  Recently, the Cachazo-He-Yuan (CHY) approach for calculating scattering
amplitudes has been extended beyond tree level. In this paper, we introduce a
way of constructing CHY integrands for $\Phi^3$ theory up to two loops from
holomorphic forms on Riemann surfaces. We give simple rules for translating
Feynman diagrams into the corresponding CHY integrands. As a complementary
result, we extend the $\Lambda$-algorithm, originally introduced in
arXiv:1604.05373, to two loops. Using this approach, we are able to
analytically verify our prescription for the CHY integrands up to seven
external particles at two loops. In addition, it gives a natural way of
extending to higher-loop orders.
