Spatial Aggregation: Theory and Applications

TL;DR

This paper introduces a unified computational paradigm called spatial aggregation, which organizes imagistic reasoning for solving complex scientific problems involving dynamical systems, fluid motion, and control by creating multi-layered spatial representations.

Contribution

It develops a general framework for imagistic problem solvers using spatial aggregation, unifying diverse reasoning tasks through a common set of operators and data structures.

Findings

Successfully describes three problem solvers (KAM, MAPS, HIPAIR) using the spatial aggregation framework.

Demonstrates that the paradigm can handle complex scientific reasoning tasks.

Provides a modular, multi-layered approach to structure and behavior inference in dynamical systems.

Abstract

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.