# Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2605.13560 · HTML: https://mlsanity.com/paper/2605.13560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 13 May 2026.

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

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth](https://mlsanity.com/paper/2209.12089/) (2022)
- [Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data](https://mlsanity.com/paper/2308.14925/) (2023)

## Abstract (arXiv)

This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-volume domain. The framework employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation and Hamiltonian Monte Carlo (HMC) sampling to estimate posterior predictive distributions and uncertainty intervals. The method was evaluated on longitudinal data from the National Lung Screening Trial (30 patients). Results show that the model captures heterogeneous tumor growth patterns while maintaining reasonable prediction accuracy under limited observations. Compared with deterministic modeling approaches, the proposed approach additionally provides calibrated uncertainty estimates. The inferred posterior parameter correlations were consistent with expected biological growth behavior. The proposed framework achieved a cohort-level log-space RMSE of approximately 0.20 together with well-calibrated 95% credible interval coverage across 30 patients. These findings suggest that Bayesian physics-informed modeling may be useful for uncertainty-aware tumor growth assessment when only limited longitudinal follow-up scans are available.