Bring it on, Complexity! Present and future of self-organising middle-out abstraction

ion is not only the essence of model building in the first place but it is also the key to expressive and efficiently solvable models. We postulate that a model should be as detailed and as comprehensive as possible, while its (numeric) utilisation for the purpose of rather specific predictions or simulations should automatically lead to model simplifications and abstractions. Whenever possible, this should happen without jeopardising the model validity; whenever necessary, the loss of accuracy the abstractions cause should be made transparent. SOMO pursues this endeavour by building and maintaining hierarchies of abstractions learned from observation. The higher the level of hierarchy, the fewer interactions have to be tested. Such tests are typically intertwined with expensive condition queries—only the state changes of the simulation will be performed to drive its evolution. Similar shortcuts by means of hierarchical organisation have been conceptualised and implemented in numerous other contexts. For instance, different levels of detail (LOD) of computer graphics resources such as meshes (differing in the numbers of vertices) and textures (differing in the numbers of pixels) are typically organised in hierarchies to allow for fast access to the most commonly used assets, whereas the graphics scenes themselves are often subjected to spatial partitioning hierarchies that allow algorithms to quickly determine which graphics objects need to be rendered in a given view port [Möller et al. (2008)]. There is a significant overlap between these culling techniques and mechanisms to speed-up the detection of collisions between geometric objects, one of the foundational functionalities of physics engines—both rely on the quick discovery of objects at specific locations. In general, the locations of the geometries may change, which is why the spatial partitioning hierarchies are dynamically created and adjusted. Dynamic adjustments of the bounding volume hierarchies are also required if the geometries themselves are dynamic, for instance if they change their scale. In this case, a method has been shown to yield rather good results that updates the upper half of the hierarchy bottom-up if one of the geometries changes. The lower half February 11, 2015 13:20 World Scientific Book 9in x 6in SOMO-bookchapter S. von Mammen & J.-Ph. Steghöfer — Present and future of SOMO abstraction 5 is only updated selectively in a top-down fashion, as soon as the changed geometry is accessed [Larsson and Akenine-Möller (2001)]. Hierarchical optimisations have also been deployed in the field of artificial intelligence. For example, costly automated planning routines can be pruned early, if high levels of a hierarchy reflect the adherence of a plan’s most critical variables [Sacerdoti (1974)]. Similarly, reflective agents need to plan their coordination—hierarchical abstractions of their interaction partners may increase their decision performance, too [Durfee (1999)]. 1.4 Emergence and Hierarchies in a Natural System In Rasmussen et al. (2001), an approach, or “Ansatz”, to capturing the emergence of physicochemical compound objects with according emergent properties is described. We want to use their example to illustrate the mechanics of SOMO. In their experiments, attracting, repelling, and bonding forces among charged monomers and water molecules are shown to result in higher-order polymer and micelle formations—at each level, the resulting compounds obtain novel physical and chemical properties. In the model, hydrophobic monomers bind to hydrophilic monomers as well as to polymerised hydrophobic monomers, which results in 2-order amphiphilic polymers which, in turn, aggregate in 3-order micelle structures. At each stage, the resultant compounds exhibit properties different from the underlying constituents; The aggregating nature of the process yields compounds of greater size but it also leads to varying qualitative, geometric structures and differentiated physiochemical behaviours. An adapted illustration of the emergent process is shown in Figure 1.1.