Junyan He, Shashank Kushwaha, Diab Abueidda et al.
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric features of a design on mechanical response, including energy absorption. We proposed a combinatorial, key-based design system to generate different lattice designs and used the finite element method to simulate their response with the Johnson-Cook material model. Using an autoencoder, we encoded the cross-sectional images of the lattices into latent design feature vectors, which were supplied to the neural network model to generate predictions. The trained models can accurately predict lattice energy absorption curves in the key-based design system and can be extended to new designs outside of the system via transfer learning.
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.
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by introducing an innovative method for real-time prediction of structural static responses using DeepOnet which relies on a novel approach to physics-informed networks driven by structural balance laws. This approach offers the flexibility to accurately predict responses under various load classes and magnitudes. The trained DeepONet can generate solutions for the entire domain, within a fraction of a second. This capability effectively eliminates the need for extensive remodeling and analysis typically required for each new case in FE modeling. We apply the proposed method to two structures: a simple 2D beam structure and a comprehensive 3D model of a real bridge. To predict multiple variables with DeepONet, we utilize two strategies: a split branch/trunk and multiple DeepONets combined into a single DeepONet. In addition to data-driven training, we introduce a novel physics-informed training approaches. This method leverages structural stiffness matrices to enforce fundamental equilibrium and energy conservation principles, resulting in two novel physics-informed loss functions: energy conservation and static equilibrium using the Schur complement. We use various combinations of loss functions to achieve an error rate of less than 5% with significantly reduced training time. This study shows that DeepONet, enhanced with hybrid loss functions, can accurately and efficiently predict displacements and rotations at each mesh point, with reduced training time.
Diab W. Abueidda, Bilal Ahmed, Panos Pantidis et al.
In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric. A low error, however, does not establish that the predicted fields satisfy the physics that matter for mechanics, such as boundary conditions, superposition, stiffness scaling, or causality. We introduce Physics-Audited Agentic SciML (PA-SciML), a verification-first workflow for agentic SciML discovery. The workflow fixes a scoring evaluator before search, derives reviewable machine-checkable physics requirements, checks each trained candidate on its outputs, and separately searches prescribed input ranges or measured load-history spans for high-violation cases without reference solution fields. A surrogate is reported as verified only under the stated checks. When enabled, the workflow also adds advisory numerical probes before training and tests one modeling change at a time to record which isolated edits are associated with score gains before reuse. In the reported computational-solid-mechanics numerical examples, the static elasticity run selects a surrogate with lower validation error than the error-only baseline while both selected models pass the common linear-elastic checks. In the transient elastodynamics run, an error-only baseline with similar mean error fails a stricter causality check by responding to future parts of the loading history, while the selected surrogate passes the stated checks. The main distinction is per-candidate physics evidence on predicted fields, not a richer aggregate score.
Raisa Bentay Hossain, Farid Ahmed, Kazuma Kobayashi et al.
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.
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.
Kazuma Kobayashi, Samrendra Roy, Seid Koric et al.
Accurate reconstruction of latent environmental fields from sparse and indirect observations is a foundational challenge across scientific domains-from atmospheric science and geophysics to public health and aerospace safety. Traditional approaches rely on physics-based simulators or dense sensor networks, both constrained by high computational cost, latency, or limited spatial coverage. We present the Temporal Radiation Operator Network (TRON), a spatiotemporal neural operator architecture designed to infer continuous global scalar fields from sequences of sparse, non-uniform proxy measurements. Unlike recent forecasting models that operate on dense, gridded inputs to predict future states, TRON addresses a more ill-posed inverse problem: reconstructing the current global field from sparse, temporally evolving sensor sequences, without access to future observations or dense labels. Demonstrated on global cosmic radiation dose reconstruction, TRON is trained on 22 years of simulation data and generalizes across 65,341 spatial locations, 8,400 days, and sequence lengths from 7 to 90 days. It achieves sub-second inference with relative L2 errors below 0.1%, representing a >58,000X speedup over Monte Carlo-based estimators. Though evaluated in the context of cosmic radiation, TRON offers a domain-agnostic framework for scientific field reconstruction from sparse data, with applications in atmospheric modeling, geophysical hazard monitoring, and real-time environmental risk forecasting.
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.
Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes. While neural operator frameworks, such as Deep Operator Networks (DeepONets), have shown considerable success in single-physics settings, their extension to multiphysics problems remains poorly understood. In particular, the challenge of learning nonlinear interactions between tightly coupled physical fields has received little systematic attention. This study addresses a foundational question: should the architectural design of a neural operator reflect the strength of physical coupling it aims to model? To answer this, we present the first comprehensive, architecture-aware evaluation of DeepONet variants across three regimes: single-physics, weakly coupled, and strongly coupled multiphysics systems. We consider a reaction-diffusion equation with dual spatial inputs, a nonlinear thermo-electrical problem with bidirectional coupling through temperature-dependent conductivity, and a viscoplastic thermo-mechanical model of steel solidification governed by transient phase-driven interactions. Two operator-learning frameworks, the classical DeepONet and its sequential GRU-based extension, S-DeepONet, are benchmarked using both single-branch and multi-branch (MIONet-style) architectures. Our results demonstrate that architectural alignment with physical coupling is crucial: single-branch networks significantly outperform multi-branch counterparts in strongly coupled settings, whereas multi-branch encodings offer advantages for decoupled or single-physics problems. Once trained, these surrogates achieve full-field predictions up to 1.8e4 times faster than high-fidelity finite-element solvers, without compromising solution accuracy.
Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM level accuracy, modeling dynamic behavior remains more challenging. This work presents a Multiple Input Operator Network (MIONet) that incorporates a second trunk network to explicitly encode temporal dynamics, enabling accurate prediction of structural responses under moving loads. Traditional DeepONet architectures using recurrent neural networks (RNNs) are limited by fixed time discretization and struggle to capture continuous dynamics. In contrast, MIONet predicts responses continuously over both space and time, removing the need for step wise modeling. It maps scalar inputs including load type, velocity, spatial mesh, and time steps to full field structural responses. To improve efficiency and enforce physical consistency, we introduce a physics informed loss based on dynamic equilibrium using precomputed mass, damping, and stiffness matrices, without solving the governing PDEs directly. Further, a Schur complement formulation reduces the training domain, significantly cutting computational costs while preserving global accuracy. The model is validated on both a simple beam and the KW-51 bridge, achieving FEM level accuracy within seconds. Compared to GRU based DeepONet, our model offers comparable accuracy with improved temporal continuity and over 100 times faster inference, making it well suited for real-time structural monitoring and digital twin applications.
Diab W. Abueidda, Seid Koric, Rashid Abu Al-Rub et al.
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Data generation usually is the main bottleneck in most data-driven models. The deep learning model is trained to learn the model's parameters yielding accurate approximate solutions. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Therefore, the deep collocation method is potentially a promising standalone technique to solve partial differential equations involved in the deformation of materials and structural systems as well as other physical phenomena.
The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing, machine learning, and simulation, searching for optimal nonlinear structures is now within reach. In this study, we develop convolutional neural network models to predict optimized designs for a given set of boundary conditions, loads, and optimization constraints. We have considered the case of materials with a linear elastic response with and without stress constraint. Also, we have considered the case of materials with a hyperelastic response, where material and geometric nonlinearities are involved. For the nonlinear elastic case, the neo-Hookean model is utilized. For this purpose, we generate datasets composed of the optimized designs paired with the corresponding boundary conditions, loads, and constraints, using a topology optimization framework to train and validate the neural network models. The developed models are capable of accurately predicting the optimized designs without requiring an iterative scheme and with negligible inference computational time. The suggested pipeline can be generalized to other nonlinear mechanics scenarios and design domains.
Diab W. Abueidda, Mohammad Almasri, Rami Ammourah et al.
In this paper, we develop a convolutional neural network model to predict the mechanical properties of a two-dimensional checkerboard composite quantitatively. The checkerboard composite possesses two phases, one phase is soft and ductile while the other is stiff and brittle. The ground-truth data used in the training process are obtained from finite element analyses under the assumption of plane stress. Monte Carlo simulations and central limit theorem are used to find the size of the dataset needed. Once the training process is completed, the developed model is validated using data unseen during training. The developed neural network model captures the stiffness, strength, and toughness of checkerboard composites with high accuracy. Also, we integrate the developed model with a genetic algorithm (GA) optimizer to identify the optimal microstructural designs. The genetic algorithm optimizer adopted here has several operators, selection, crossover, mutation, and elitism. The optimizer converges to configurations with highly enhanced properties. For the case of the modulus and starting from randomly-initialized generation, the GA optimizer converges to the global maximum which involves no soft elements. Also, the GA optimizers, when used to maximize strength and toughness, tend towards having soft elements in the region next to the crack tip.