Related papers: A Hybrid Lagrangian-Eulerian Model for the Structu…

Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2)…

Managing fluid balance in dialysis patients is crucial, as improper management can lead to severe complications. In this paper, we propose a multimodal approach that integrates visual features from lung ultrasound images with clinical data…

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory. The space- time vector flow is naturally introduced from the mean velocity, which provides the Lagrangian picture based on the mean field in totally…

Hybrid modeling aims to augment traditional theory-driven models with machine learning components that learn unknown parameters, sub-models or correction terms from data. In this work, we build on FluxRGNN, a recently developed hybrid model…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…

This review examined the current advancements in data-driven methods for analyzing flow and transport in porous media, which has various applications in energy, chemical engineering, environmental science, and beyond. Although there has…

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles,…

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…

We present a Lagrangian-Eulerian strategy for proving uniqueness and local existence of solutions in path spaces of limited smoothness for a class of incompressible hydrodynamic models including Oldroyd-B type complex fluid models and zero…

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…

Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

Currently, the most common motion representation for action recognition is optical flow. Optical flow is based on particle tracking which adheres to a Lagrangian perspective on dynamics. In contrast to the Lagrangian perspective, the…

A hybrid physics-machine learning modeling framework is proposed for the surface vehicles' maneuvering motions to address the modeling capability and stability in the presence of environmental disturbances. From a deep learning perspective,…

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics…

In this work, we propose a Bayesian statistical model to simultaneously characterize two or more social networks defined over a common set of actors. The key feature of the model is a hierarchical prior distribution that allows us to…

Generating high-quality novel view renderings of 3D Gaussian Splatting (3DGS) in scenes featuring transient objects is challenging. We propose a novel hybrid representation, termed as HybridGS, using 2D Gaussians for transient objects per…