Angiogenesis is a biological process that plays an important role in tumor growth and metastasis. Many mathematical models have been used to study cancer cell invasion through numerical computation of PDEs (partial differential equations). In this proceeding, we study a Parabolic-Hyperbolic Keller-Segel (PHKS) system in one and two space dimensions. The model arises in the angiogenesis literature. To compute solutions to the PHKS system, we develop a stochastic interacting particle-field (SIPF) method where the PDE solutions are approximated as empirical measures of particles coupled with a smoother field (concentration of chemo-attractant) variable approximated by the classical spline interpolation method. We describe an algorithm for updating the stochastic particle positions and chemical concentration (field). We present analytical form and numerical simulations of self-similar solutions, and discuss challenges to be addressed with machine learning approaches. The numerical experiments show diffusive spreading behavior of the system from a Gaussian shaped initial data and zero flux boundary conditions. Finally, we provide preliminary results of a neural interpolator based on a deep convolutional network and discuss its potential in SIPF for computing higher dimensional solutions to the system.