Deep neural network approach to solve coupled differential equations with multiple delays

Abstract This paper proposes a scientific machine learning approach based on Physics Informed Neural Networks (PINNs) to solve the delay differential equations (DDEs) of higher order with multiple delay, neutral DDEs (NDDEs) and system of DDEs. Using optimization algorithms and automatic differentiation, we modify the network parameters in PINN to minimize the loss function. As a result, the delay differential equations (DDEs) can be numerically solved without the grid dependency and polynomial interpolation that come with conventional numerical techniques. Numerous numerical examples have demonstrated our method’s high precision in a variety of challenges, demonstrating its efficacy and great potential in addressing various DDEs.