Artificial intelligence can watch a video of cancer cells and write down the fundamental mathematical laws governing their growth.
April 23, 2026
Original Paper
Physics-Informed Neural Networks for Biological 2Dt Reaction-Diffusion Systems
arXiv · 2604.18548
The Takeaway
Instead of humans trying to guess the formulas for tumor expansion, this AI uses symbolic regression to discover them from scratch. It identifies the exact reaction diffusion equations that describe how lung cancer populations move and multiply. These aren't just predictions, they are the actual closed form physics rules of the disease. This allows doctors to model a patient's specific cancer progression with the same mathematical certainty used in aerodynamics.
From the abstract
Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential operator structure (e.g., reaction-diffusion) while learning constitutive terms via trainable neural subnetworks, enforced through soft residual penalties. Existing BINN studies are limited to $1\mathrm{D}{+}t$ reaction-diffusion systems and focus on forward