Neural Reaction-Diffusion Operators for Spatially Heterogeneous Tumor Modeling

Keywords: Neural operators, Reaction-diffusion equations, Tumor spatial-temporal modeling, Physics-informed machine learning, Computational oncology, Multi-scale modeling

TL;DR: We created the first neural operator that works on spatially heterogeneous biological systems, achieving 250× speedup for real-time tumor modeling.

Abstract: We introduce Neural Reaction-Diffusion Operators (NRDOs), the first neural operator framework specifically designed for spatially heterogeneous reaction-diffusion partial differential equations (PDEs) arising in tumor modeling. Traditional neural operators like DeepONet and Fourier Neural Operators excel on homogeneous PDEs but struggle with spatially varying coefficients that characterize biological tissues. Our method extends neural operator theory through heterogeneity-aware architectures, adaptive spectral convolutions, and physics-informed training that enforces conservation laws and biological constraints. We establish theoretical approximation bounds for heterogeneous coefficient fields and demonstrate convergence guarantees under physics-informed training. Experimental evaluation on five diverse heterogeneity scenarios achieves exceptionally low errors (average MSE = 5.46 $\times$ 10$^{-5}$, maximum absolute error < 0.02) while providing 2-3 orders of magnitude speedup over traditional numerical methods. Our approach enables real-time tumor simulation with applications to personalized treatment planning and drug delivery optimization, establishing a new paradigm for physics-informed machine learning in computational biology.

Submission Number: 255