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by mturmon
2204 days ago
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I also didn't care for the coarse characterizations nearby. I take your point about the distinction between models that reproduce behavior ("simply predictive") vs. models of underlying components, and what you can learn from both. This comes up in fields I work on with machine learning models vs. physics-based models. E.g., ML models that take a field of wind vectors at time t, and predict the wind at time t+1, vs. physical models that implement the flow equations. You can fit parameters of both flavors of models to match observations, but we certainly have more confidence in the robustness of the physics-based models. About mathematically-challenged biologists - here's a hypothesis. I'll bet that if you started scanning conference abstracts in your domain for "uncertainty quantification," then some more carefully-posed modeling activities would crop up. (As you suggest, probably in the domains where more quantitative work is done.) |
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That is interesting. I don't know to what extent wind vectors are considered chaotic in the technical sense, but I would have guessed that chaotic systems would be more robustly modeled by ML instead of a physics approach. This is because I have a vague idea in my mind that ML would somehow compensate for the initial condition dependence in a way physics modeling would not. ML models tend to also have more parameters with smaller coefficients which I would identify with robustness (up to a point). I'm not gainsaying you, just expressing that I find this counterintuitive.
Of course the physics models would provide more insight into the nature of the problem.
And more generally it is my understanding that one way to define the difference between a "complex system" and a "system" is that a complex system is not predictable by physics simulations because of emergent properties and so forth.
For this reason, I interpreted OP's call for a "mathematical epistemology" not so much as a call for more physics-based modeling, or for opaque ML models, but as an expression of the need for a (currently undefined) new type of mathematical language to model, describe, and predict complex emergent systems.
> I'll bet that if you started scanning conference abstracts in your domain for "uncertainty quantification," then some more carefully-posed modeling activities would crop up.
I'm sure you're right. I let my wistful longing that there would be more of this type of thinking in biology drag me into hyperbole suggesting that there is none of it.
I appreciate the pointers to terms and books that could get me up to speed on modeling. It's not really relevant to my primary area, but I do wish these approaches well from afar. And who knows, if I learn more, maybe I can apply more of this type of approach in my work. Getting audiences to understand it would be another task entirely...