# Data-driven Uncertainty Quantification in Computational Human Head Models

arXiv: https://arxiv.org/abs/2110.15553 · HTML: https://mlsanity.com/paper/2110.15553/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 61 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs](https://mlsanity.com/paper/2011.15110/) (2020)
- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [Grassmannian diffusion maps based dimension reduction and classification for high-dimensional data](https://mlsanity.com/paper/2009.07547/) (2020)
- [Grassmannian diffusion maps based surrogate modeling via geometric harmonics](https://mlsanity.com/paper/2109.13805/) (2021)

## Built on by (most cited first, 3 of 3)

- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications](https://mlsanity.com/paper/2302.08329/) (2023)
- [Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography](https://mlsanity.com/paper/2607.14193/) (2026)

## Abstract (arXiv)

Computational models of the human head are promising tools for estimating the impact-induced response of brain, and thus play an important role in the prediction of traumatic brain injury. Modern biofidelic head model simulations are associated with very high computational cost, and high-dimensional inputs and outputs, which limits the applicability of traditional uncertainty quantification (UQ) methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of strain fields highlight significant spatial variation in model uncertainty, and reveal key differences in uncertainty among commonly used strain-based brain injury predictor variables.