I'm interested in establishing a framework to dynamically reduce explicit/classical representations into various orders of abstraction with intent to simplify computation necessary for the simulation of systems. If you prefer that I specify how I imagine these systems might be, consider a very large set of points which may exhert various forces upon each other (classically, like particles) within the system e.g. exhibits contact dynamics and supports modelling external forces and fields from outside the system of points. Consider a large number of these points behave like a fluid, and they're contained in a way that can be approximated using a planar-surface fluid approximation method. I haven't researched these enough yet (planar fluid approximations; something to do with wavelets), but I think it's an interesting idea to explore means to adaptively approximate systems using poweful mathematical generalizations. Of course, this particular type of fluid approximation I just gave for example is very limited (planar), but that's why I'm interested in adaptiveness; specifically a broad framework of malleate abstraction devices that can effectively perform these adaptations.

 

I like to think of this strategy like the theme of the book "A Wrinkle In Time"; virtually traversing spacetime by welding two points together into one. Rather than brute forcing the simulation, congruences may be identified (transitive actions, linear dependence, fractal phenomena etc.) to yield shortcuts and inherently simplify computation. You may call this an adaptive model or approximation.

I'm thinking of some kind of "tensor automaton, " if you can imagine what I mean by that (think of an intelligent lego sculpture). Are you aware of any ideas or do you know of information that is relevant and maybe interesting to this topic? Please discuss your thoughts.

Edited March 31, 201312 yr by Ben Banana

*bump*

 

Shall I repost this in a different community? This place...