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Data-driven modeling has become a key building block in computational scienceand engineering. However, data that are available in science and engineeringare typically scarce, often polluted with noise and affected by measurementerrors and other perturbations, which makes learning the dynamics of systemschallenging. In this work, we propose to combine data-driven modeling viaoperator inference with the dynamic training via roll outs of neural ordinarydifferential equations. Operator inference with roll outs inheritsinterpretability, scalability, and structure preservation of traditionaloperator inference while leveraging the dynamic training via roll outs overmultiple time steps to increase stability and robustness for learning fromlow-quality and noisy data. Numerical experiments with data describing shallowwater waves and surface quasi-geostrophic dynamics demonstrate that operatorinference with roll outs provides predictive models from training trajectorieseven if data are sampled sparsely in time and polluted with noise of up to 10%.

Operator inference with roll outs for learning reduced models from scarce and low-quality data