A machine learning-based soft finite element method

The Soft Finite Element Method (SoftFEM) has recently been introduced as a generalised optimisation framework for engineering and physical problems [1]. SoftFEM
acts as a “black box”, in which continuous or discontinuous problems can be considered by leveraging simultaneously 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.
To enhance the computational performance of SoftFEM, complementary learning
methods can be employed to model the behaviour of the fitness function without the
need to run additional FEM simulations beyond the learning phase. In this work, we
further enhance 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.
The so-called ML-accelerated SoftFEM is applied here to optimise different engineering problems. First, a 2D geometric optimisation is developed for the design of a
metamaterial [2] and an idealised protecting structure. Secondly, this framework is
used to find the optimal set of 3D printing parameters to reduce residual stress in the
manufacture of an industrial component by selective laser melting.
In conclusion, this framework can be applied to optimise different complex engineering
problems whose common limitation is their high computational cost. REFERENCES
[1] J. M. Peña, A. LaTorre, A. Jérusalem, SoftFEM: The Soft Finite Element Method,
Int. J. Numer. Methods Eng., 118:606–630, 2019.
[2] S. Bonfanti, R. Guerra, F. Font-Clos, D. Rayneau-Kirkhope, S. Zapperi, Automatic
design of mechanical metamaterial actuators. Nat. Commun., 11:4162, 2020.