Predictive data science for physical systems: From model reduction to scientific machine learning
Achieving predictive data science for physical systems requires a synergistic combination of data and physics-based models, as well as a critical need to quantify uncertainties. For many frontier science and engineering challenge problems, a purely data-focused perspective will fall short -- these problems are characterized by complex multi-scale multi-physics dynamics, high-dimensional uncertain parameters that cannot be observed directly, and a need to issue predictions that go beyond the specific conditions where data may be available. Learning from data through the lens of models is a way to bring structure to an otherwise intractable problem: it is a way to respect physical constraints, to embed domain knowledge, to bring interpretability to results, and to endow the resulting predictions with quantified uncertainties. This talk highlights how formulations and methods from projection-based model reduction can be combined with machine learning methods to achieve this. Our examples, drawn from a variety of engineering applications, demonstrate the importance of embedding physical constraints within learned models, and also highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models.