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Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Spatially varying spectral modulation can be implemented using a liquid crystal spatial light modulator (SLM) since it provides an array of liquid crystal cells, each of which can be purposed to act as a programmable spectral filter array.…
We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…
Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous…
This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the…
We consider how mathematical models enable predictions for conditions that are qualitatively different from the training data. We propose techniques based on information topology to find models that can apply their learning in regimes for…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM…
Lab measurements showed that identification (ID) and monitoring of objects using remote sensing of their vibration signatures are limited in a couple rare cases. This work provides two necessary conditions to infer that the identification…
The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we…
We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective…
Foundation models are typically trained at a fixed computational capacity, while real-world applications require deployment across platforms with different resource constraints. Current approaches usually rely on training families of model…
We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a…