Related papers: Data-driven Prediction of General Hamiltonian Dyna…

We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic…

Charting cortical growth trajectories is of paramount importance for understanding brain development. However, such analysis necessitates the collection of longitudinal data, which can be challenging due to subject dropouts and failed…

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns…

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and…

The process of automatic generation of a road map from GPS trajectories, called map inference, remains a challenging task to perform on a geospatial data from a variety of domains as the majority of existing studies focus on road maps in…

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative…

Recently, adaptive graph convolutional network based traffic prediction methods, learning a latent graph structure from traffic data via various attention-based mechanisms, have achieved impressive performance. However, they are still…

Heterogeneous Graph Neural Networks (HGNNs) have achieved promising results in various heterogeneous graph learning tasks, owing to their superiority in capturing the intricate relationships and diverse relational semantics inherent in…

The development of self-supervised graph pre-training methods is a crucial ingredient in recent efforts to design robust graph foundation models (GFMs). Structure-based pre-training methods are under-explored yet crucial for downstream…

Tabular data prediction (TDP) is one of the most popular industrial applications, and various methods have been designed to improve the prediction performance. However, existing works mainly focus on feature interactions and ignore sample…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

We study the problem of synthetic generation of samples of environmental features for autonomous vehicle navigation. These features are described by a spatiotemporally varying scalar field that we refer to as a threat field. The threat…

Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making…

Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…

Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…

This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…