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The rapid evolution of generative adversarial networks (GANs) and diffusion models has made synthetic media increasingly realistic, raising societal concerns around misinformation, identity fraud, and digital trust. Existing deepfake…

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two…

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and…

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…

The accurate representation of numerous physical, chemical, and biological processes relies heavily on differential equations (DEs), particularly nonlinear differential equations (NDEs). While understanding these complex systems…

We propose a novel {\it Equilibrated Recurrent Neural Network} (ERNN) to combat the issues of inaccuracy and instability in conventional RNNs. Drawing upon the concept of autapse in neuroscience, we propose augmenting an RNN with a…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Exemplar replay has become an effective strategy for mitigating catastrophic forgetting in federated continual learning (FCL) by retaining representative samples from past tasks. Existing studies focus on designing sample-importance…

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

Accurate dynamic modeling is critical for autonomous racing vehicles, especially during high-speed and agile maneuvers where precise motion prediction is essential for safety. Traditional parameter estimation methods face limitations such…

We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Networks (EFENN) introduced with the Hierarchical Deep-learning…

Human motion modelling is a classical problem at the intersection of graphics and computer vision, with applications spanning human-computer interaction, motion synthesis, and motion prediction for virtual and augmented reality. Following…

The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…

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,…

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…