# Use of Deep Neural Networks for Uncertain Stress Functions with Extensions to Impact Mechanics

arXiv: https://arxiv.org/abs/2311.16135 · HTML: https://mlsanity.com/paper/2311.16135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 3 of 3)

- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting](https://mlsanity.com/paper/2211.02989/) (2022)
- [Predictive Factors of Kinematics in Traumatic Brain Injury from Head Impacts Based on Statistical Interpretation](https://mlsanity.com/paper/2102.05020/) (2021)

## Abstract (arXiv)

Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific material. Further, large deformations, high strain-rates, temperature sensitivity, and effect of material parameters compound modeling challenges. We propose a generalized deep neural network approach to model stress as a state function with quantile regression to capture uncertainty. We extend these models to uniaxial impact mechanics using stochastic differential equations to demonstrate a use case and provide a framework for implementing this uncertainty-aware stress function. We provide experiments benchmarking our approach against leading constitutive, machine learning, and transfer learning approaches to stress and impact mechanics modeling on publicly available and newly presented data sets. We also provide a framework to optimize material parameters given multiple competing impact scenarios.