  Integrable systems have provided various insights into physical phenomena and
mathematics. The way of constructing many-body integrable systems is limited to
few ansatzes for the Lax pair, except for highly inventive findings of
conserved quantities. Machine learning techniques have recently been applied to
broad physics fields and proven powerful for building non-trivial
transformations and potential functions. We here propose a machine learning
approach to a systematic construction of classical integrable systems. Given
the Hamiltonian or samples in latent space, our neural network simultaneously
learns the corresponding natural Hamiltonian in real space and the canonical
transformation between the latent space and the real space variables. We also
propose a loss function for building integrable systems and demonstrate
successful unsupervised learning for the Toda lattice. Our approach enables
exploring new integrable systems without any prior knowledge about the
canonical transformation or any ansatz for the Lax pair.
