fund

So every contribution I make is pretty large (let's say $1000 - $2000 at a time)

But now look 5 years in the future

I'm probably living alone now, so now I got actual bills to pay

That reduces the amount of money I can throw into my fund per contribution, so now I might only be contributing $500 at a time

Then maybe one day I unexpectedly get fired

Now I can't afford to contribute any money because I have no income - I'll have to live off my savings until I can afford a new job

So you see how the size of your contribution, as well as the frequency of how often you contribute, can change depending on your personal financial situation?

Now let's look 5 more years into the future

I've got a great job again, I'm probably married now, maybe even have some kids

I've been saving for a long time and I'm looking at buying a house

Well, that's likely gonna require me financing the majority of the house cost

But the interest rate my bank gives me on my finance can also depend on the economic state at the time and what the Fed has set their baseline rate to

So if I decide to buy at a time when we're in economic situation A, and the rates are high (inflation), that means I'm paying much more over the course of the loan

Or we could be in economic situation B (strong economy), and the rate is actually lower than it might typically be!

I could have a great credit score and get better rates, or a poor credit score and worse rates

Then you have to consider how frequently the economy is changing too

Economic parameters tends to be self-correcting towards some mean (exhibit mean reversion), so depending on how long we've been in, say, a recession, my expenses might go up relative to the value of my money (meaning I can contribute less per period), but then the economy starts getting okay again and now my expenses are less relative to the value of my money (meaning I can contribute more per period)

The point is, you see how many changing variables there are, and how they can change how much I contribute (or whether I contribute at all)?

The economy is stochastic in this sense; you never know what's going to happen next, so while you can make some predictions about how things will evolve, they might go completely another way

There's a billion ways you can model this

The way I'm choosing is by assuming that at certain ages of my life, I'll be in certain stages of my life (my salary will be x1 at stage 1, x2 at stage 2, my expenses will be e1 at stage 1, e2 at stage 2, etc), so I can "roughly predict" how my personal financial situation might look

Then, I've assumed that our economy can be in one of six states: expansion, boom, recession, depression, equilibrium, and stagflation

I've written down some important rates that'd affect either my personal expenses or how my retirement fund grows

(as you can see, I'm still filling it out)

Each rate in each economic regime has three parameters associated with it: a "mean reversion strength", a mean, and a variance

(These are the vectors in each table entry)

I also have a length column for the approximate length of time any one state might last

Then, I've created a Markov table to model the way the economy might switch from one state to another every time it switches (I've defined the switching rate as "once the current regime ends, we switch")

I also have inputs associated to my expenses per stage

My plan is to then simulate what the economy and my personal financial situation might look like over the course of my life, and how it effects how much I can contribute to my savings and retirement funds

(ignore the dates and empty columns, I'm still working on it lol)

I'll also create an event manager that will throw in random shock events, like something that causes the economy to want to enter a boom, something that raises my income for the year or lowers it, one-time costs like when I have my wedding and take that money out of my savings, etc

So you see how I'm trying to use real-life situations to create a mathematical/programmatic way of simulating real life?

In real life my money and expenses and so many other things change depending on my age, family status, a billion things

[lean walrus]

So I've modeled that in this way (there's more tables)

[lean walrus]

In real life, rate parameters change over time, so I've modeled that in this way

In real life, you have shock events that change the economy unexpectedly

[lean walrus]

So I tried to model that this way

So I'm trying to see how I can structure data and computations to reflect real life situations

[strong fox]

Interesting, will give my 2c later on if I have any 2c

[lean walrus]

That's what modeling is to me :)

I'm by no means financially literate or an expert on money or the economy so this is all just using my very basic knowledge and learning as I go

But at least now I can kinda see what might happen over a variety of situations, and I've given myself the flexibility to be able to change my model parameters in a lot of ways; I can change how my personal finance situation evolves, I can change how the economy evolves (somewhat). I can change a lot of things, some of them by editing a few parameters, and others by completely reprogramming my simulator to model real life in a different way

[void crystal]

Hi @lean walrus my graduate background revolved around NP-hard problems & category theory; but I got swooped up into the world of finance doing model validation for algorithmic trading strategies.

