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Image-based simulation is becoming an appealing technique to homogenize properties of real microstructures of heterogeneous materials. However fast computation techniques are needed to take decisions in a limited timescale. Techniques based on standard computational homogenization are seriously compromised by the real-time constraint. The combination of model reduction techniques and high performance computing contribute to alleviate such a constraint but the amount of computation remains excessive in many cases. In this paper we consider an alternative route that makes use of techniques traditionally considered for machine learning purposes in order to extract the manifold in which data and fields can be interpolated accurately and in real-time and with minimum amount of online computation. Locallly Linear Embedding-LLE-is considered in this work for the real-time thermal homogenization of heterogeneous microstructures.

An efficient numerical approach is presented for the simulation of mold filling process with random fibrous permeability as input.