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

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…

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…

The performance analytics domain in High Performance Computing (HPC) uses tabular data to solve regression problems, such as predicting the execution time. Existing Machine Learning (ML) techniques leverage the correlations among features…

In this work, a novel learning-based approach has been developed to generate driving paths by integrating LIDAR point clouds, GPS-IMU information, and Google driving directions. The system is based on a fully convolutional neural network…

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…

Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…

Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of semi-supervised node classification tasks. Despite their great success, training GCNs on large graphs suffers from computational and…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

We present GeGnn, a learning-based method for computing the approximate geodesic distance between two arbitrary points on discrete polyhedra surfaces with constant time complexity after fast precomputation. Previous relevant methods either…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we…

Commonly, learning-based topological navigation approaches produce a local policy while preserving some loose connectivity of the space through a topological map. Nevertheless, spurious or missing edges in the topological graph often lead…

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…

Spatio-temporal processes often exhibit highly heterogeneous and non-intuitive responses to localized disruptions, limiting the effectiveness of conventional message passing approaches in modeling local heterogeneity. We reformulate…