Related papers: Geometric Numerical Integration of the Assignment …

This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…

We present a novel data-driven approach of learning traffic flow patterns of a transportation network given that many instances of origin to destination (OD) travel demand and link flows of the network are available. Instead of estimating…

The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…

Gradient descent, or negative gradient flow, is a standard technique in optimization to find minima of functions. Many implementations of gradient descent rely on discretized versions, i.e., moving in the gradient direction for a set step…

When interacting with highly dynamic environments, scene flow allows autonomous systems to reason about the non-rigid motion of multiple independent objects. This is of particular interest in the field of autonomous driving, in which many…

Scene flow estimation is the task of describing 3D motion between temporally successive observations. This thesis aims to build the foundation for building scene flow estimators with two important properties: they are scalable, i.e. they…

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical…

In this paper, we dive into the reliability concerns of Integrated Gradients (IG), a prevalent feature attribution method for black-box deep learning models. We particularly address two predominant challenges associated with IG: the…

Scene flow estimation, which extracts point-wise motion between scenes, is becoming a crucial task in many computer vision tasks. However, all of the existing estimation methods utilize only the unidirectional features, restricting the…

Graph-language models (GLMs) have demonstrated great potential in graph-based semi-supervised learning. A typical GLM consists of two key stages: graph generation and text embedding, which are usually implemented by inferring a latent graph…

We propose the joint graph attention neural network (GAT), clustering with adaptive neighbors (CAN) and probabilistic graphical model for dynamic power flow analysis and fault characteristics. In fact, computational efficiency is the main…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We propose a physics-informed data-driven framework for urban wind estimation. This framework validates and incorporates the Reynolds number independence for flows under various working conditions, thus allowing the extrapolation for wind…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical…

The rapid expansion of Internet of Things (IoT) ecosystems has led to increasingly complex and heterogeneous network topologies. Traditional network monitoring and visualization tools rely on aggregated metrics or static representations,…

Flow Matching (FM) has recently emerged as a leading approach for high-fidelity visual generation, offering a robust continuous-time alternative to ordinary differential equation (ODE) based models. However, despite their success, FM models…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…