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 …

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of
partial differential equation (PDE)-constrained optimization problems with initial conditions …

By now Bayesian methods are routinely used in practice for solving inverse problems. In
inverse problems the parameter or signal of interest is observed only indirectly, as an image …

This work presents a method for constructing online-efficient reduced models of large-scale
systems governed by parametrized nonlinear scalar conservation laws. The solution …

Mode-based model-reduction is used to reduce the degrees of freedom of high-dimensional
systems, often by describing the system state by a linear combination of spatial modes …

When approximating a function that depends on a parameter, one encounters many
practical examples where linear interpolation or linear approximation with respect to the …

The use of reduced-order models (ROMs) for the numerical approximation of the solution of
partial differential equations is a topic of current interest, being motivated by the high …

An extension of Radon transform by using a measure function capturing the user need is
proposed. The new transform, called scale space Radon transform, is devoted to the case …

Classical reduced models are low-rank approximations using a fixed basis designed to
achieve dimensionality reduction of large-scale systems. In this work, we introduce reduced …

The global optimal scheduling of UAV (unmanned aerial vehicle) navigation channel is
studied. Firstly, a multi-channel optimal scheduling mathematical model based on the …