# A Learnable Prior Improves Inverse Tumor Growth Modeling

arXiv: https://arxiv.org/abs/2403.04500 · HTML: https://mlsanity.com/paper/2403.04500/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [The Relative Performance of Ensemble Methods with Deep Convolutional Neural Networks for Image Classification](https://mlsanity.com/paper/1704.01664/) (2017)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [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)
- [Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect](https://mlsanity.com/paper/2006.09932/) (2020)
- [Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans](https://mlsanity.com/paper/2311.16536/) (2023)
- [Continuous-Time Deep Glioma Growth Models](https://mlsanity.com/paper/2106.12917/) (2021)
- [Ensemble inversion for brain tumor growth models with mass effect](https://mlsanity.com/paper/2106.06016/) (2021)
- [Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)](https://mlsanity.com/paper/2308.09467/) (2023)
- [PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems](https://mlsanity.com/paper/2305.11056/) (2023)

## Built on by (most cited first, 9 of 9)

- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)
- [PREDICT-GBM: A multi-center platform to advance personalized glioblastoma radiotherapy planning](https://mlsanity.com/paper/2509.13360/) (2025)
- [TumorFlow: Physics-Guided Longitudinal MRI Synthesis of Glioblastoma Growth](https://mlsanity.com/paper/2603.04058/) (2026)
- [A Lightweight Optimization Framework for Estimating 3D Brain Tumor Infiltration](https://mlsanity.com/paper/2412.13811/) (2024)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [A Biophysically-Conditioned Generative Framework for 3D Brain Tumor MRI Synthesis](https://mlsanity.com/paper/2510.09365/) (2025)
- [Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory](https://mlsanity.com/paper/2606.28630/) (2026)
- [Observation-Anchored Selective Assimilation for Longitudinal Tumor-State Proxy Forecasting in Post-Treatment Glioma](https://mlsanity.com/paper/2609.12435/) (2026)

## Abstract (arXiv)

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%.