arXiv subjects

Hadi Meidani

Publications and source records attributed to Hadi Meidani.

At least 19 recordsLinked to original sources

arXiv2026

PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit. To address these challenges, we propose PGD-NO, a neural operator with Precomputed Geometry Decomposition, that relocates the computational overhead of geometric encoding to a deterministic pre-computation phase. By utilizing an iterative geometry decomposition algorithm to extract geometry tokens, our model decouples feature extraction from solution querying. This architecture enables linear memory scalability, allowing high fidelity learning on meshes exceeding 10 million nodes, a scale where existing architectures typically encounter memory exhaustion. PGD-NO demonstrates competitive predictive accuracy across diverse industrial benchmarks and provides intrinsic interpretability through attention mechanisms. By effectively overcoming traditional mesh-size constraints, PGD-NO offers a robust and efficient solution for the next generation of large-scale, high-fidelity industrial design applications.

cs.LG↗

arXiv2025

A comprehensive comparison of neural operators for 3D industry-scale engineering designs

Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in engineering design evaluation, a wide range of neural operator architectures have been proposed for various problem settings. However, model selection remains challenging due to the absence of fair and comprehensive comparisons. To address this, we propose and standardize six representative 3D industry-scale engineering design datasets spanning thermal analysis, linear elasticity, elasto-plasticity, time-dependent plastic problems, and computational fluid dynamics. All datasets include fully preprocessed inputs and outputs for model training, making them directly usable across diverse neural operator architectures. Using these datasets, we conduct a systematic comparison of four types of neural operator variants, including Branch-Trunk-based Neural Operators inspired by DeepONet, Graph-based Neural Operators inspired by Graph Neural Networks, Grid-based Neural Operators inspired by Fourier Neural Operators, and Point-based Neural Operators inspired by PointNet. We further introduce practical enhancements to adapt these models to different engineering settings, improving the fairness of the comparison. Our benchmarking study evaluates each model strengths and limitations in terms of predictive performance, computational efficiency, memory usage, and deployment complexity. The findings provide actionable insights to guide future neural operator development.

cs.CE↗

arXiv2025

NuGraph2 with Explainability: Post-hoc Explanations for Geometric Neural Network Predictions

With the growing popularity of artificial intelligence used for scientific applications, the ability of attribute a result to a reasoning process from the network is in high demand for robust scientific generalizations to hold. In this work we aim to motivate the need for and demonstrate the use of post-hoc explainability methods when applied to AI methods used in scientific applications. To this end, we introduce explainability add-ons to the existing graph neural network (GNN) for neutrino tagging, NuGraph2. The explanations take the form of a suite of techniques examining the output of the network (node classifications) and the edge connections between them, and probing of the latent space using novel general-purpose tools applied to this network. We show how none of these methods are singularly sufficient to show network "understanding", but together can give insights into the processes used in classification. While these methods are tested on the NuGraph2 application, they can be applied to a broad range of networks, not limited to GNNs. The code for this work is publicly available on GitHub at https://github.com/voetberg/XNuGraph.

hep-ex↗

arXiv2025

NuGraph2 with Context-Aware Inputs: Physics-Inspired Improvements in Semantic Segmentation

Graph neural networks have recently shown strong promise for event reconstruction tasks in Liquid Argon Time Projection Chambers, yet their performance remains limited for underrepresented classes of particles, such as Michel electrons. In this work, we investigate physics-informed strategies to improve semantic segmentation within the NuGraph2 architecture. We explore three complementary approaches: (i) enriching the input representation with context-aware features derived from detector geometry and track continuity, (ii) introducing auxiliary decoders to capture class-level correlations, and (iii) incorporating energy-based regularization terms motivated by Michel electron energy distributions. Experiments on MicroBooNE public datasets show that physics-inspired feature augmentation yields the largest gains, particularly boosting Michel electron precision and recall by disentangling overlapping latent space regions. In contrast, auxiliary decoders and energy-regularization terms provided limited improvements, partly due to the hit-level nature of NuGraph2, which lacks explicit particle- or event-level representations. Our findings highlight that embedding physics context directly into node-level inputs is more effective than imposing task-specific auxiliary losses, and suggest that future hierarchical architectures such as NuGraph3, with explicit particle- and event-level reasoning, will provide a more natural setting for advanced decoders and physics-based regularization. The code for this work is publicly available on Github at https://github.com/vitorgrizzi/nugraph_phys/tree/main_phys.

