A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, ...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be confident on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority of existing models lack of generality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. This technique is based on the use of manifold learning methodologies, that allow to extract the relevant information from large experimental datasets

Dynamic-data-driven real-time computational mechanics environment

The proliferation of sensor networks in various areas of technology has enabled real-time behavioral monitoring of various physical systems in various length and time scales. The opportunity to use these data dynamically for improving speed, accuracy, and general performance of predictive behavior modeling simulation is of paramount importance. The present paper identifies enabling modeling methods and computational strategies that are critical for achieving real-time simulation response of very large and complex systems. It also discusses our choices of these technologies in the context of sample multidisciplinary computational mechanics applications

Dynamic-data-driven real-time computational mechanics environment

Abstract. The proliferation of sensor networks in various areas of technology has enabled real-time behavioral monitoring of various physical systems in various length and time scales. The opportunity to use these data dynamically for improving speed, accuracy, and general performance of predictive behavior modeling simulation is of paramount importance. The present paper identifies enabling modeling methods and computational strategies that are critical for achieving real-time simulation response of very large and complex systems. It also discusses our choices of these technologies in the context of sample multidisciplinary computational mechanics applications.