A note on data-driven methods for mechanical problems with non-unique solutions

Abstract This article explores certain limitations of some well-known methods employed in machine learning when applied for regression of mechanical models that might exhibit multiple solutions. Using the buckling of a beam as a prototypical example of a mechanical problem with multiple solutions, we show that neural networks, Bayesian methods, random forest, and similar forward techniques are ill-suited for approximating the solution to such problems. Instead, data-driven methods based on set projections are intrinsically capable of coping with multiple solution paths satisfactorily, incorporating in addition the stochasticity of the response.