# Explainable Deep Learning for Tumor Dynamic Modeling and Overall Survival Prediction using Neural-ODE

arXiv: https://arxiv.org/abs/2308.01362 · HTML: https://mlsanity.com/paper/2308.01362/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Dimensionless machine learning: Imposing exact units equivariance](https://mlsanity.com/paper/2204.00887/) (2022)
- [Deep learning prediction of patient response time course from early data via neural-pharmacokinetic/pharmacodynamic modeling](https://mlsanity.com/paper/2010.11769/) (2020)
- [Computing the Hazard Ratios Associated with Explanatory Variables Using Machine Learning Models of Survival Data](https://mlsanity.com/paper/2102.00637/) (2021)

## Built on by (most cited first, 5 of 5)

- [Integration of Graph Neural Network and Neural-ODEs for Tumor Dynamic Prediction](https://mlsanity.com/paper/2310.00926/) (2023)
- [Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach](https://mlsanity.com/paper/2506.05245/) (2025)
- [Artifacts of Numerical Integration in Learning Dynamical Systems](https://mlsanity.com/paper/2507.14491/) (2025)
- [From Noise to Signal: Unveiling Treatment Effects from Digital Health Data through Pharmacology-Informed Neural-SDE](https://mlsanity.com/paper/2403.03274/) (2024)
- [Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2511.16427/) (2025)

## Abstract (arXiv)

While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic Neural-ODE (TDNODE) as a pharmacology-informed neural network to enable model discovery from longitudinal tumor size data. We show that TDNODE overcomes a key limitation of existing models in its ability to make unbiased predictions from truncated data. The encoder-decoder architecture is designed to express an underlying dynamical law which possesses the fundamental property of generalized homogeneity with respect to time. Thus, the modeling formalism enables the encoder output to be interpreted as kinetic rate metrics, with inverse time as the physical unit. We show that the generated metrics can be used to predict patients' overall survival (OS) with high accuracy. The proposed modeling formalism provides a principled way to integrate multimodal dynamical datasets in oncology disease modeling.