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Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…

Soft fracture in highly deformable solids involves both geometric and constitutive nonlinearities, necessitating advanced theoretical and computational frameworks for its accurate understanding. Tensile fractures subjected to mixed-mode…

Federated learning (FL) offers privacy-preserving decentralized machine learning, optimizing models at edge clients without sharing private data. Simultaneously, foundation models (FMs) have gained traction in the artificial intelligence…

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…

The existing federated learning (FL) methods for spatio-temporal forecasting fail to capture the inherent spatio-temporal heterogeneity, which calls for personalized FL (PFL) methods to model the spatio-temporally variant patterns. While…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Semantic communication can significantly improve bandwidth utilization in wireless systems by exploiting the meaning behind raw data. However, the advancements achieved through semantic communication are closely dependent on the development…

Federated learning (FL) has emerged as a key technique for distributed machine learning (ML). Most literature on FL has focused on ML model training for (i) a single task/model, with (ii) a synchronous scheme for updating model parameters,…

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the…

Predicting disease states from functional brain connectivity is critical for the early diagnosis of severe neurodegenerative diseases such as Alzheimer's Disease and Parkinson's Disease. Existing studies commonly employ Graph Neural…

Federated Learning (FL) is a popular distributed learning paradigm to break down data silo. Traditional FL approaches largely rely on gradient-based updates, facing significant issues about heterogeneity, scalability, convergence, and…

While many recent Physics-Informed Neural Networks (PINNs) variants have had considerable success in solving Partial Differential Equations, the empirical benefits of feature mapping drawn from the broader Neural Representations research…

Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…

In this paper, we investigate the relationship between deep neural networks (DNN) with rectified linear unit (ReLU) function as the activation function and continuous piecewise linear (CPWL) functions, especially CPWL functions from the…

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…

Federated Learning (FL) has emerged as a key paradigm for building Trustworthy AI systems by enabling privacy-preserving, decentralized model training. However, FL is highly susceptible to adversarial attacks that compromise model integrity…