Assessing the performance of physics-informed neural networks for tumor growth prediction under noisy and sparse data conditions.

Cancer presents multiple challenges for its study, which is why mathematical models have become essential tools to understand its dynamics and reduce reliance on costly biological experiments. This investigation explores the use of Physics-Informed Neural Networks (PINNs) to approximate and predict cancer progression based on a simplified ordinary differential system mathematical model, which describes the interactions among tumor, normal, and immune cells. Synthetic data are generated using the implicit Euler method, incorporating noise to simulate real clinical measurements. The study evaluates how the amount of data, temporal spacing, and noise level affect the network's performance. Results show that having at least 40 days of data enables accurate predictions in most evaluated scenarios. A comparative analysis with a Multi-Layer Perceptron (MLP) and a Least Squares (LS) approach using RK45 demonstrated that the PINN is significantly more robust for learning and predicting future dynamics, especially under limited or noisy data conditions. The inclusion of the physical loss allowed the model to extrapolate beyond the observed domain, although it did not fully compensate for data scarcity. Accurately modeling the immune cell population proved particularly challenging. These findings help identify the limitations and obstacles that such techniques must overcome to be effectively applied in real-world clinical settings, ultimately supporting data-driven medical decision-making through robust, model-based predictions.