We make connections between complexity of training of physics-informed neural networks
(PINNs) and Kolmogorov n-width of the solution. Leveraging this connection, we then …

We present a nonlinear interpolation technique for parametric fields that exploits optimal
transportation of coherent structures of the solution to achieve accurate performance. The …

We propose an automated nonlinear model reduction and mesh adaptation framework for
rapid and reliable solution of parameterized advection-dominated problems, with emphasis …

Using nonlinear projections and preserving structure in model order reduction (MOR) are
currently active research fields. In this paper, we provide a novel differential geometric …

Solving optimal control problems for transport-dominated partial differential equations
(PDEs) can become computationally expensive, especially when dealing with high …

This paper presents a neural network-based methodology for the decomposition of transport-
dominated fields using the shifted proper orthogonal decomposition (sPOD). Classical sPOD …

We construct a new representation of entropy solutions to nonlinear scalar conservation
laws with a smooth convex flux function in a single spatial dimension. The representation is …

We present a new methodology for decomposing flows with multiple transports that further
extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to …

While computational fluid dynamics (CFD) simulations are an indispensable tool in modern
aerospace engineering design, they bear a severe computational burden in applications …