hep-ex↗

arXiv2025

Towards Signed Distance Function based Metamaterial Design: Neural Operator Transformer for Forward Prediction and Diffusion Model for Inverse Design

The inverse design of metamaterial architectures presents a significant challenge, particularly for nonlinear mechanical properties involving large deformations, buckling, contact, and plasticity. Traditional methods, such as gradient-based optimization, and recent generative deep-learning approaches often rely on binary pixel-based representations, which introduce jagged edges that hinder finite element (FE) simulations and 3D printing. To overcome these challenges, we propose an inverse design framework that utilizes a signed distance function (SDF) representation combined with a conditional diffusion model. The SDF provides a smooth boundary representation, eliminating the need for post-processing and ensuring compatibility with FE simulations and manufacturing methods. A classifier-free guided diffusion model is trained to generate SDFs conditioned on target macroscopic stress-strain curves, enabling efficient one-shot design synthesis. To assess the mechanical response of the generated designs, we introduce a forward prediction model based on Neural Operator Transformers (NOT), which accurately predicts homogenized stress-strain curves and local solution fields for arbitrary geometries with irregular query meshes. This approach enables a closed-loop process for general metamaterial design, offering a pathway for the development of advanced functional materials.

physics.comp-ph↗

arXiv2025

Geometry-Informed Neural Operator Transformer

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions on arbitrary geometries. GINOT employs a sampling and grouping strategy together with an attention mechanism to encode surface point clouds that are unordered, exhibit non-uniform point densities, and contain varying numbers of points for different geometries. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its high accuracy and strong generalization capabilities for complex and arbitrary 2D and 3D geometries.

cs.LG↗

arXiv2025

Graph Neural Networks for Travel Distance Estimation and Route Recommendation Under Probabilistic Hazards

Estimating the shortest travel time and providing route recommendation between different locations in a city or region can quantitatively measure the conditions of the transportation network during or after extreme events. One common approach is to use Dijkstra's Algorithm, which produces the shortest path as well as the shortest distance. However, this option is computationally expensive when applied to large-scale networks. This paper proposes a novel fast framework based on graph neural networks (GNNs) which approximate the single-source shortest distance between pairs of locations, and predict the single-source shortest path subsequently. We conduct multiple experiments on synthetic graphs of different size to demonstrate the feasibility and computational efficiency of the proposed model. In real-world case studies, we also applied the proposed method of flood risk analysis of coastal urban areas to calculate delays in evacuation to public shelters during hurricanes. The results indicate the accuracy and computational efficiency of the GNN model, and its potential for effective implementation in emergency planning and management.

cs.LG↗

arXiv2025

Multi-Class Traffic Assignment using Multi-View Heterogeneous Graph Attention Networks

Solving traffic assignment problem for large networks is computationally challenging when conventional optimization-based methods are used. In our research, we develop an innovative surrogate model for a traffic assignment when multi-class vehicles are involved. We do so by employing heterogeneous graph neural networks which use a multiple-view graph attention mechanism tailored to different vehicle classes, along with additional links connecting origin-destination pairs. We also integrate the node-based flow conservation law into the loss function. As a result, our model adheres to flow conservation while delivering highly accurate predictions for link flows and utilization ratios. Through numerical experiments conducted on urban transportation networks, we demonstrate that our model surpasses traditional neural network approaches in convergence speed and predictive accuracy in both user equilibrium and system optimal versions of traffic assignment.

cs.LG↗

arXiv2025

PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.

cs.LG↗

arXiv2024

A Multi-Fidelity Graph U-Net Model for Accelerated Physics Simulations

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. Data-driven networks like GNN, Neural Operators have proved to be very effective in generalizing the model across unseen domain and resolutions. But one of the most critical issues in these data-based models is the computational cost of generating training datasets. Complex phenomena can only be captured accurately using deep networks with large training datasets. Furthermore, numerical error of training samples is propagated in the model errors, thus requiring the need for accurate data, i.e. FEM solutions on high-resolution meshes. Multi-fidelity methods offer a potential solution to reduce the training data requirements. To this end, we propose a novel GNN architecture, Multi-Fidelity U-Net, that utilizes the advantages of the multi-fidelity methods for enhancing the performance of the GNN model. The proposed architecture utilizes the capability of GNNs to manage complex geometries across different fidelity levels, while enabling flow of information between these levels for improved prediction accuracy for high-fidelity graphs. We show that the proposed approach performs significantly better in accuracy and data requirement and only requires training of a single network compared to other benchmark multi-fidelity approaches like transfer learning. We also present Multi-Fidelity U-Net Lite, a faster version of the proposed architecture, with 35% faster training, with 2 to 5% reduction in accuracy. We carry out extensive validation to show that the proposed models surpass traditional single-fidelity GNN models in their performance, thus providing feasible alternative for addressing computational and accuracy requirements where traditional high-fidelity simulations can be time-consuming.

cs.LG↗

arXiv2024

Physics-informed Discretization-independent Deep Compositional Operator Network

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE parameter inputs}, have been successfully used. However, the training of neural operators typically demands large training datasets, the acquisition of which can be prohibitively expensive. To address this challenge, physics-informed training can offer a cost-effective strategy. However, current physics-informed neural operators face limitations, either in handling irregular domain shapes or in in generalizing to various discrete representations of PDE parameters. In this research, we introduce a novel physics-informed model architecture which can generalize to various discrete representations of PDE parameters and irregular domain shapes. Particularly, inspired by deep operator neural networks, our model involves a discretization-independent learning of parameter embedding repeatedly, and this parameter embedding is integrated with the response embeddings through multiple compositional layers, for more expressivity. Numerical results demonstrate the accuracy and efficiency of the proposed method. All the codes and data related to this work are available on GitHub: https://github.com/WeihengZ/PI-DCON.

math.NA↗

arXiv2024

Physics-Informed Geometry-Aware Neural Operator

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly predicting the PDE solutions. However, training these neural operators typically requires large datasets, the acquisition of which can be prohibitively expensive. To overcome this, physics-informed training offers an alternative way of building neural operators, eliminating the high computational costs associated with Finite Element generation of training data. Nevertheless, current physics-informed neural operators struggle with limitations, either in handling varying domain geometries or varying PDE parameters. In this research, we introduce a novel method, the Physics-Informed Geometry-Aware Neural Operator (PI-GANO), designed to simultaneously generalize across both PDE parameters and domain geometries. We adopt a geometry encoder to capture the domain geometry features, and design a novel pipeline to integrate this component within the existing DCON architecture. Numerical results demonstrate the accuracy and efficiency of the proposed method. All the codes and data related to this work are available on GitHub: https://github.com/WeihengZ/Physics-informed-Neural-Foundation-Operator.

cs.LG↗

arXiv2024

End-to-End Heterogeneous Graph Neural Networks for Traffic Assignment

The traffic assignment problem is one of the significant components of traffic flow analysis for which various solution approaches have been proposed. However, deploying these approaches for large-scale networks poses significant challenges. In this paper, we leverage the power of heterogeneous graph neural networks to propose a novel end-to-end surrogate model for traffic assignment, specifically user equilibrium traffic assignment problems. Our model integrates an adaptive graph attention mechanism with auxiliary "virtual" links connecting origin-destination node pairs, This integration enables the model to capture spatial traffic patterns across different links, By incorporating the node-based flow conservation law into the overall loss function, the model ensures the prediction results in compliance with flow conservation principles, resulting in highly accurate predictions for both link flow and flow-capacity ratios. We present numerical experiments on urban transportation networks and show that the proposed heterogeneous graph neural network model outperforms other conventional neural network models in terms of convergence rate and prediction accuracy. Notably, by introducing two different training strategies, the proposed heterogeneous graph neural network model can also be generalized to different network topologies. This approach offers a promising solution for complex traffic flow analysis and prediction, enhancing our understanding and management of a wide range of transportation systems.

cs.LG↗

arXiv2024

Supply Chain Network Extraction and Entity Classification Leveraging Large Language Models

