ITR: Validating simulation to observed data with source coding methods

University Of California-San Diego, La Jolla CA

Investigators

Abstract

Project Summary Objectives - This project aims to develop new applied mathematical technologies that add res a widespread need in computational and simulation science: the quantitative optimization and verifi- cation of dynamical models, incorporating both chaotic and stochastic behaviors, against observed data. In the last couple of decades, great effort has been devoted to constructing simulation-based models for complex phenomena, with profound advances in both analytic techniques for numerical approximation and implementation technology on digital computers. Progress along one of the final steps to gaining scientific insight, the verification of models against Nature, has been more haphazard. When model and natural physical system produce temporally unpredictable variables one cannot match any specific time-dependent behavior but only compare statistical quantities extracted from both. Here, common practice is frequently quite crude, and is where we direct our investigation. Methods to be employed - We exploit recent developments in coding theory, specifically, context- tree methods developed for universal data compression by the information theory community. These techniques are computationally rapid, have excellent empirical performance and theoretical properties. Our goal is not literally to compress data, of course, but to use the data structures and models of the coding methods as high-quality statistical intermediaries between computational models and observed data sets, providing a common mathematical "meeting ground" where fair, and theoretically justifiable comparisons may be made. Potential impact of the project - Large scale simulations play an increasingly important role in the study of complex phenomena of national and global importance, from the efficiency, capability and byproducts of complex industrial combustion and reaction systems, to environmental moni- toring, culminating with global climate models. Predictions derived from these models inevitably enter into the public discourse about policies, with significant legal and economic impact upon many. The scientific community thus bears a burden to ensure that the models have been tested against actual experiment and cross validated with intellectually sound approaches, and herein lies the principal scientific value of the proposed investigation. The Institute for Nonlinear Science at UCSD has an excellent international reputation and has been able to attract high-quality post and pre-doctoral students with diverse backgrounds and educational emphasis. This particular project offers will offer an opportunity for the students to simultaneously learn about intriguing statistical and theoretical developments from the engineering and applied mathematics community applied, in an novel cross-disciplinary approach, to models of realistic, and important engineering problems, all set in the Institute's milieu and language of "applied theoretical" physics. The skills that a successful student will take from this project com- prise as are some mathematical fluency, physical intuition, engineering practicality and integrated numerical and symbolic computational skills. Finally, to the computational community, we anticipate developing and universally offering free-standing software to perform the analyses described in the project proposal. We hope to lower the barrier to entry for on-the-front-line computational and experimental scientists to employ these algorithms, raising the quality of common scientific practice in dynamical model verification without being so impractical or esoteric that few are able to successfully adopt our viewpoint.