# Learn-Morph-Infer: a new way of solving the inverse problem for brain tumor modeling

arXiv: https://arxiv.org/abs/2111.04090 · HTML: https://mlsanity.com/paper/2111.04090/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 7 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans and Bayesian Inference](https://mlsanity.com/paper/1807.00499/) (2018)
- [FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2002.03014/) (2020)
- [Neural parameters estimation for brain tumor growth modeling](https://mlsanity.com/paper/1907.00973/) (2019)
- [Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect](https://mlsanity.com/paper/2006.09932/) (2020)
- [Coupling Brain-Tumor Biophysical Models and Diffeomorphic Image Registration](https://mlsanity.com/paper/1710.06420/) (2017)
- [Quantitative in vivo imaging to enable tumor forecasting and treatment optimization](https://mlsanity.com/paper/2102.12602/) (2021)
- [Automatic MRI-Driven Model Calibration for Advanced Brain Tumor Progression Analysis](https://mlsanity.com/paper/2001.09173/) (2020)

## Built on by (most cited first, 19 of 19)

- [The Brain Tumor Sequence Registration (BraTS-Reg) Challenge: Establishing Correspondence Between Pre-Operative and Follow-up MRI Scans of Diffuse Glioma Patients](https://mlsanity.com/paper/2112.06979/) (2021)
- [Evaluation of pseudo-healthy image reconstruction for anomaly detection with deep generative models: Application to brain FDG PET](https://mlsanity.com/paper/2401.16363/) (2024)
- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)
- [The Brain Tumor Segmentation (BraTS) Challenge: Local Synthesis of Healthy Brain Tissue via Inpainting](https://mlsanity.com/paper/2305.08992/) (2023)
- [BiLO: Bilevel Local Operator Learning for PDE Inverse Problems](https://mlsanity.com/paper/2404.17789/) (2024)
- [BraTS orchestrator : Democratizing and Disseminating state-of-the-art brain tumor image analysis](https://mlsanity.com/paper/2506.13807/) (2025)
- [fastWDM3D: Fast and Accurate 3D Healthy Tissue Inpainting](https://mlsanity.com/paper/2507.13146/) (2025)
- [Brain Tumour Removing and Missing Modality Generation using 3D WDM](https://mlsanity.com/paper/2411.04630/) (2024)
- [Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation](https://mlsanity.com/paper/2507.17019/) (2025)
- [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)
- [Prediction of brain tumor recurrence location based on multi-modal fusion and nonlinear correlation learning](https://mlsanity.com/paper/2304.13725/) (2023)
- [A Lightweight Optimization Framework for Estimating 3D Brain Tumor Infiltration](https://mlsanity.com/paper/2412.13811/) (2024)
- [Efficient Deep Learning-based Forward Solvers for Brain Tumor Growth Models](https://mlsanity.com/paper/2501.08226/) (2025)
- [Framing image registration as a landmark detection problem for label-noise-aware task representation (HitR)](https://mlsanity.com/paper/2308.01318/) (2023)
- [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)

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.