Related papers: Dimensional analysis with constraints
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is…
We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data.…
The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…