arXiv subjects

Diab Abueidda

Publications and source records attributed to Diab Abueidda.

At least 19 recordsLinked to original sources

arXiv2026

A hybrid IFENN solver for generalizable modeling of phase-field fracture initiation and propagation

In this paper we demonstrate how the Integrated Finite Element Neural Network (IFENN) framework can effectively model the entire evolution of phase-field fracture, including the initiation and propagation stage, across generalizable geometries. IFENN is a hybrid scheme for coupled computational mechanics problems, tightly coupling a standard FEM solver (mechanical equilibrium) with a pre-trained neural network (coupled field). In this work, the phase-field diffusion equation is approximated with: i) a DeepONet architecture with Kolmogorov-Arnold networks in the trunk and branch (DeepOKAN) for the initiation stage, and ii) a Convolution Neural Network (CNN) for the propagation stage. Both networks are trained only once, on a benchmark geometry, using a purely physics-informed approach based on the maximum strain energy and the phase-field variable. The training process utilizes an extremely small number of training increments and only a limited number of Gauss points that are strategically sampled from the fracture process zone. These features enable a substantial decrease of the offline training cost. To address the extrapolation of the DeepOKAN predictions in regions away from the crack tip during the inference stage, we implement a set of artificial boundary conditions to enforce the near-zero values in the far-field predictions. We showcase the flexibility and numerical accuracy of the proposed methodology across both the training and unseen geometries.

cs.CE↗

arXiv2025

Agentic Physical AI toward a Domain-Specific Foundation Model for Energy Systems: A Case Study on Nuclear Reactor Control

The prevailing paradigm in AI for physical systems: scaling general-purpose foundation models toward universal multimodal reasoning, confronts a barrier at the control interface. Frontier vision-language models achieve only 50-53% accuracy on basic quantitative physics tasks, behaving as approximate guessers that preserve semantic plausibility while violating physical constraints. Safety-critical control demands outcome-space guarantees over executed actions, not parameter-space imitation. Here we present a pathway toward domain-specific foundation models through compact language models operating as Agentic Physical AI: policy optimization driven by physics-based simulator validation rather than perceptual inference. We train a 360M-parameter model on synthetic nuclear reactor scenarios scaled from 10^3 to 10^5 examples. Scaling produces strong, regime-dependent reliability gains under nominal simulated conditions, with variance collapse of approximately 500x and elimination of >10% terminal-power excursions on the sampled distribution. Despite balanced exposure to four actuation families, the model concentrates 95% of runtime execution on a single-bank strategy, without reinforcement learning or reward engineering. Representations transfer across simulators without architectural change. We position the system as a candidate decision component within a verification, monitoring, and defense-in-depth architecture, not as a stand-alone safety solution: the demonstrated behavior speaks to closed-loop reliability on a single-step task in simulation and does not yet address off-nominal operation, sensor faults, or uncertainty quantification.

cs.AI↗

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

Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions

Video-diffusion models have recently set the standard in video generation, inpainting, and domain translation thanks to their training stability and high perceptual fidelity. Building on these strengths, we repurpose conditional video diffusion as a physics surrogate for spatio-temporal fields governed by partial differential equations (PDEs). Our two-stage surrogate first applies a Sequential Deep Operator Network (S-DeepONet) to produce a coarse, physics-consistent prior from the prescribed boundary or loading conditions. The prior is then passed to a conditional video diffusion model that learns only the residual: the point-wise difference between the ground truth and the S-DeepONet prediction. By shifting the learning burden from the full solution to its much smaller residual space, diffusion can focus on sharpening high-frequency structures without sacrificing global coherence. The framework is assessed on two disparate benchmarks: (i) vortex-dominated lid-driven cavity flow and (ii) tensile plastic deformation of dogbone specimens. Across these data sets the hybrid surrogate consistently outperforms its single-stage counterpart, cutting the mean relative L2 error from 4.57% to 0.83% for the flow problem and from 4.42% to 2.94% for plasticity, a relative improvements of 81.8% and 33.5% respectively. The hybrid approach not only lowers quantitative errors but also improves visual quality, visibly recovering fine spatial details. These results show that (i) conditioning diffusion on a physics-aware prior enables faithful reconstruction of localized features, (ii) residual learning reduces the problem, accelerating convergence and enhancing accuracy, and (iii) the same architecture transfers seamlessly from incompressible flow to nonlinear elasto-plasticity without problem-specific architectural modifications, highlighting its broad applicability to nonlinear, time-dependent continua.

