The intersection of machine learning and GIS is getting broader as we ask increasingly pragmatic questions related to complex spatial phenomena. Whether it is predicting traffic patterns in L.A. or the probability of being hit by the next big storm, we need answers to critical questions to make impactful decisions. In this blog, we'll explore an essential component needed towards answering such a question: what will the future climate be in U.S.? This question requires calibrating a global climate model with spatially-limited local temperature measurements. In a planet that is constantly warming, calibrating global climate models is vital to answer questions ranging from what will the average temperature be in Redlands in November 2050 to which Canadian cities will be wine country in the future.

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR system as an extension to a SOAR-like problem solving architecture. The work is in a framework in which DR is modeled as a process where subtasks are solved, as appropriate, either by inference from symbolic representations or by interaction with a diagram, i.e., perceiving specified information from a diagram or modifying/creating objects in a diagram in specified ways according to problem solving needs. The perceptions and actions in most DR systems built so far are hand-coded for the specific application, even when the rest of the system is built using the general architecture. The absence of a general framework for executing perceptions/actions poses as a major hindrance to using them opportunistically -- the essence of open-ended search in problem solving. Our goal is to develop a framework for executing a wide variety of specified perceptions and actions across tasks/domains without human intervention. We observe that the domain/task-specific visual perceptions/actions can be transformed into domain/task-independent spatial problems. We specify a spatial problem as a quantified constraint satisfaction problem in the real domain using an open-ended vocabulary of properties, relations and actions involving three kinds of diagrammatic objects -- points, curves, regions. Solving a spatial problem from this specification requires computing the equivalent simplified quantifier-free expression, the complexity of which is inherently doubly exponential. We represent objects as configuration of simple elements to facilitate decomposition of complex problems into simpler and similar subproblems. We show that, if the symbolic solution to a subproblem can be expressed concisely, quantifiers can be eliminated from spatial problems in low-order polynomial time using similar previously solved subproblems. This requires determining the similarity of two problems, the existence of a mapping between them computable in polynomial time, and designing a memory for storing previously solved problems so as to facilitate search. The efficacy of the idea is shown by time complexity analysis. We demonstrate the proposed approach by executing perceptions and actions involved in DR tasks in two army applications.

In many spatial problems, it can be difficult to create a state representation that is abstract enough so that irrelevant details are ignored, but also accurate enough so that important states of the problem can be differentiated. This is especially difficult for agents that address a variety of problems. A potential way to resolve this difficulty is by using two representations of the spatial state of the problem: one abstract and one concrete, along with internal (imagery) operations that modify the concrete representation based on the contents of the abstract representation. In this paper, we argue that such a system can allow plans and policies to be expressed that can better solve a wider class of problems than would otherwise be possible. An example of such a plan is described. The theoretical aspects of what imagery is, how it differs from other techniques, and why it provides a benefit are explored.

This paper is concerned with spatial aspects of perception and action in a simple robot. To this end, the problem of designing a robot-controller for a robot in a simulated environment is considered. The environment is a two-dimensional tabletop with movable polygonal shapes on it. The robot has an eye which'sees' an area of the tabletop centred on itself, with a resolution which decreases from the centre to the periphery. Algorithms are oresented for simulating the motion and collision of two dimensional shapes in this environment.