Improving reduced-order models through nonlinear decoding of projection-dependent outputs.

A fundamental hindrance to building data-driven reduced-order models (ROMs) is the poor topological quality of a low-dimensional data projection. This includes behavior such as overlapping, twisting, or large curvatures or uneven data density that can generate nonuniqueness and steep gradients in quantities of interest (QoIs). Here, we employ an encoder-decoder neural network architecture for dimensionality reduction. We find that nonlinear decoding of projection-dependent QoIs, when embedded in a dimensionality reduction technique, promotes improved low-dimensional representations of complex multiscale and multiphysics datasets. When data projection (encoding) is affected by forcing accurate nonlinear reconstruction of the QoIs (decoding), we minimize nonuniqueness and gradients in representing QoIs on a projection. This in turn leads to enhanced predictive accuracy of a ROM. Our findings are relevant to a variety of disciplines that develop data-driven ROMs of dynamical systems such as reacting flows, plasma physics, atmospheric physics, or computational neuroscience.

Cost function for low-dimensional manifold topology assessment.

In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

Mitigation strategies for airborne disease transmission in orchestras using computational fluid dynamics.

The COVID-19 pandemic forced performing arts groups to cancel shows and entire seasons due to safety concerns for the audience and performers. It is unclear to what extent aerosols generated by wind instruments contribute to exposure because their fate is dependent on the airflow onstage. We use transient, second-order accurate computational fluid dynamics (CFD) simulations and quantitative microbial risk assessment to estimate aerosol concentrations and the associated risk and assess strategies to mitigate exposure in two distinct concert venues. Mitigation strategies involved rearranging musicians and altering the airflow by changing HVAC settings, opening doors, and introducing flow-directing geometries. Our results indicate that the proposed mitigation strategies can reduce aerosol concentrations in the breathing zone by a factor of 100, corresponding to a similar decrease in the probability of infection.