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Coarse-grained models describe the macroscopic mean response of a process at large scales, which derives from stochastic processes at small scales. Common examples include accounting for velocity fluctuations in a turbulent fluid flow model and cloud evolution in climate models. Most existing techniques for constructing coarse-grained models feature ill-defined parameters whose values are arbitrarily chosen (e.g., a window size), are narrow in their applicability (e.g., only applicable to time series or spatial data), or cannot readily incorporate physics information. Here, we introduce the concept of physics-guided Gaussian process regression as a machine-learning-based coarse-graining technique that is broadly applicable and amenable to input from known physics-based relationships. Using a pair of case studies derived from molecular dynamics simulations, we demonstrate the attractive properties and superior performance of physics-guided Gaussian processes for coarse-graining relative to prevalent benchmarks. The key advantage of Gaussian-process-based coarse-graining is its ability to seamlessly integrate data-driven and physics-based information.