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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA


Benjamin Koo

Class of 2004


Benjamin Koo is a doctoral student at MIT's Engineering Systems Division. His research focuses on the theoretical foundation of system architecting. Specifically, he is designing a visual simulation language that can be used by architects across disciplinary boundaries.

Prior to this full-time research endeavor, he practiced software architecting in the information industry, serving primarily telecommunication and financial industry clients. Based on his work experience, he found that the working language utilized for design and implementation of engineered artifacts plays a central role in coordinating the interactive events in product and organizational development. The book, A New Kind of Science (NKS), captured his imagination about a new kind of visual programming language, a graphical language that can represent the evolutionary and revolutionary behavior of interacting systems.

Project: Visualizing Bayesian Belief Networks as Colored Cellular Automata

Reasoning forward and backward in time is a desired feature in many decision-making scenarios. Furthermore, decision makers need a general yet intuitive mechanism to visualize and to assess interactive effects given partial information about a set of variables. This project will utilize multicolored cellular automata (CA) as a visual metaphor to represent variable interactions over space and time. To support both forward and backward reasoning mechanisms, we will create a user interface that allows users to specify known cell colors at arbitrary points in time and observe the changes in cell colors triggered by user inputs. To provide a generalizable calculation rule that can infer cell states along both directions in time, Bayes' Theorem and conditional probability functions will be utilized to encode the rules of cell interactions. A well-known Bayesian Belief Network (BBN) algorithm will serve as the computational basis of these time-independent probabilistic automata. This approach may provide a more intuitive interface to explore NKS-related problems.

Bidirectional Inference in Cellular Automata

To demonstrate the utility of this bidirectional inference, we will apply this probabilistic CA model to analyze tradeoffs between modularity options in engineering systems. Since BBN algorithms can assess cell interactions bidirectionally in time, this approach allows decision makers to formulate their problems by either specifying known initial states to identify reachable future states or, given the desired future state, to infer backward about likely initial conditions. This study will demonstrate that the BBN formulation of cell interaction rules is generalizable to a wide range of problems, since it allows users to represent domain-specific knowledge based on conditional probability tables without changing the underlying computational algorithms.

Applications to Engineering Systems

The Design Structure Matrix (DSM) is a well-known technique for representing the modularity of engineering systems. DSM analysis is often applied to help system designers identify modularity choices in complex systems based on binary interactive relationships. The structure of the DSM can be modeled as a variable-range 1D cellular automaton. However, the strength of interactions between modules is often neglected in DSM. In this project, we will show that a bidirectional CA inference engine can encode the strength of relationships between different modules and therefore provide additional expressive power for DSM and expand its analytical utility in making modularity choices for engineering systems.