Related papers: Model Error Resonance: The Geometric Nature of Err…

Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling…

Large-scale traffic forecasting relies on fixed sensor networks that often exhibit blackouts: contiguous intervals of missing measurements caused by detector or communication failures. These outages are typically handled under a Missing At…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of…

Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary…

Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper…

Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…

Graph Neural Networks struggle to capture long-range dependencies due to over-squashing, where information from exponentially growing neighborhoods must pass through a small number of structural bottlenecks. While recent rewiring methods…

The modeling of gravitational wave ringdown has traditionally relied on linear perturbation theory, which mainly describes the late-time behavior of a perturbed black hole after a binary merger. However, the need for more accurate ringdown…

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation…

The bulk-boundary correspondence, which relates topological properties of a material in the bulk to the presence of robust modes localized on the edge, is at the core of the now mature field of topological wave physics. More recently, it…

The geometric structure of latent representations in large language models (LLMs) is an active area of research, driven in part by its implications for model transparency and AI safety. Existing literature has focused mainly on general…

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable…

Single-image 3D reconstruction with large reconstruction models (LRMs) has advanced rapidly, yet reconstructions often exhibit geometric inconsistencies and misaligned details that limit fidelity. We introduce GeoFusionLRM, a geometry-aware…

Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…

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…

Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…

AI training datasets will inevitably contain AI-generated examples, leading to ``feedback'' in which the output of one model impacts the training of another. It is known that such iterative feedback can lead to model collapse, yet the…

We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…