cs.CE↗

arXiv2025

Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems

`Real-time prediction of complex physical systems requires surrogate models that learn from data while representing strong multiphysics coupling. Deep Operator Networks have shown success in single-physics problems, yet their effectiveness in capturing nonlinear interactions in coupled systems (such as thermo-mechanical or electro-thermal coupling) remains underexplored. Here we pose a practical question: should the architecture of a neural operator reflect the strength of physical coupling it aims to model? We compare single-branch and multi-branch designs, in both feedforward and sequential recurrent forms, across three representative systems: a reaction--diffusion problem with heterogeneous sources, a nonlinear thermo-electrical problem with temperature-dependent conductivity and Joule heating, and a viscoplastic thermo-mechanical model of steel solidification. Single-branch networks consistently outperform multi-branch variants in tightly coupled regimes by encouraging shared latent representations, whereas multi-branch designs remain favorable for decoupled or single-physics tasks. Once trained, these surrogates deliver full-field predictions up to $1.8 \times 10^4$ times faster than physics-based solvers.

cs.LG↗

arXiv2025

Integrated Finite Element Neural Network (IFENN) for Phase-Field Fracture with Minimal Input and Generalized Geometry-Load Handling

We present a novel formulation for modeling phase-field fracture propagation based on the Integrated Finite Element Neural Network (IFENN) framework. IFENN is a hybrid solver scheme that utilizes neural networks as PDE solvers within FEM, preserving accuracy via residual minimization while achieving speed-up via swift network predictions and reduction of the size of system of equations in coupled problems. In this work, we introduce a radically new formulation of IFENN in which the phase-field variable is calculated using physics-informed convolutional networks (PICNNs), while the equilibrium equation is still solved using FEM to maintain the solver robustness. Unlike conventional approaches, which rely on sequence or time-dependent models, we eliminate the need to include temporal features in the training setup and inference stage. Instead, we show that it is sufficient to learn only the spatial coupling between the strain energy density and the phase-field variable in the vicinity of the fracture process zone, and utilize this information along the advancing crack simulation. We train a single CNN in a purely physics-based, unsupervised manner on just two load increments from a single-notch tension problem, with a total training time of only 5 minutes. Following this exceptionally minimal and fast training, we show that the same PICNN can (when embedded within IFENN) model crack propagation in a very wide range of unseen scenarios, including arbitrarily rectangular domains, single and multiple interacting cracks, varying mesh densities, and arbitrary loading paths. The proposed formulation delivers breakthroughs that address many of the limitations in the existing literature of hybrid modeling, introducing a new paradigm for the development of generalizable, physics-consistent hybrid models that are applicable to fracture and other coupled problems.

cs.CE↗

arXiv2025

From Proxies to Fields: Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences

Accurate reconstruction of latent environmental fields from sparse, indirect observations is a fundamental challenge across scientific domains, from atmospheric science and geophysics to public health and aerospace safety. Existing approaches typically rely on physics-based simulations or dense sensor networks; however, these methods are hampered by high computational cost, latency, and limited spatial coverage. Here we introduce the \textbf{Temporal Radiation Operator Network (TRON)}, a spatiotemporal neural operator architecture that infers continuous global scalar fields solely from sequences of sparse, non-uniform proxy measurements. Unlike recent prediction models that require dense, gridded inputs to predict system states, TRON tackles sparse-to-dense, cross-domain field reconstruction. It reconstructs the current global field in real time from sparse, temporally evolving sensor data, without access to any future observations or dense ground-truth fields. We demonstrate this approach on global cosmic radiation dose mapping: TRON, trained on daily reference fields spanning 2001 to 2023, generalizes across 65,341 spatial locations with input sequences ranging from 7 to 90 days. It achieves sub-second inference with relative $L_2$ errors below 0.1\%, representing over a 58,000$\times$ speedup compared to physics-based estimators. Although showcased in the radiation application, TRON provides a domain-agnostic framework for continuous field reconstruction from sparse data, with broad applications in atmospheric modeling, geophysical hazard monitoring, and real-time environmental risk prediction.

