  Curie's principle states that "when effects show certain asymmetry, this
asymmetry must be found in the causes that gave rise to them". We demonstrate
that symmetry equivariant neural networks uphold Curie's principle and can be
used to articulate many symmetry-relevant scientific questions into simple
optimization problems. We prove these properties mathematically and demonstrate
them numerically by training a Euclidean symmetry equivariant neural network to
learn symmetry-breaking input to deform a square into a rectangle and to
generate octahedra tilting patterns in perovskites.
