A manifold learning approach to data-driven computational materials and processes

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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. 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 universal laws while minimizing the need of explicit, often phenomenological, models. They are based on manifold learning methodologies.