# Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids

arXiv: https://arxiv.org/abs/2407.10732 · HTML: https://mlsanity.com/paper/2407.10732/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2024.

## Built on by (most cited first, 5 of 5)

- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [Autoencoder-based non-intrusive model order reduction in continuum mechanics](https://mlsanity.com/paper/2509.02237/) (2025)
- [Machine learning surrogate models of many-body dispersion interactions in polymer melts](https://mlsanity.com/paper/2503.15149/) (2025)
- [Adaptive Fusion Graph Network for 3D Strain Field Prediction in Solid Rocket Motor Grains](https://mlsanity.com/paper/2512.23443/) (2025)
- [Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates](https://mlsanity.com/paper/2608.11435/) (2026)

## Abstract (arXiv)

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.