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Computational modeling is a key resource to gather insight into physicalsystems in modern scientific research and engineering. While access to largeamount of data has fueled the use of Machine Learning (ML) to recover physicalmodels from experiments and increase the accuracy of physical simulations,purely data-driven models have limited generalization and interpretability. Toovercome these limitations, we propose a framework that combines SymbolicRegression (SR) and Discrete Exterior Calculus (DEC) for the automateddiscovery of physical models starting from experimental data. Since thesemodels consist of mathematical expressions, they are interpretable and amenableto analysis, and the use of a natural, general-purpose discrete mathematicallanguage for physics favors generalization with limited input data.Importantly, DEC provides building blocks for the discrete analogue of fieldtheories, which are beyond the state-of-the-art applications of SR to physicalproblems. Further, we show that DEC allows to implement a strongly-typed SRprocedure that guarantees the mathematical consistency of the recovered modelsand reduces the search space of symbolic expressions. Finally, we prove theeffectiveness of our methodology by re-discovering three models of ContinuumPhysics from synthetic experimental data: Poisson equation, the Euler'sElastica and the equations of Linear Elasticity. Thanks to theirgeneral-purpose nature, the methods developed in this paper may be applied todiverse contexts of physical modeling.

Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus