Related papers: LBM-GNN: Graph Neural Network Enhanced Lattice Bol…
This paper presents a novel strategy for constructing body source terms in the high-order lattice Boltzmann method (LBM), designed to efficiently introduce various physical phenomena by modifying the non-equilibrium distribution function.…
Transformer based models, especially large language models (LLMs) dominate the field of NLP with their mass adoption in tasks such as text generation, summarization and fake news detection. These models offer ease of deployment and…
In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct…
In the present paper a lattice Boltzmann scheme is presented which exhibits an increased stability and accuracy with respect to standard single- or multi-relaxation-time (MRT) approaches. The scheme is based on a single-relaxation-time…
A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is…
Volatility, as a measure of uncertainty, plays a crucial role in numerous financial activities such as risk management. The Econometrics and Machine Learning communities have developed two distinct approaches for financial volatility…
Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer…
We propose a novel multi-domain grid refinement technique with extensions to entropic incompressible, thermal and compressible lattice Boltzmann models. Its validity and accuracy are accessed by comparison to available direct numerical…
In recent years, Graph Neural Network (GNN) has bloomly progressed for its power in processing graph-based data. Most GNNs follow a message passing scheme, and their expressive power is mathematically limited by the discriminative ability…
To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…
Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional…
Despite their success in various domains, the growing dependence on GNNs raises a critical concern about the nature of the combinatorial reasoning underlying their predictions, which is often hidden within their black-box architectures.…
For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different…
Stability of graph neural networks (GNNs) characterizes how GNNs react to graph perturbations and provides guarantees for architecture performance in noisy scenarios. This paper develops a self-regularized graph neural network (SR-GNN)…
This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively nonlinear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilizes the moment chain approach, where the…
Factors such as the proliferation of renewable energy and electrification contribute to grid congestion as a pressing problem. Topology control is an appealing method for relieving congestion, but traditional approaches for topology…
In massive multi-input multi-output (MIMO) systems, the main bottlenecks of location- and orientation-assisted beam alignment using deep neural networks (DNNs) are large training overhead and significant performance degradation. This paper…
Model Checking is widely applied in verifying complicated and especially concurrent systems. Despite of its popularity, model checking suffers from the state space explosion problem that restricts it from being applied to certain systems,…
The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…
In terms of accuracy, Graph Neural Networks (GNNs) are the best architectural choice for the node classification task. Their drawback in real-world deployment is the latency that emerges from the neighbourhood processing operation. One…