Related papers: Towards Complex Dynamic Physics System Simulation …

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Graph Neural Networks have emerged as an effective machine learning tool for multi-disciplinary tasks such as pharmaceutical molecule classification and chemical reaction prediction, because they can model non-euclidean relationships…

Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…

We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual…

Modeling the structure and events of the physical world constitutes a fundamental objective of neural networks. Among the diverse approaches, Graph Network Simulators (GNS) have emerged as the leading method for modeling physical phenomena,…

Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and…

Predictive Physics has been historically based upon the development of mathematical models that describe the evolution of a system under certain external stimuli and constraints. The structure of such mathematical models relies on a set of…

Exploring the missing values is an essential but challenging issue due to the complex latent spatio-temporal correlation and dynamic nature of time series. Owing to the outstanding performance in dealing with structure learning potentials,…

High-precision scientific simulation faces a long-standing trade-off between computational efficiency and physical fidelity. To address this challenge, we propose NeuralOGCM, an ocean modeling framework that fuses differentiable programming…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

We designed a new artificial neural network by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the 2D mode profile in both the linear growth and nonlinear saturated stages.…

Digital twins provide a powerful paradigm for diagnostic and prognostic tasks in the monitoring and control of engineered systems; however, their deployment for complex structures remains challenged by model-form uncertainty, arising from…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

Delicate cloth simulations have long been desired in computer graphics. Various methods were proposed to improve engaged force interactions, collision handling, and numerical integrations. Deep learning has the potential to achieve fast and…

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…

The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…