Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great solution. However, selecting the architecture that emulates the FEA with great accuracy is a challenge. This paper presents a comprehensive evaluation of graph neural networks (GNNs) and 3D U-Nets as surrogates for FEA of parametric I-beams. We introduce a Physics-Informed Neural Network (PINN) framework, governed by the Navier Cauchy equations, to enforce physical laws. Crucially, we demonstrate that a curriculum learning strategy, pretraining on data followed by physics informed fine tuning, is essential for stabilizing training. Our results show that GNNs fundamentally outperform the U-Net. Even the worst performer among GNNs, the GCN framework, achieved a relative L2 error of 8.7% while the best framework among U Net, U Net with attention mechanism trained on high resolution data, achieved 13.0% score. Among the graph-based architectures, the Message Passing Neural Networks (MPNN) and Graph Transformers achieved the highest accuracy, achieving a relative L2 score of 3.5% and 2.6% respectively. The inclusion of physics fundamental laws (PINN) significantly improved the generalization, reducing error by up to 11.3% on high-signal tasks. While the Graph Transformer is the most accurate model, it is more 37.5% slower during inference when compared to second best model, MPNN PINN. The PINN enhanced MPNN (MPNN PINN) provides the most practical solution. It offers a good compromise between predictive performance, model size, and inference speed.

Aortic aneurysm disease ranks consistently in the top 20 causes of death in the U.S. population. Thoracic aortic aneurysm is manifested as an abnormal bulging of thoracic aortic wall and it is a leading cause of death in adults. From the perspective of biomechanics, rupture occurs when the stress acting on the aortic wall exceeds the wall strength. Wall stress distribution can be obtained by computational biomechanical analyses, especially structural Finite Element Analysis. For risk assessment, probabilistic rupture risk of TAA can be calculated by comparing stress with material strength using a material failure model. Although these engineering tools are currently available for TAA rupture risk assessment on patient specific level, clinical adoption has been limited due to two major barriers: labor intensive 3D reconstruction current patient specific anatomical modeling still relies on manual segmentation, making it time consuming and difficult to scale to a large patient population, and computational burden traditional FEA simulations are resource intensive and incompatible with time sensitive clinical workflows. The second barrier was successfully overcome by our team through the development of the PyTorch FEA library and the FEA DNN integration framework. By incorporating the FEA functionalities within PyTorch FEA and applying the principle of static determinacy, we reduced the FEA based stress computation time to approximately three minutes per case. Moreover, by integrating DNN and FEA through the PyTorch FEA library, our approach further decreases the computation time to only a few seconds per case. This work focuses on overcoming the first barrier through the development of an end to end deep neural network capable of generating patient specific finite element meshes of the aorta directly from 3D CT images.

-- In this project, we focus on human-robot interaction in caregiving scenarios like bathing, where physical contact is inevitable and necessary for proper task execution because force must be applied to the skin. Using finite element analysis, we designed a 3D-printed gripper combining positive and negative pressure for secure yet compliant handling. Preliminary tests showed it exerted a lower, more uniform pressure profile than a standard rigid gripper . In a user study, participants' trust in robots significantly increased after they experienced a brief bathing demonstration performed by a robotic arm equipped with the soft gripper . These results suggest that soft robotics can enhance perceived safety and acceptance in intimate caregiving scenarios.

Contact-rich manipulation remains a major challenge in robotics. Optical tactile sensors like GelSight Mini offer a low-cost solution for contact sensing by capturing soft-body deformations of the silicone gel. However, accurately inferring shear and normal force distributions from these gel deformations has yet to be fully addressed. In this work, we propose a machine learning approach using a U-net architecture to predict force distributions directly from the sensor's raw images. Our model, trained on force distributions inferred from Finite Element Analysis (FEA), demonstrates promising accuracy in predicting normal and shear force distributions. It also shows potential for generalization across sensors of the same type and for enabling real-time application. The codebase, dataset and models are open-sourced and available at https://feats-ai.github.io .

The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains or are too restrictive in terms of possible field properties. Because of these limitations, techniques leveraging the historically established link between stochastic PDEs (SPDEs) and random fields have been gaining interest. The SPDE representation is especially appealing for engineering applications which already have a finite element discretisation for solving the physical conservation equations. In contrast to the dense covariance matrix of a random field, its inverse, the precision matrix, is usually sparse and equal to the stiffness matrix of an elliptic SPDE. We use the SPDE representation to develop a scalable framework for large-scale statistical finite element analysis and Gaussian process (GP) regression on complex geometries. The statistical finite element method (statFEM) introduced by Girolami et al. (2022) is a novel approach for synthesising measurement data and finite element models. In both statFEM and GP regression, we use the SPDE formulation to obtain the relevant prior probability densities with a sparse precision matrix. The properties of the priors are governed by the parameters and possibly fractional order of the SPDE so that we can model on bounded domains and manifolds anisotropic, non-stationary random fields with arbitrary smoothness. The observation models for statFEM and GP regression are such that the posterior probability densities are Gaussians with a closed-form mean and precision. The respective mean vector and precision matrix and can be evaluated using only sparse matrix operations. We demonstrate the versatility of the proposed framework and its convergence properties with Poisson and thin-shell examples.

