Related papers: A nonlinear extension of parametric model embeddin…

This paper presents two novel hyperspectral mixture models and associated unmixing algorithms. The two models assume a linear mixing model corrupted by an additive term whose expression can be adapted to account for multiple scattering…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings.…

Numerical solving parameterised partial differential equations (P-PDEs) is highly practical yet computationally expensive, driving the development of reduced-order models (ROMs). Recently, methods that combine latent space identification…

Non-local thermodynamic equilibrium (NLTE) calculations remain a major computational bottleneck in radiation--hydrodynamics, while most existing machine-learning surrogates treat NLTE as a static input--output mapping rather than a kinetic…

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…

Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…

Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low dimensional descriptions from high dimensional observations. However, existing…

Simultaneously achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Non-local priors (NLPs) possess appealing properties for high-dimensional model choice, but their use for estimation has not…

Various logit-adjusted parameterizations of the cross-entropy (CE) loss have been proposed as alternatives to weighted CE for training large models on label-imbalanced data far beyond the zero train error regime. The driving force behind…

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration…

In this paper, we present a non-parametric structured latent variable model for image generation, called NP-DRAW, which sequentially draws on a latent canvas in a part-by-part fashion and then decodes the image from the canvas. Our key…

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and…

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

We propose a composable framework for latent space image augmentation that allows for easy combination of multiple augmentations. Image augmentation has been shown to be an effective technique for improving the performance of a wide variety…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

Accurately modeling and controlling vehicle exhaust emissions during transient events, such as rapid acceleration, is critical for meeting environmental regulations and optimizing powertrains. Conventional data-driven methods, such as…