相关论文: Active Manifolds: A non-linear analogue to Active …

This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…

Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…

Image-level weakly supervised semantic segmentation (WSSS) is a fundamental yet challenging computer vision task facilitating scene understanding and automatic driving. Most existing methods resort to classification-based Class Activation…

Computation methods for solving entropy-regularized reward optimization -- a class of problems widely used for fine-tuning generative models -- have advanced rapidly. Among those, Adjoint Matching (AM, Domingo-Enrich et al., 2025) has…

This paper applies the Newman-Penrose formalism-a technique primarily used in General Relativity-to the analysis of three-dimensional almost contact metric (ACM) manifolds. We reformulate and discuss several known notions and properties…

Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than…

Comparing neuronal bursting models (NBM) with slow-fast autonomous dynamical systems (S-FADS), it appears that the specific features of a (NBM) do not allow a determination of the analytical slow manifold equation with the singular…

Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden layers, have been very successfully used in a series of…

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…

Deep neural networks achieve remarkable performance in multiple fields. However, after proper training they suffer from an inherent vulnerability against adversarial examples (AEs). In this work we shed light on inner representations of the…

Active learning is a machine learning paradigm that aims to improve the performance of a model by strategically selecting and querying unlabeled data. One effective selection strategy is to base it on the model's predictive uncertainty,…

We study various asymptotic approximations of Good's special functions arising in atomic physics. These special functions are situated beyond Anger's functions to which they are closely related. Our major tool is the method of the…

Atomic Force Microscopy (AFM) operating in the frequency modulation mode with a metal tip functionalized with a CO molecule images the internal structure of molecules with an unprecedented resolution. The interpretation of these images is…

The problem of approximating smooth, multivariate functions from sample points arises in many applications in scientific computing, e.g., in computational Uncertainty Quantification (UQ) for science and engineering. In these applications,…

We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…