I will present a general framework for inferring constitutive relations from data, with an emphasis on compressible and incompressible fluid mechanics. The method relies on expressing isotropic constitutive laws as scalar functions of the principal invariants of the strain-rate tensor. To ensure that the learned models are well-posed, we infer a convex potential of dissipation rather than directly learning bulk and shear viscosity functions. Moreover, to avoid imposing a specific functional form for the constitutive law, we represent the dissipation potential using neural networks trained on data. In particular, we employ input-convex neural networks to enforce convexity. By combining PyTorch with the finite element library Firedrake, we embed the governing PDE into the training procedure, which leads to a PDE-constrained optimization problem for the network parameters. This strategy enables us to infer the constitutive relation from velocity data, as opposed to stress measurements. We apply this approach to learn concentration-dependent compressible constitutive laws in Lagrangian sea ice flow models that involve many interacting Lagrangian ice floes. This is a joint work with Gonzalo G. De Diego (NYU).