# Efficient Deep Learning-based Forward Solvers for Brain Tumor Growth Models

arXiv: https://arxiv.org/abs/2501.08226 · HTML: https://mlsanity.com/paper/2501.08226/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 14 Jan 2025.

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

- [Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans and Bayesian Inference](https://mlsanity.com/paper/1807.00499/) (2018)
- [Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling](https://mlsanity.com/paper/2111.04090/) (2021)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)

## Built on by (most cited first, 1 of 1)

- [Multi-encoder nnU-Net outperforms transformer models with self-supervised pretraining](https://mlsanity.com/paper/2504.03474/) (2025)

## Abstract (arXiv)

Glioblastoma, a highly aggressive brain tumor, poses major challenges due to its poor prognosis and high morbidity rates. Partial differential equation-based models offer promising potential to enhance therapeutic outcomes by simulating patient-specific tumor behavior for improved radiotherapy planning. However, model calibration remains a bottleneck due to the high computational demands of optimization methods like Monte Carlo sampling and evolutionary algorithms. To address this, we recently introduced an approach leveraging a neural forward solver with gradient-based optimization to significantly reduce calibration time. This approach requires a highly accurate and fully differentiable forward model. We investigate multiple architectures, including (i) an enhanced TumorSurrogate, (ii) a modified nnU-Net, and (iii) a 3D Vision Transformer (ViT). The nnU-Net achieved the best overall results, excelling in both tumor outline matching and voxel-level prediction of tumor cell concentration. It yielded the lowest MSE in tumor cell concentration compared to ground truth numerical simulation and the highest Dice score across all tumor cell concentration thresholds. Our study demonstrates significant enhancement in forward solver performance and outlines important future research directions.