Supply chain networks are critical to the operational efficiency of industries, yet their increasing complexity presents significant challenges in mapping relationships and identifying the roles of various entities. Traditional methods for constructing supply chain networks rely heavily on structured datasets and manual data collection, limiting their scope and efficiency. In contrast, recent advancements in Natural Language Processing (NLP) and large language models (LLMs) offer new opportunities for discovering and analyzing supply chain networks using unstructured text data. This paper proposes a novel approach that leverages LLMs to extract and process raw textual information from publicly available sources to construct a comprehensive supply chain graph. We focus on the civil engineering sector as a case study, demonstrating how LLMs can uncover hidden relationships among companies, projects, and other entities. Additionally, we fine-tune an LLM to classify entities within the supply chain graph, providing detailed insights into their roles and relationships. The results show that domain-specific fine-tuning improves classification accuracy, highlighting the potential of LLMs for industry-specific supply chain analysis. Our contributions include the development of a supply chain graph for the civil engineering sector, as well as a fine-tuned LLM model that enhances entity classification and understanding of supply chain networks.

cs.LG↗

arXiv2024

Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is computationally challenging as it requires repetitive finite element solutions for different candidate designs and different samples of random inputs. To address this challenge, a neural network method is proposed that offers computational efficiency because (1) it builds and explores a low dimensional search space which is parameterized using deterministically optimal designs corresponding to different realizations of random inputs, and (2) the probabilistic performance measure for each design candidate is predicted by a neural network surrogate. This method bypasses the numerous finite element response evaluations that are needed in the standard RTO approaches and with minimal training can produce optimal designs with better performance measures compared to those observed in the training set. Moreover, a multi-fidelity framework is incorporated to the proposed approach to further improve the computational efficiency. Numerical application of the method is shown on the robust design of L-bracket structure with single point load as well as multiple point loads.

cs.LG↗

arXiv2024

Heterogeneous Graph Sequence Neural Networks for Dynamic Traffic Assignment

Traffic assignment and traffic flow prediction provide critical insights for urban planning, traffic management, and the development of intelligent transportation systems. An efficient model for calculating traffic flows over the entire transportation network could provide a more detailed and realistic understanding of traffic dynamics. However, existing traffic prediction approaches, such as those utilizing graph neural networks, are typically limited to locations where sensors are deployed and cannot predict traffic flows beyond sensor locations. To alleviate this limitation, inspired by fundamental relationship that exists between link flows and the origin-destination (OD) travel demands, we proposed the Heterogeneous Spatio-Temporal Graph Sequence Network (HSTGSN). HSTGSN exploits dependency between origin and destination nodes, even when it is long-range, and learns implicit vehicle route choices under different origin-destination demands. This model is based on a heterogeneous graph which consists of road links, OD links (virtual links connecting origins and destinations) and a spatio-temporal graph encoder-decoder that captures the spatio-temporal relationship between OD demands and flow distribution. We will show how the graph encoder-decoder is able to recover the incomplete information in the OD demand, by using node embedding from the graph decoder to predict the temporal changes in flow distribution. Using extensive experimental studies on real-world networks with complete/incomplete OD demands, we demonstrate that our method can not only capture the implicit spatio-temporal relationship between link traffic flows and OD demands but also achieve accurate prediction performance and generalization capability.

cs.LG↗

arXiv2024

Graph Neural Network Surrogate for Seismic Reliability Analysis of Highway Bridge Systems

Rapid reliability assessment of transportation networks can enhance preparedness, risk mitigation, and response management procedures related to these systems. Network reliability analysis commonly considers network-level performance and does not consider the more detailed node-level responses due to computational cost. In this paper, we propose a rapid seismic reliability assessment approach for bridge networks based on graph neural networks, where node-level connectivities, between points of interest and other nodes, are evaluated under probabilistic seismic scenarios. Via numerical experiments on transportation systems in California, we demonstrate the accuracy, computational efficiency, and robustness of the proposed approach compared to the Monte Carlo approach.

cs.LG↗

arXiv2023

FO-PINNs: A First-Order formulation for Physics Informed Neural Networks

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems. PINNs also have a soft implementation of boundary conditions resulting in boundary conditions not being exactly imposed everywhere on the boundary. With these challenges at hand, we present first-order physics-informed neural networks (FO-PINNs). These are PINNs that are trained using a first-order formulation of the PDE loss function. We show that, compared to standard PINNs, FO-PINNs offer significantly higher accuracy in solving parameterized systems, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, FO-PINNs can enable exact imposition of boundary conditions using approximate distance functions, which pose challenges when applied on high-order PDEs. Through three examples, we demonstrate the advantages of FO-PINNs over standard PINNs in terms of accuracy and training speedup.

cs.LG↗