Related papers: Hierarchical Dimensionless Learning (Hi-{\pi}): A …

Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear…

The interpretation of deep learning as a dynamical system has gained a considerable attention in recent years as it provides a promising framework. It allows for the use of existing ideas from established fields of mathematics for studying…

Learning rich representation from data is an important task for deep generative models such as variational auto-encoder (VAE). However, by extracting high-level abstractions in the bottom-up inference process, the goal of preserving all…

Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples…

Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing…

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…

Image retrieval has become an increasingly appealing technique with broad multimedia application prospects, where deep hashing serves as the dominant branch towards low storage and efficient retrieval. In this paper, we carried out in-depth…

This paper reports an unexpected finding: in a deterministic hyperdimensional computing (HDC) architecture **that inverts the conventional role of Galois-field algebra -- employing it not for error correction toward a unique answer but as…

Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential…

High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but rather is estimated using (typically…

We present the Physics-Informed Optimal Homotopy Analysis Method (PI-OHAM) for solving nonlinear differential equations. PI-OHAM, based on classical HAM, employs a physics-informed residual loss to optimize convergence-control parameters…

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven…

Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…

A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis.…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…