Carbon fiber composite can be a potential candidate for replacing metal-based battery enclosures of current electric vehicles (E.V.s) owing to its better strength-to-weight ratio and corrosion resistance. However, the strength of carbon fiber-based structures depends on several parameters that should be carefully chosen. In this work, we implemented high throughput finite element analysis (FEA) based thermoforming simulation to virtually manufacture the battery enclosure using different design and processing parameters. Subsequently, we performed virtual crash simulations to mimic a side pole crash to evaluate the crashworthiness of the battery enclosures. This high throughput crash simulation dataset was utilized to build predictive models to understand the crashworthiness of an unknown set. Our machine learning (ML) models showed excellent performance (R2 > 0.97) in predicting the crashworthiness metrics, i.e., crush load efficiency, absorbed energy, intrusion, and maximum deceleration during a crash. We believe that this FEA-ML work framework will be helpful in down select process parameters for carbon fiber-based component design and can be transferrable to other manufacturing technologies.

Learning from nature has been a quest of humanity for millennia. While this has taken the form of humans assessing natural designs such as bones, butterfly wings, or spider webs, we can now achieve generating designs using advanced computational algorithms. In this paper we report novel biologically inspired designs of diatom structures, enabled using transformer neural networks, using natural language models to learn, process and transfer insights across manifestations. We illustrate a series of novel diatom-based designs and also report a manufactured specimen, created using additive manufacturing. The method applied here could be expanded to focus on other biological design cues, implement a systematic optimization to meet certain design targets, and include a hybrid set of material design sets.

Numerical analysis methods, such as Finite Element Analysis (FEA), are typically used to conduct stress analysis of various structures and systems for which it is impractical or hard to determine an analytical solution. Researchers commonly use FEA methods to evaluate the design, safety and maintenance of different structures in various fields, including aerospace, automotive, architecture and civil structural systems. The current workflow for FEA applications includes: (i) modeling the geometry and its components, (ii) specifying material properties, boundary conditions, meshing, and loading, (iii) dynamic analysis, which may be time-consuming based on the complexity of the model. The time requirement constraint and the complexity of the current FEA workflow make it impractical for real-time or near real-time applications, such as in the aftermath of a disaster or during extreme disruptive events that require immediate corrections to avoid catastrophic failures. Based on the steps of FEA described above, performing a complete stress analysis with conventional FEA has a high computational cost.

3D microstructural datasets are commonly used to define the geometrical domains used in finite element modelling. This has proven a useful tool for understanding how complex material systems behave under applied stresses, temperatures and chemical conditions. However, 3D imaging of materials is challenging for a number of reasons, including limited field of view, low resolution and difficult sample preparation. Recently, a machine learning method, SliceGAN, was developed to statistically generate 3D microstructural datasets of arbitrary size using a single 2D input slice as training data. In this paper, we present the results from applying SliceGAN to 87 different microstructures, ranging from biological materials to high-strength steels. To demonstrate the accuracy of the synthetic volumes created by SliceGAN, we compare three microstructural properties between the 2D training data and 3D generations, which show good agreement. This new microstructure library both provides valuable 3D microstructures that can be used in models, and also demonstrates the broad applicability of the SliceGAN algorithm.

During the design process of an autonomous underwater vehicle (AUV), the pressure vessel has a critical role. The pressure vessel contains dry electronics, power sources, and other sensors that can not be flooded. A traditional design approach for a pressure vessel design involves running multiple Finite Element Analysis (FEA) based simulations and optimizing the design to find the best suitable design which meets the requirement. Running these FEAs are computationally very costly for any optimization process and it becomes difficult to run even hundreds of evaluation. In such a case, a better approach is the surrogate design with the goal of replacing FEA-based prediction with some learning-based regressor. Once the surrogate is trained for a class of problem, then the learned response surface can be used to analyze the stress effect without running the FEA for that class of problem. The challenge of creating a surrogate for a class of problems is data generation. Since the process is computationally costly, it is not possible to densely sample the design space and the learning response surface on sparse data set becomes difficult. During experimentation, we observed that a Deep Learning-based surrogate outperforms other regression models on such sparse data. In the present work, we are utilizing the Deep Learning-based model to replace the costly finite element analysis-based simulation process. By creating the surrogate we speed up the prediction on the other design much faster than direct Finite element Analysis. We also compared our DL-based surrogate with other classical Machine Learning (ML) based regression models( random forest and Gradient Boost regressor). We observed on the sparser data, the DL-based surrogate performs much better than other regression models.