  Climate change will jeopardize food security. Food security involves the
robustness of the global agri-food system. This agri-food system is intricately
connected to systems centering around health, economy, social-cultural
diversity, and global political stability. A systematic way to determine
acceptable interventions in the global agri-food systems involves analyses at
different spatial and temporal scales. Such multi-scale analyses are common
within physics. Unfortunately, physics alone is not sufficient. Machine
learning techniques may aid. We focus on neural networks (NN) into which
physics-based information is encoded (PeNN) and apply it to a sub-problem
within the agri-food system. We show that the mean squared error of the PeNN is
always smaller than that of the NNs, in the order of a factor of thousand.
Furthermore, the PeNNs capture extra and interpolation very well, contrary to
the NNs. It is shown that PeNNs need a much smaller data set size than the NNs
to achieve a similar mse. Our results suggest that the incorporation of physics
into neural networks architectures yields promise for addressing food security.
