Deep Neural Network Based Differential Equation Solver for HIV Enzyme Kinetics

Abstract: Purpose: We seek to use neural networks (NNs) to solve a well-known system of differential equations describing the balance between T cells and HIV viral burden. Materials and Methods: In this paper, we employ a 3-input parallel NN to approximate solutions for the system of first-order ordinary differential equations describing the above biochemical relationship. Results: The numerical results obtained by the NN are very similar to a host of numerical approximations from the literature. Conclusion: We have demonstrated use of NN integration of a well-known and medically important system of first order coupled ordinary differential equations. Our trial-and-error approach counteracts the system's inherent scale imbalance. However, it highlights the need to address scale imbalance more substantively in future work. Doing so will allow more automated solutions to larger systems of equations, which could describe increasingly complex and biologically interesting systems.