cs.LG↗

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

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↗

arXiv2024

Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators

Effective real-time monitoring is a foundation of digital twin technology, crucial for detecting material degradation and maintaining the structural integrity of nuclear systems to ensure both safety and operational efficiency. Traditional physical sensor systems face limitations such as installation challenges, high costs, and difficulty measuring critical parameters in hard-to-reach or harsh environments, often resulting in incomplete data coverage. Machine learning-driven virtual sensors, integrated within a digital twin framework, offer a transformative solution by enhancing physical sensor capabilities to monitor critical degradation indicators like pressure, velocity, and turbulence. However, conventional machine learning models struggle with real-time monitoring due to the high-dimensional nature of reactor data and the need for frequent retraining. This paper introduces the use of Deep Operator Networks (DeepONet) as a core component of a digital twin framework to predict key thermal-hydraulic parameters in the hot leg of an AP-1000 Pressurized Water Reactor (PWR). DeepONet serves as a dynamic and scalable virtual sensor by accurately mapping the interplay between operational input parameters and spatially distributed system behaviors. In this study, DeepONet is trained with different operational conditions, which relaxes the requirement of continuous retraining, making it suitable for online and real-time prediction components for digital twin. Our results show that DeepONet achieves accurate predictions with low mean squared error and relative L2 error and can make predictions on unknown data 1400 times faster than traditional CFD simulations. This speed and accuracy enable DeepONet to synchronize with the physical system in real-time, functioning as a dynamic virtual sensor that tracks degradation-contributing conditions.

cs.LG↗

arXiv2024

Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturing

Under some initial and boundary conditions, the rapid reaction-thermal diffusion process taking place during frontal polymerization (FP) destabilizes the planar mode of front propagation, leading to spatially varying, complex hierarchical patterns in thermoset polymeric materials. Although modern reaction-diffusion models can predict the patterns resulting from unstable FP, the inverse design of patterns, which aims to retrieve process conditions that produce a desired pattern, remains an open challenge due to the non-unique and non-intuitive mapping between process conditions and manufactured patterns. In this work, we propose a probabilistic generative model named univariate conditional variational autoencoder (UcVAE) for the inverse design of hierarchical patterns in FP-based manufacturing. Unlike the cVAE, which encodes both the design space and the design target, the UcVAE encodes only the design space. In the encoder of the UcVAE, the number of training parameters is significantly reduced compared to the cVAE, resulting in a shorter training time while maintaining comparable performance. Given desired pattern images, the trained UcVAE can generate multiple process condition solutions that produce high-fidelity hierarchical patterns.

physics.comp-ph↗

arXiv2024

Nonlinear Inverse Design of Mechanical Multi-Material Metamaterials Enabled by Video Denoising Diffusion and Structure Identifier

Metamaterials, synthetic materials with customized properties, have emerged as a promising field due to advancements in additive manufacturing. These materials derive unique mechanical properties from their internal lattice structures, which are often composed of multiple materials that repeat geometric patterns. While traditional inverse design approaches have shown potential, they struggle to map nonlinear material behavior to multiple possible structural configurations. This paper presents a novel framework leveraging video diffusion models, a type of generative artificial Intelligence (AI), for inverse multi-material design based on nonlinear stress-strain responses. Our approach consists of two key components: (1) a fields generator using a video diffusion model to create solution fields based on target nonlinear stress-strain responses, and (2) a structure identifier employing two UNet models to determine the corresponding multi-material 2D design. By incorporating multiple materials, plasticity, and large deformation, our innovative design method allows for enhanced control over the highly nonlinear mechanical behavior of metamaterials commonly seen in real-world applications. It offers a promising solution for generating next-generation metamaterials with finely tuned mechanical characteristics.

cs.AI↗

arXiv2024

Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturing

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to complete solution fields. In this paper, two newly devised DeepONet formulations with sequential learning and Residual U-Net (ResUNet) architectures are trained for the first time to simultaneously predict complete thermal and mechanical solution fields under variable loading, loading histories, process parameters, and even variable geometries. Two real-world applications are demonstrated: 1- coupled thermo-mechanical analysis of steel continuous casting with multiple visco-plastic constitutive laws and 2- sequentially coupled direct energy deposition for additive manufacturing. Despite highly challenging spatially variable target stress distributions, DeepONets can infer reasonably accurate full-field temperature and stress solutions several orders of magnitude faster than traditional and highly optimized finite-element analysis (FEA), even when FEA simulations are run on the latest high-performance computing platforms. The proposed DeepONet model's ability to provide field predictions almost instantly for unseen input parameters opens the door for future preliminary evaluation and design optimization of these vital industrial processes.

