Kenneth Man-kam Yip

AIJ Journal 1996 Journal Article

Model simplification by asymptotic order of magnitude reasoning

• Kenneth Man-kam Yip

One of the hardest problems in reasoning about a physical system is finding an approximate model that is mathematically tractable and yet captures the essence of the problem. This paper describes an implemented program AOM which automates a powerful simplification method. AOM is based on two domain-independent ideas: self-consistent approximations and asymptotic order of magnitude reasoning. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i. e. , terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels. We demonstrate its power by showing how the program simplifies difficult fluid models described by coupled nonlinear partial differential equations with several parameters. We believe the derivation given by AOM is more systematic and easily understandable than those given in published papers.

AAAI Conference 1993 Conference Paper

Model Simplification by Asymptotic Order of Magnitude Reasoning

• Kenneth Man-kam Yip

One of the hardest problems in reasoning about a physical system is finding an approximate model that is mathematically tractable and yet captures the essence of the problem. Approximate models in science are often constructed by informal reasoning based on consideration of limiting cases, knowledge of relative importance of terms in the model, and understanding of gross features of the solution. We show how an implemented program can combine such knowledge with a heuristic simplification procedure and an inequality reasoner to simplify difficult fluid equations.

AIJ Journal 1991 Journal Article

Understanding complex dynamics by visual and symbolic reasoning

• Kenneth Man-kam Yip

Professional scientists and engineers routinely use nonverbal reasoning processes and graphical representations to organize their thoughts and as part of the process of solving otherwise verbally presented problems. This paper presents a computational theory and an implemented system that capture some aspects of this style of reasoning. The system, consisting of a suite of computer programs collectively known as KAM, uses numerical methods as a means to shift back and forth between symbolic and geometric methods of reasoning. The KAM program has three novel features: (1) it articulates the idea that “visual mechanisms are useful for problem solving” into a workable computational theory, (2) it applies the approach to a domain of great technical difficulty, the field of complex nonlinear chaotic dynamics, and (3) it demonstrates the power of the approach by solving problems of real interest to working scientists and engineers.

AAAI Conference 1988 Conference Paper

Generating Global Behaviors Using Deep Knowledge of Local Dynamics

• Kenneth Man-kam Yip

AAAI Conference 1987 Conference Paper

Extracting Qualitative Dynamics from Numerical Experiments

• Kenneth Man-kam Yip

The Phase Space is a powerful tool for representing and reasoning about the qualitative behavior of non-linear dynamical systems. Significant physical phenomena of the dynamical system - periodicity, recurrence, stability and the like - are reflected by outstanding geometric features of the trajectories in the phase space. Successful use of numerical computations to completely explore the dynamics of the phase space depends on the ability to (1) interpret the numerical results, and (2) control the numerical experiments. This paper presents an approach for the automatic reconstruction of the full dynamical behavior from the numerical results. The approach exploits knowledge of Dynamical Systems Theory which, for certain classes of dynamical systems, gives a complete classification of all the possible types of trajectories, and a list of bifurcation rules which govern the way trajectories can fit together in the phase space. These bifurcation rules are analogous to Waltz’s consistency rules used in labeling of line drawings. The approach is applied to an important class of dynamical system: the area-preserving maps, which often arise from the study of Hamiltonian systems. Finally, the paper describes an implemented program which solves the interpretation problem by using techniques from computational geometry and computer vision.

IJCAI Conference 1985 Conference Paper

Tense, Aspect, and Cognitive Representation of Time

• Kenneth Man-kam Yip