# Modeling Adoptive Cell Therapy in Bladder Cancer from Sparse Biological Data using PINNs

arXiv: https://arxiv.org/abs/2510.13431 · HTML: https://mlsanity.com/paper/2510.13431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 15 Oct 2025.

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

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Deep Learning for Solving and Estimating Dynamic Macro-Finance Models](https://mlsanity.com/paper/2305.09783/) (2023)
- [Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks](https://mlsanity.com/paper/2404.08019/) (2024)
- [Evaluating the Impact of Data Augmentation on Predictive Model Performance](https://mlsanity.com/paper/2412.02108/) (2024)
- [An efficient estimation of time-varying parameters of dynamic models by combining offline batch optimization and online data assimilation](https://mlsanity.com/paper/2110.12522/) (2021)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology. Here, we seek to learn time-varying interactions due to a combination therapy in a tumor microenvironment. In oncology, experimental data are often sparse and composed of a few time points of tumor volume. By embedding inductive biases derived from prior information about a dynamical system, we extend the physics-informed neural networks (PINN) and incorporate observed biological constraints as regularization agents. The modified PINN algorithm is able to steer itself to a reasonable solution and can generalize well with only a few training examples. We demonstrate the merit of our approach by learning the dynamics of treatment applied intermittently in an ordinary differential equation (ODE) model of a combination therapy. The algorithm yields a solution to the ODE and time-varying forms of some of the ODE model parameters. We demonstrate a strong convergence using metrics such as the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).