CDS&E: Extracting Models from Data - A Novel Data-Driven Simulation Strategy for Reacting Flows

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Numerical simulation of reacting flows of real systems is computationally challenging because of the large number variables involved. This research will develop a new data-driven modelling approach that directly incorporates information from canonical or reference test cases to extract simplified models with user-defined error limits. In particular, novel machine learning concepts will be used to generate simplified models that are suitable for use in practical, engineering-scale simulations. Such computationally efficient models can have a direct impact in addressing a range of relevant energy and environmental problems, for example oxy-fuel combustion (for easier CO2 capture and sequestration), pollutant and particulate formation in stationary and mobile combustion systems, etc. The techniques developed here are also applicable to other fields where many reaction manifolds or pathways exist such as in plasma physics or atmospheric chemistry.Many systems in nature evolve along manifolds, which are smooth and reduced complexity subspaces of a parameter space which satisfy, often unknown, physical constraints. However, developing models to describe this evolution is challenging. A key challenge to this modeling approach is dealing with the source terms that arise in the reduced order model. These are a reflection of the source terms in the full (high-fidelity) model, but must be well-parameterized by the reduced-order model parameters without causing unphysical behavior like divergence near manifold boundaries and spurious source/sink points. This will harness the power of data science to characterize the geometry of the low-dimensional manifold and use that information to improve the behavior of the derived models. Extracting the low-dimensional model is challenging because it requires identifying a moderate dimensional shape where gridding and meshing techniques which scale exponentially in dimension will fail. This work will instead be limited by properties such as boundary curvature and vector field acceleration which are well-controlled for most physics-defined systems. Moreover, these models will be learned in a robust manner consistent with a simple physical model, in spite of noise in training data which may otherwise result in spurious critical saddle points in the resulting vector field.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.