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For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al.…
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…
We investigate new developments of the combined Reduced-Basis and Empirical Interpolation Methods (RB-EIM) for parametrized nonlinear parabolic problems. In many situations, the cost of the EIM in the offline stage turns out to be…
Physics-informed operator learning is an attractive candidate for surrogate modeling of microstructures, especially in multiscale finite-element simulations. Its practical use, however, is often limited by the high cost of loss evaluation.…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the…
A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
The versatility of recent machine learning approaches makes them ideal for improvement of next generation video compression solutions. Unfortunately, these approaches typically bring significant increases in computational complexity and are…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…
Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of…
Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
We study iterative blind symbol detection for block-fading linear inter-symbol interference channels. Based on the factor graph framework, we design a joint channel estimation and detection scheme that combines the expectation maximization…