A Diffusion Maps workflow enabled by Neural Networks and Equation-free calculations for multi scale material and process modelling

The ambition of this fellowship, hosted by Professor S.P.A.

Bordas (UL), is to propose a nonlinear manifold learning framework, in particular to implement the Diffusion Maps methodology, enabled by “equation-free” calculations and Artificial Neural Networks, in the context of multi-scale materials and process modeling and design.

The goal is to push the boundaries of the “Digital Twins” paradigm beyond the current-state-of-the-art and to establish a methodological framework that links macro-scale process parameters and conditions to properties of complex materials, in an effort to meet the current market-driven demands for efficiency, scalability, safety, sustainability and innovation.

The proposed approach is based on the current trends in materials and process modeling, on which the host is in the best possible position to advise as a world leading expert.

Effectively, the fellowship sets the stage for interdisciplinary integration: Starting from the requirement for a specific set of properties, we must be able to predict the appropriate material structure, its capabilities and limitations and to propose ideal processing steps that will enable large-scale production.

In this context, machine learning in the form of Diffusion Maps will be implemented for dimensionality reduction aiming to the reach the maximum possible size compression.

The equation-free approach will be integrated with Diffusion Maps, in order to efficiently explore the, typically large, parameter space and Artificial Neural Networks will be applied as a means of leveraging the abundantly available digitized images to “learn” the long-term dynamics of the material behavior.