Neural networks & partial differential equations Keywords: ConvNet, ResNet, PDE, heat equation, optimal control, flow of vector field, rotation & scale-invariant, Even bigger is the claim to explain (deep) neural networks by way of partial differential equations (PDE). Instead of presenting a polished theory, if there is one? I'd like to stay close to the path that led me to this. Naturally many have noticed it before, including (but not limitited) Weinan E, A proposal on machine learning via dynamical systems (2017) Lars Ruthotto, Eldad Haber, Deep Neural Networks Motivated by Partial Differential Equations (2018) Ricky T. Q. Chen, et al., Neural Ordinary Differential Equations (2018) A workshop on PDE and Inverse Problem Methods in Machine Learning (2020)