# Towards out of distribution generalization for problems in mechanics

arXiv: https://arxiv.org/abs/2206.14917 · HTML: https://mlsanity.com/paper/2206.14917/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 119 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 30 of 56)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [An Introduction to Deep Reinforcement Learning](https://mlsanity.com/paper/1811.12560/) (2018)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)

## Built on by (most cited first, 11 of 11)

- [Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2311.11114/) (2023)
- [Interpreting and generalizing deep learning in physics-based problems with functional linear models](https://mlsanity.com/paper/2307.04569/) (2023)
- [A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty](https://mlsanity.com/paper/2403.08901/) (2024)
- [SLE-FNO: Single-Layer Extensions for Task-Agnostic Continual Learning in Fourier Neural Operators](https://mlsanity.com/paper/2603.20410/) (2026)
- [Segmenting mechanically heterogeneous domains via unsupervised learning](https://mlsanity.com/paper/2308.15697/) (2023)
- [Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators](https://mlsanity.com/paper/2511.05456/) (2025)
- [Quantifying Robustness: A Benchmarking Framework for Deep Learning Forecasting in Cyber-Physical Systems](https://mlsanity.com/paper/2504.03494/) (2025)
- [Machine Learning-Guided Design of Non-Reciprocal and Asymmetric Elastic Chiral Metamaterials](https://mlsanity.com/paper/2404.13215/) (2024)
- [Trimming the Risk: Towards Reliable Continuous Training for Deep Learning Inspection Systems](https://mlsanity.com/paper/2409.09108/) (2024)
- [Learning to Test: Latent Representation Learning for Dynamic Instability Detection](https://mlsanity.com/paper/2604.10967/) (2026)
- [A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling](https://mlsanity.com/paper/2606.19378/) (2026)

## Abstract (arXiv)

There has been a massive increase in research interest towards applying data driven methods to problems in mechanics. While traditional machine learning (ML) methods have enabled many breakthroughs, they rely on the assumption that the training (observed) data and testing (unseen) data are independent and identically distributed (i.i.d). Thus, traditional ML approaches often break down when applied to real world mechanics problems with unknown test environments and data distribution shifts. In contrast, out-of-distribution (OOD) generalization assumes that the test data may shift (i.e., violate the i.i.d. assumption). To date, multiple methods have been proposed to improve the OOD generalization of ML methods. However, because of the lack of benchmark datasets for OOD regression problems, the efficiency of these OOD methods on regression problems, which dominate the mechanics field, remains unknown. To address this, we investigate the performance of OOD generalization methods for regression problems in mechanics. Specifically, we identify three OOD problems: covariate shift, mechanism shift, and sampling bias. For each problem, we create two benchmark examples that extend the Mechanical MNIST dataset collection, and we investigate the performance of popular OOD generalization methods on these mechanics-specific regression problems. Our numerical experiments show that in most cases, while the OOD generalization algorithms perform better compared to traditional ML methods on these OOD problems, there is a compelling need to develop more robust OOD generalization methods that are effective across multiple OOD scenarios. Overall, we expect that this study, as well as the associated open access benchmark datasets, will enable further development of OOD generalization methods for mechanics specific regression problems.