Physics-Informed Neural ODEs for Tumor-Immune Dynamics Modeling

Learn to implement physics-informed neural ordinary differential equations (PNODEs) in Julia for modeling complex tumor-immune system interactions in this 11-minute conference talk. Discover how to combine established Gompertz growth dynamics with neural-learned immune effects using a dual neural network architecture that separates immune-mediated suppression from general model corrections. Explore the physics-informed loss function incorporating five key components: volume prediction accuracy, derivative matching for physics consistency, growth smoothness penalties, biological constraints ensuring volume positivity, and L2 regularization. Master the Julia implementation leveraging six core packages including DifferentialEquations.jl for robust ODE solving, Flux.jl for neural networks, SciMLSensitivity.jl for efficient gradient computation, and Optimization.jl for training coordination. Understand the two-phase training strategy combining AdamW and LBFGS optimization algorithms that achieves convergence in under one hour. Examine results demonstrating prediction accuracy exceeding R² = 0.95 across multiple tumor scenarios, capturing 30.25% tumor volume reduction through immune effect modeling, and revealing strong negative correlation between immune response strength and tumor growth rates. Access the complete dataset from Kevin Atsou's tumor growth repository, partial source code, and presentation materials to implement this approach for biological system modeling where mechanistic understanding must be combined with data-driven learning.