Chaos researchers can now predict perilous points of no return

https://www.quantamagazine.org/ai-algorithm-foresees-chaotic-tipping-points-20220915/

by theafh • 4 years ago

145 20 4 years ago

c-linkage2• 4 years ago

This sounds similar to work I did years ago to combine phase-space manifolds with a rule-based expert system to address problems diagnosing failures in mechanical systems exhibiting multi-modal operating regimes.

Hopefully the researchers found a simpler computational method than I did in trying to mate those two systems together. :)

What really caught my attention was the output of a probability curve showing how the system might operate in the never-before-seen regimes once the tipping point was reached. The ability to predict behavior outside the training set is a huge win. My method was only predictive while the the system operated in the training regime; outside that regime it was useless.

uoaei• 4 years ago

Did your manifolds incorporate any notion of system dynamics, or was it a simpler curve-fitting procedure?

c-linkage2• 4 years ago

I computed a bounding volume in a hyper-dimensional space containing all sensor instruments on the system. The volume was constructed to encompass the entire sensor state space of many previously recorded "normal" operating periods (from startup through steady-state and shutdown).

New operating regimes where then compared to the volume, and any excursions were considered diagnostically relevant conditions.

The cool part (to me, at least) was that the direction of the vector as system state trajectory exited the volume could be put through a classifier that would effectively tell you what went wrong.

isoprophlex2• 4 years ago

The researchers appear to use reservoir computing approaches, which usually aren't terribly costly in terms of cpu cycles.

I'm unsure about real life applications though because one of the quoted papers [0] only uses idealized strange attractors or whatever they're called -- only systems described by math.

I'd be very interested to learn how the methods apply to real-world mechanical chaotic systems.

This isn't my field of expertise at all, maybe someone has some experience with this?

[0] https://arxiv.org/pdf/2207.00521.pdf

rch• 4 years ago

Abstract link for convenience:

https://arxiv.org/abs/2207.00521

westurner• 4 years ago

Could this detect/predict/diagnose e.g. mechanical failures in engines and/or motors, and health conditions, given sensor fusion?

Sensor fusion https://en.wikipedia.org/wiki/Sensor_fusion

Steady state https://en.wikipedia.org/wiki/Steady_state :

In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. [1]

https://github.com/topics/steady-state

Control systems https://en.wikipedia.org/wiki/Control_system

https://github.com/topics/control-theory

Flap (disambiguation) > Computing and networks > "Flapping" (nagios alert fatigue,) https://en.wikipedia.org/wiki/Flap

Perceptual Control Theory (PCT) > Distinctions from engineering control theory https://en.wikipedia.org/wiki/Perceptual_control_theory :

In the artificial systems that are specified by engineering control theory, the reference signal is considered to be an external input to the 'plant'.[7] In engineering control theory, the reference signal or set point is public; in PCT, it is not, but rather must be deduced from the results of the test for controlled variables, as described above in the methodology section. This is because in living systems a reference signal is not an externally accessible input, but instead originates within the system. In the hierarchical model, error output of higher-level control loops, as described in the next section below, evokes the reference signal r from synapse-local memory, and the strength of r is proportional to the (weighted) strength of the error signal or signals from one or more higher-level systems. [26]
In engineering control systems, in the case where there are several such reference inputs, a 'Controller' is designed to manipulate those inputs so as to obtain the effect on the output of the system that is desired by the system's designer, and the task of a control theory (so conceived) is to calculate those manipulations so as to avoid instability and oscillation. The designer of a PCT model or simulation specifies no particular desired effect on the output of the system, except that it must be whatever is required to bring the input from the environment (the perceptual signal) into conformity with the reference. In Perceptual Control Theory, the input function for the reference signal is a weighted sum of internally generated signals (in the canonical case, higher-level error signals), and loop stability is determined locally for each loop in the manner sketched in the preceding section on the mathematics of PCT (and elaborated more fully in the referenced literature). The weighted sum is understood to result from reorganization.
Engineering control theory is computationally demanding, but as the preceding section shows, PCT is not. For example, contrast the implementation of a model of an inverted pendulum in engineering control theory [27] with the PCT implementation as a hierarchy of five simple control systems. [28]

Structural Equation Modeling: https://en.wikipedia.org/wiki/Structural_equation_modeling https://github.com/topics/structural-equation-modeling

ros2_control https://control.ros.org/master/index.html

Limit cycle https://en.wikipedia.org/wiki/Limit_cycle

Finite Element Analysis https://en.wikipedia.org/wiki/Finite_element_method

#FEM: Finite Element Method (for ~solving coupled PDEs Partial Differential Equations)
#FEA: Finite Element Analysis (applied FEM)

awesome-mecheng > Finite Element Analysis: https://github.com/m2n037/awesome-mecheng#fea

Animats• 4 years ago

Actual paper: https://journals.aps.org/prresearch/abstract/10.1103/PhysRev...

More useful than Quanta Magazine hype.

The basic idea is that you've got a process with feedback that behaves like a chaotic attractor, moving around a lot but staying in a stable regime. Where's the edge of that regime?

Here's a video of a leaky bucket waterwheel that exhibits chaotic behavior.[1] If all you had was a graph of rotational velocity, could you tell when it was about to reverse? Probably. Could you train a machine learning system to do that? Yes.

It's not clear how general a result this is, but undoubtedly someone is already trying it on financial data.

[1] https://www.youtube.com/watch?v=7A_rl-DAmUE

mellavora• 4 years ago

yes, back in 1990-2000. See https://www.econstor.eu/bitstream/10419/40278/1/338823255.pd... though I was thinking of another paper which I couldn't find with a quick google.

See also Mandelbrot, fractals and scaling in finance, 1997 https://link.springer.com/book/10.1007/978-1-4757-2763-0

thenanante• 4 years ago

Using a chaotic system to predict a chaotic system.

makach• 4 years ago

does that mean we can keep entropy in check?

tbalsam• 4 years ago

Entropy is like Mundo -- it goes where it pleases.

airstrike• 4 years ago

Reading this as I download patch 3.4 for WR, I believe in the simulation just a bit more

golemotron2• 4 years ago

I wonder whether this approach can be used to predict the behavior of social systems, given enough historical data.

sroussey• 4 years ago

Phycohistory.

;)

golemotron2• 4 years ago

..on ML

FunnyBadger• 4 years ago

I call BS on this. It would require negating entropy.

suoduandao2• 4 years ago

Our current understanding of entropy is probably about as accurate as Newton's understanding of gravity, not something we want to get dogmatic about.

pishpash• 4 years ago

Even looking at the title only you can tell this is from Quantum Mag. What is it about Quantum Mag that produces these pseudoscientific-sounding titles (regardless of content)?

fedeb95• 4 years ago

Misleading title, second time this week. "Can" becomes a "could in the future" in the article.

Chaos researchers can now predict perilous points of no return

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