A machine learning-based soft finite element method

The Soft Finite Element Method (SoftFEM) has recently been introduced as a generalised optimisation framework seamlessly combining two numerical methods: a partial differential equation solver (FEM) and a wrapper made of several stochastic heuristic optimisation methods taken from soft computing to provide a generalised optimisation framework for engineering and physical problems [1]. SoftFEM uses Multiple Offspring Sampling (MOS) [2] as the overarching framework used as a “black box” in which continuous or discontinuous problems can be considered by leveraging simultaneously optimisation techniques for exploration and exploitation in the search for the optimum configurations without the need to know a priori which one of the two strategies is best fitted to the problem at hand. The use of a fitness function based on FEM calculations leads to considerable computational cost. To enhance the computational performance of SoftFEM in this work, we further enrich SoftFEM with machine learning (ML) based surrogate models that approximate the results of the actual FEM calculations, thus allowing the optimisation methods to explore more areas of the search space without the need to run additional FEM simulations beyond the learning phase. The developed ML-accelerated SoftFEM is applied here to a series of engineering challenges, ranging from metamaterials to civil engineering.
REFERENCES
[1] J. M. Pe˜na, A. LaTorre, A. J´erusalem, SoftFEM: The Soft Finite Element Method.
Int. J. Numer. Methods Eng., Vol. 118, pp. 606–630, 2019.
[2] A. LaTorre, S. Muelas, J. M. Pena. Evaluating the multiple offspring sampling framework on complex continuous optimization functions. Memetic Computing, Vol. 5, pp.
295–309, 2013