Combining the excellent thermal and electrical properties of Cu with the high abrasion resistance and thermal stability of W, Cu-W nanoparticle-reinforced metal matrix composites and nano-multilayers are finding applications as brazing fillers and shielding material for plasma and radiation. Due to the large lattice mismatch between fcc Cu and bcc W, these systems have complex interfaces that are beyond the scales suitable for ab initio methods, thus motivating the development of chemically accurate interatomic potentials. Here, a neural network potential (NNP) for Cu-W is developed within the Behler-Parrinello framework using a curated training dataset that captures metallurgically relevant local atomic environments. The Cu-W NNP accurately predicts (i) the metallurgical properties (elasticity, stacking faults, dislocations, thermodynamic behavior) in elemental Cu and W, (ii) energies and structures of Cu-W intermetallics and solid solutions, and (iii) a range of fcc Cu/bcc W interfaces, and exhibits physically reasonable behavior for solid W/liquid Cu systems. As will be demonstrated in forthcoming work, this near ab initio accurate NNP can be applied to understand complex phenomena involving interface-driven processes and properties in Cu-W composites.