cs.CE↗

arXiv2024

Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide design insights. Nevertheless, few available NNs can handle solution prediction on varying 3D shapes. We present a novel deep operator network (DeepONet) variant called Geom-DeepONet, which encodes parameterized 3D geometries and predicts full-field solutions on an arbitrary number of nodes. To the best of the authors' knowledge, this is the first attempt in the literature and is our primary novelty. In addition to expressing shapes using mesh coordinates, the signed distance function for each node is evaluated and used to augment the inputs to the trunk network of the Geom-DeepONet, thereby capturing both explicit and implicit representations of the 3D shapes. The powerful geometric encoding capability of a sinusoidal representation network (SIREN) is also exploited by replacing the classical feedforward neural networks in the trunk with SIREN. Additional data fusion between the branch and trunk networks is introduced by an element-wise product. A numerical benchmark was conducted to compare Geom-DeepONet to PointNet and vanilla DeepONet, where results show that our architecture trains fast with a small memory footprint and yields the most accurate results among the three with less than 2 MPa stress error. Results show a much lower generalization error of our architecture on unseen dissimilar designs than vanilla DeepONet. Once trained, the model can predict vector solutions, and speed can be over $10^5$ times faster than implicit finite element simulations for large meshes.

cs.CE↗

arXiv2024

I-FENN with Temporal Convolutional Networks: expediting the load-history analysis of non-local gradient damage propagation

In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors, can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework's ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton-Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

cs.CE↗

arXiv2024

Material-Response-Informed DeepONet and its Application to Polycrystal Stress-strain Prediction in Crystal Plasticity

Crystal plasticity (CP) simulations are a tool for understanding how microstructure morphology and texture affect mechanical properties and are an essential component of elucidating the structure-property relations. However, it can be computationally expensive. Hence, data-driven machine learning models have been applied to predict the mean-field response of a polycrystal representative volume element to reduce computation time. In this work, we proposed a novel Deep Operator Network (DeepONet) architecture for predicting microstructure stress-strain response. It employs a convolutional neural network in the trunk to encode the microstructure. To account for different material properties, boundary conditions, and loading, we proposed using single crystal stress-strain curves as inputs to the branch network, furnishing a material-response-informed DeepONet. Using four numerical examples, we demonstrate that the current DeepONet can be trained on a single material and loading and then generalized to new conditions via transfer learning. Results show that using single crystal responses as input outperforms a similar model using material properties as inputs and overcomes limitations with changing boundary conditions and temporal resolution. In all cases, the new model achieved a $R^2$ value of above 0.99, and over 95\% of predicted stresses have a relative error of $\le$ 5\%, indicating superior accuracy. With as few as 20 new data points and under 1min training time, the trained DeepONet can be fine-tuned to generate accurate predictions on different materials and loading. Once trained, the prediction speed is almost $1\times10^{4}$ times faster the CP simulations. The efficiency and high generalizability of our DeepONet render it a powerful data-driven surrogate model for CP simulations in multi-scale analyses.

cs.CE↗

arXiv2024

Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an $R^2$ value of above 0.99 and a relative $L_2$ error of less than 10\% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4\% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8\% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model is highly efficient and accurate.

cs.CE↗

arXiv2023

Designing impact-resistant bio-inspired low-porosity structures using neural networks

Biological structural designs in nature, like hoof walls, horns, and antlers, can be used as inspiration for generating structures with excellent mechanical properties. A common theme in these designs is the small percent porosity in the structure ranging from 1 - 5\%. In this work, the sheep horn was used as an inspiration due to its higher toughness when loaded in the radial direction compared to the longitudinal direction. Under dynamic transverse compression, we investigated the structure-property relations in low porosity structures characterized by their two-dimensional (2D) cross-sections. A diverse design space was created by combining polygonal tubules with different numbers of sides placed on a grid with varying numbers of rows and columns. The volume fraction and the orientation angle of the tubules were also varied. The finite element (FE) method was used with a rate-dependent elastoplastic material model to generate the stress-strain curves under plane strain conditions. A gated recurrent unit (GRU) model was trained to predict the structures' stress-strain response and energy absorption under different strain rates and applied strains. The parameter-based model uses eight discrete parameters to characterize the design space and as inputs to the model. The trained GRU model can efficiently predict the response of a new design in as little as 0.16 ms and allows rapid performance evaluation of 128000 designs in the design space. The GRU predictions identified high-performance structures, and four design trends that affect the specific energy absorption were extracted and discussed.

cs.CE↗