22 papers · ranked by Valyu relevance
Zachary Grey, Paul G. Constantine
Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active…
Mario Teixeira Parente, Jonas Wallin, Barbara Wohlmuth
In this article, we consider scenarios in which traditional estimates for the active subspace method based on probabilistic Poincar´e inequalities are not valid due to unbounded Poincar´e constants. Consequently, we propose a framework that allows to derive generalized estimates in the sense that it enables to control…
Francesco Romor, Marco Tezzele, Gianluigi Rozza
Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse problems, sensitivity analysis, and surrogate models' design, especially when in presence of high-dimensional parametrized systems. In this work we propose a new method called…
Yulin Guo, Paromita Nath, Sankaran Mahadevan, Paul Witherell
This paper investigates a novel approach to efficiently construct and improve surrogate models in problems with high-dimensional input and output. In this approach, the principal components and corresponding features of the high-dimensional output are first identified. For each feature, the active subspace technique is…
Kellin Rumsey, Devin Francom, Scott Vander Wiel
Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in…
Paul G. Constantine, Paul Diaz
Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' total sensitivity indices and…
Fabio Nobile, Matteo Raviola, Raúl Tempone
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient number of gradient evaluations (samples) of the input output map to achieve…
Marco Tezzele, Filippo Salmoiraghi, Andrea Mola, Gianluigi Rozza
We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is…
Francesco Romor, Marco Tezzele, Andrea Lario, Gianluigi Rozza
Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular, we introduce it in a broader mathematical framework that contemplates also the reduction in…
Ishaan Batta, Anees Abrol, Zening Fu, Vince D. Calhoun
Here we introduce a multimodal framework to identify subspaces in the human brain that are defined by collective changes in structural and functional measures and are actively linked to demographic, biological and cognitive indicators in a population. We determine the multimodal subspaces using principles of active…
Oskar Weser, Kai Guther, Khaldoon Ghanem, Giovanni Li Manni
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction…
Pablo T. Wentz, Scott L. Brincat, Anitha Pasupathy, Earl K. Miller
Cortical spiking activity in areas like prefrontal cortex (PFC) encodes information only along a small number of dimensions, a subspace of the full space of population activity patterns. PFC often uses distinct subspaces to represent incoming sensory information and to maintain it in working memory. However, it’s…
Authors not listed
We introduce localized active space state interaction singles (LASSIS), a multireference electronic structure method that uses two-step diagonalization to model systems characterized by multiple distinct localized centers of strong electron correlation, with weaker but not negligible electron correlation between the…
Andrew B. Lehr, Arvind Kumar, Christian Tetzlaff
In the central nervous system, sequences of neural activity form trajectories on low dimensional neural manifolds. The neural computation underlying flexible cognition and behavior relies on dynamic control of these structures. For example different tasks or behaviors are represented on different subspaces, requiring…
Charles Audet, Warren Hare, Gabriel Jarry–Bolduc
The cosine measure was introduced in 2003 to quantify the richness of finite positive spanning sets of directions in the context of derivative-free directional methods. A positive spanning set is a set of vectors whose nonnegative linear combinations span the whole space. The present work extends the definition of…
Andrew B. Lehr, Arvind Kumar, Christian Tetzlaff
Neural activity in the brain traces sequential trajectories on low dimensional subspaces. For flexible behavior, these neural subspaces must be manipulated and reoriented within short timescales of tens of milliseconds. Using mathematical analysis and simulation of a recurrently connected neural circuit for sequence…
Camden J. MacDowell, Alexandra Libby, Caroline I. Jahn, Sina Tafazoli + 1 more
Cognition is flexible. Behaviors can change on a moment-by-moment basis. Such flexibility is thought to rely on the brain’s ability to route information through different networks of brain regions in order to support different cognitive computations. However, the mechanisms that determine which network of brain regions…
Authors not listed
Excited states of transition metal complexes are generally strongly correlated due to the near-degeneracy of the metal d orbitals. Consequently, electronic structure calculations of such species often necessitate multireference approaches. However, widespread use of multireference methods is hindered due to the active…
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For n points in $\mathbb{R}^d$, we present a scheme to construct a 2-approximation of the filtration of the Rips…
Nickolas Gantzler, Adrian Henle, Praveen Thallapally, Xiaoli Fern + 1 more
A gravimetric, MOF-based (MOF = metal-organic framework) sensor array functions by measuring the mass of gas adsorbed in an array of MOFs. Changes in the gas composition are expected to produce detectable changes in the mass of gas adsorbed in the MOFs. In practical settings, multiple components of the gas adsorb into…
Zheng Zuo, Ziqiang Li, Pengsen Cheng, Jian Zhao
Subspace outlier detection has emerged as a practical approach for outlier detection. Classical full space outlier detection methods become ineffective in high dimensional data due to the “curse of dimensionality”. Subspace outlier detection methods have great potential to overcome the problem. However, the challenge…
Chris Zhang, Mary Pitman, Anjali Dixit, Sumudu Leelananda + 7 more
DNA-encoded libraries (DELs) provide the means to make and screen millions of diverse compounds against a target of interest in a single experiment. However, despite producing large volumes of binding data at a relatively low cost, the DEL selection process is susceptible to noise, necessitating computational follow-up…