The automated discovery of constitutive laws forms an emerging area that focuses on automatically obtaining symbolic expressions describing the constitutive behavior of solid materials from experimental data. Existing symbolic/sparse regression methods rely on availability of libraries of material models, which are typically hand-designed by a human expert relying on known models as reference, or deploy generative algorithms with exponential ...

We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A novel training strategy leveraging the semi-group property of time-dependent PDEs to allow for significant scaling-up of the training data is also proposed. Poseidon is pretrained on a diverse, large scale dataset for the ...