Related papers: A Subspace Framework for ${\mathcal H}_\infty$-Nor…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive…
This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
In this paper, we study the $H_\infty$-norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the $H_\infty$-norm subject to allocation of the weights on the edges. The…
In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value…
In this paper, the $\mathcal{H}_{2}$ optimal approximation of a $n_{y}\times{n_{u}}$ transfer function $\mathbf{G}(s)$ by a finite dimensional system $\hat{\mathbf{H}}_{d}(s)$ including input/output delays, is addressed. The underlying…
Latent-space interpolation is commonly used to demonstrate the generalization ability of deep latent variable models. Various algorithms have been proposed to calculate the best trajectory between two encodings in the latent space. In this…
An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…
We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by gradient descent. Our formulation scales efficiently beyond the…
We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…
In this paper, we compute a low order approximation of a system of large order $n$ that matches $\nu$ moments of order $j_i$ of the transfer function, at $\nu$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric…
For a quadratic matrix polynomial dependent on parameters and a given tolerance $\epsilon > 0$, the minimization of the $\epsilon$-pseudospectral abscissa over the set of permissible parameter values is discussed, with applications in…
A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…
The growing scale of deep learning models has rendered standard hyperparameter (HP) optimization prohibitively expensive. A promising solution is the use of scale-aware hyperparameters, which can enable direct transfer of optimal HPs from…