Related papers: PhyMPGN: Physics-encoded Message Passing Graph Net…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work…

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

The rapid development of deep learning has significant implications for the advancement of Computational Fluid Dynamics (CFD). Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced…

Knowledge graphs (KGs) facilitate a wide variety of applications. Despite great efforts in creation and maintenance, even the largest KGs are far from complete. Hence, KG completion (KGC) has become one of the most crucial tasks for KG…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

Graph Neural Networks (GNNs) learn from graph-structured data by passing local messages between neighboring nodes along edges on certain topological layouts. Typically, these topological layouts in modern GNNs are deterministically computed…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…

Spatio-temporal signals forecasting plays an important role in numerous domains, especially in neuroscience and transportation. The task is challenging due to the highly intricate spatial structure, as well as the non-linear temporal…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

Recent advances in integrating positional and structural encodings (PSEs) into graph neural networks (GNNs) have significantly enhanced their performance across various graph learning tasks. However, the general applicability of these…

Better machine understanding of pedestrian behaviors enables faster progress in modeling interactions between agents such as autonomous vehicles and humans. Pedestrian trajectories are not only influenced by the pedestrian itself but also…

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Accurate energy consumption forecasting is essential for efficient resource management and sustainability in the building sector. Deep learning models are highly successful but struggle with limited historical data and become unusable when…