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Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and…
With broad applications in various public services like aviation management and urban disaster warning, numerical precipitation prediction plays a crucial role in weather forecast. However, constrained by the limitation of observation and…
The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…
Terrain elevation modeling for off-road navigation aims to accurately estimate changes in terrain geometry in real-time and quantify the corresponding uncertainties. Having precise estimations and uncertainties plays a crucial role in…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed:…
Online nonparametric estimators are gaining popularity due to their efficient computation and competitive generalization abilities. An important example includes variants of stochastic gradient descent. These algorithms often take one…
The concept of sharpness has been successfully applied to traditional architectures like MLPs and CNNs to predict their generalization. For transformers, however, recent work reported weak correlation between flatness and generalization. We…
We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…