In order to respect how vauge our understanding we have of aggregated national econometrics.. I suggest you check out Ito's lemma & how stochastic calculus can be applied to orderbook dynamics, etc.. mathematical finance & microstructrue.

[void crystal]

It will give you an idea of what we are actually taking the aggregate of when speaking about macroeconomics.

& it will make you kinder to yourself. These sorts of modeling problems are very hard before they become decently practical.

[graceful kindle]

Now I get it, thanks for explaining 👍

[lean walrus]

i hate finite elements

my solution go boom boom explode

unfortunate.

[upper stump]

Good luck

[silent marsh]

have you tried doing it backwards \silly

wait no that's actually a thing you can do

have you tried doing it backwards \srs

[lean walrus]

Wtf is doing it backwards? Using an implicit solver?

[silent marsh]

wait no i am misremembering things

ignore me

[lean walrus]

LOL

I know what's causing the issue but not how to fix it

[upper stump]

Some pdes you can solve backwards in time just be reversing the sign of the time derivative

[strong fox]

I think you might be interested in regime-switching models, like

• https://papers.ssrn.com/sol3/papers.cfm?abstract_id=146531
• https://www.sciencedirect.com/science/article/abs/pii/S0165188906002272
• https://periodicos.fgv.br/rbfin/article/view/85622

In any case #modeling's a very applied thing. Sadly that also means a lot of quants and quant math, if not #optimization math come in very typically

In theory you can model a lot of things but unless it's allowed to be very academic, then it's common for finance to come in. Another good #modeling area is epidemiology, which is less quant-sy and more biostats-y, which could be nice

[neat pine]

https://tenor.com/view/haii-hai-cat-cat-face-colon-three-gif-7065253899130675783

[lean walrus]

Thanks for sharing! I'll get back to this once I finish my current model, been a few days since I've worked on it since I've had other priorities

[lean walrus]

Yeah 😔

[vivid geode]

Biological modeling involves a lot more than just epidemiology.

Like, obviously, it’s where people have put a lot of focus (see 2020 and also generally good needing to influence fast action wrt infectious diseases). But it’s been super useful in oncological models of different cancer processes, understanding enzyme kinetics, a zillion different molecular dynamics simulations, protein modeling, the list goes on

I’m biased and think math oncology is the best

But that’s because that’s my field

[jagged palm]

(Go neuroscience!)

[azure jolt]

how good is ur mesh

[heady bison]

this is sort of a modeling/numerical inquiry but does anyone know of any information or readings on molecular optimization of API, and also if there is a technique for photopharmaceuticals

[lean walrus]

@strong fox @jagged palm @neat pine Hope you enjoy!

This is my finished draft, got all the base functionality. If you want to try it out make sure macros are enabled and run the RunSimulation macro (or you can just view whatever data is already there without running a macro in case you're worried about security).

I'm hoping to polish it by next weekend 😌

Ignore the fact that I am millions in debt by retirement age 💀 I am still debugging and optimizing parameters, most of these are fill-in values

[jagged palm]

Standard mathematician strategy

[rocky garnet]

@jagged palm what causes continual learning to work so well in the human brain that doesnt translate to LLMs/neural networks

asking since i remember you said you model brain mechanics

[jagged palm]

Hmmm can you be more specific about what you think neural networks are bad at in terms of continual learning? Are you thinking of "catastrophic forgetting"?

[rocky garnet]

yea catastrophic forgetting

[jagged palm]

One thing that might be helpful to think about is that the human brain has a ton of innate structure that neural networks don't; this is true on the level of cells (very diverse cell types with specific firing patterns and properties), circuits (the cortex has a "canonical microcircuit"), and systems (the way that different brain areas are connected together). So there's not the same risk of catastrophic forgetting because there's such a strong inductive bias on what is learnable in the first place. The brain also has critical periods, e.g. in language, after which it can dynamically shut down its flexibility to prevent forgetting crucial things.

I think this is a big open question though

[rocky garnet]

oh damn this is helpful

also another question, do you think AGI will be achieved by modeling the brain or do u think current ML methods r sufficient

[jagged palm]

I know very little about AGI but I am very skeptical about anyone who thinks the way forward is just to keep throwing more compute at things

The brain is absurdly more energy efficient than current artificial neural network systems