# Predicting Brain Morphometry with MT-GNN: Mesh Evolution in Continuous Time with Graph-Based Metric Tensor Embeddings

arXiv: https://arxiv.org/abs/2608.05132 · HTML: https://mlsanity.com/paper/2608.05132/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [TransforMesh: A Transformer Network for Longitudinal modeling of Anatomical Meshes](https://mlsanity.com/paper/2109.00532/) (2021)
- [Predicting Shape Development: a Riemannian Method](https://mlsanity.com/paper/2212.04740/) (2022)

## Abstract (arXiv)

Predicting how a subcortical structure's shape will evolve from a few prior scans could support prognosis and clinical-trial enrichment. Existing longitudinal mesh predictors either extrapolate shape trajectories via high-dimensional embeddings or regress vertex deformations directly. We instead predict the surface's intrinsic geometry in continuous time: a single per-structure graph network predicts the future per-vertex first fundamental form (metric tensor) for an arbitrary causal multiple-visit history and an arbitrary prediction horizon, conditioned on a Fourier encoding of the lead time. The predicted metric is decoded into a surface by a differentiable As-Rigid-As-Possible solver, and the model is trained end-to-end on the rigid-aligned vertex error. Training through the reconstruction keeps the decoded prediction a valid surface and consistently improves it. On 14 subcortical structures from the ADNI dataset, the proposed mesh evolution model (MT-GNN) predicts best among the evaluated methods at every horizon (-2.29% mean vertex error vs. the temporal mean, p=6.1×10-5, beating it on 14/14 structures), ahead of geodesic shape regression (DCM, -0.19%) and a mesh transformer (TransforMesh, -0.45%; p=1.2×10-4), with the lead widening as the horizon grows.