Epistemic Uncertainty-Aware Barlow Twins Reduced Order Modeling for Nonlinear Contact Problems

Abstract

This study presents a method for constructing machine learning-based reduced order models (ROMs) that accurately simulate nonlinear contact problems while quantifying epistemic uncertainty. These purely non-intrusive ROMs significantly lower computational costs compared to traditional full order models (FOMs). The technique utilizes adversarial training combined with an ensemble of Barlow twins reduced order models (BT-ROMs) to maximize the information content of the nonlinear reduced manifolds. These lower-dimensional manifolds are equipped with Gaussian error estimates, allowing for quantifying epistemic uncertainty in the ROM predictions. The effectiveness of these ROMs, referred to as UQ-BT-ROMs, is demonstrated in the context of contact between a rigid indenter and a hyperelastic substrate under finite deformations. The ensemble of BT-ROMs improves accuracy and computational efficiency compared to existing alternatives. The relative error between the UQ-BT-ROM and FOM solutions ranges from approximately 3% to 8% across all benchmarks. Remarkably, this high level of accuracy is achieved at a significantly reduced computational cost compared to FOMs. For instance, the online phase of the UQ-BT-ROM takes only 0.001 seconds, while a single FOM evaluation requires 63 seconds. Furthermore, the error estimate produced by the UQ-BT-ROMs reasonably captures the errors in the ROMs, with increasing accuracy as training data increases. The ensemble approach improves accuracy and computational efficiency compared to existing alternatives. The UQ-BT-ROMs provide a cost-effective solution with significantly reduced computational times while maintaining a high level of accuracy.

Keywords

• Reduced order modeling
• data-driven modeling
• uncertainty quantification
• nonlinear contact problems
• material science