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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月26日

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  • Ignacio Romero,
  • Michael Ortiz

摘要

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.