Nahil Sobh

Veena Kaustaban, Qinle Ba, Ipshita Bhattacharya et al.

Recent years have seen great advancements in the development of deep learning models for histopathology image analysis in digital pathology applications, evidenced by the increasingly common deployment of these models in both research and clinical settings. Although such models have shown unprecedented performance in solving fundamental computational tasks in DP applications, they suffer from catastrophic forgetting when adapted to unseen data with transfer learning. With an increasing need for deep learning models to handle ever changing data distributions, including evolving patient population and new diagnosis assays, continual learning models that alleviate model forgetting need to be introduced in DP based analysis. However, to our best knowledge, there is no systematic study of such models for DP-specific applications. Here, we propose CL scenarios in DP settings, where histopathology image data from different sources/distributions arrive sequentially, the knowledge of which is integrated into a single model without training all the data from scratch. We then established an augmented dataset for colorectal cancer H&E classification to simulate shifts of image appearance and evaluated CL model performance in the proposed CL scenarios. We leveraged a breast tumor H&E dataset along with the colorectal cancer to evaluate CL from different tumor types. In addition, we evaluated CL methods in an online few-shot setting under the constraints of annotation and computational resources. We revealed promising results of CL in DP applications, potentially paving the way for application of these methods in clinical practice.

Nahil Sobh, Rini Jasmine Gladstone, Hadi Meidani

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.

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.

Diab W. Abueidda, Seid Koric, Nahil A. Sobh

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.