Data-Driven Acceleration and Discovery of Computational Models (White Paper Tracking Number: A671)
Abstract
The proposed work addresses the urgent need for the development of a mathematical frameworkfor the analysis and development of model,-centric and data-informed predictive computationalscience and engineering; this will allow for the integration of centuries of math,ematical modelingexperience, decades of computational modeling experience, and recent innovations in algorithms,computer design and,hardware stemming from the current revolution in the data sciences. Creatingthis framework requires a new theory at the interfaces o,f machine learning, numerical analysis andstatistics. This theory will underpin computational science and engineering in the twenty,firstcentury. The proposed research will address this problem in the specific setting of the learning ofmappings between spaces of f,unctions ? input-output maps. This setting has numerous applicationsin the solution of system-level tasks arising in science and eng,ineering. The proposed fundamentalresearch will be developed in tandem withapplications, some of direct of interest to DoD, such asc,limate modeling, materials science and robotics. The goal of the proposed research is to develop the mathematical framework need,ed for algorithmsthat accelerate execution of black box computer code, by means of a data-informed surrogate,or algorithms that disc,over a structured computational model when a first principles modelis not available, as often arises for cyber-physical systems. The, technical approach is to viewthe black box or cyber-physical system as an input-output map and approximate it by a cheaper(in terms, of computational cost) or safer surrogate. It is natural to exploit ideas from machinelearning to identify a surrogate. However, st,andard machine learning tools do not scale to the highdimensional input and outputs encountered in physical science applications, no,r do they readily incorporate domain-specific knowledge. The novelty underpinning the approach proposed here is toview the map as ac,ting between Banach spaces of functions, the setting needed to allow for a principleddevelopment and analysis of data-driven scalabl,e surrogates. It is also a natural setting inwhich to incorporate (physical) laws representing domain-specific conceptual understand,ing. Theapproach requires development of a new theory at the interfaces of machine learning, numericalanalysis and statistics. The o,bjectives are to introduce novel designs for surrogate maps, to proveerror bounds on the surrogates in order to certify computations, and evaluate the relative efficiencyof different methods, and to develop new data-generation processes in order to learn the surrog,atemaps in an optimal fashion from limited data; additional applied objectives focus on applicationsto inverse problems and data ass,imilation. The proposed perspective on surrogate maps between spaces of functions constitutes a paradigm shift with wide-rangi,ng anticipated outcomes over a decadal time-horizon. The work will lead to a new mathematical framework for algorithm development an,d analysis. And the deep understanding arising from this framework will enable, through acceleration of the repeated evaluation of t,he core input-output map, solution of system level tasks in key areas such as optimal design, uncertainty quantification, inversion,and time-stepping. The understanding will also lead to solution of system-level tasks arising in cyber-physical systems, currently n,ot even contemplated, through discovery of data-driven models which respect physical and mathematical principles. Approved for p,ublic release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 08, 2022
- Source ID
- N000142212790
Entities
People
- Andrew M. Stuart
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy