Physically-informed machine learning offers a promising novel approach to modeling biological, chemical and physical systems. This talk will describe a particular framework (SPIDER) for inferring interpretable equivariant continuum models that has been thoroughly validated in several settings where sufficiently extensive experimental or numerical data are available. Applications of this framework to data-driven inference of a coarse-grained description will be discussed for systems whose microscopic models are either continuum or discrete. Two specific examples will be considered: subgrid-scale modeling of fluid turbulence and the inference of a continuum model for a molecular gas with repelling interactions.
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