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An evolutionary multi-objective aerodynamic design optimization method using the computational fluid dynamics (CFD) simulations incorporating deep neural network (DNN) to reduce the required computational time is proposed. In this approach,…

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

As FMs drive progress toward Artificial General Intelligence (AGI), fine-tuning them under privacy and resource constraints has become increasingly critical particularly when highquality training data resides on distributed edge devices.…

In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

Recently, innovative model aggregation methods based on knowledge distillation (KD) have been proposed for federated learning (FL). These methods not only improved the robustness of model aggregation over heterogeneous learning environment,…

We consider the problem of using diffusion models to generate fast, smooth, and temporally consistent robot motions. Although diffusion models have demonstrated superior performance in robot learning due to their task scalability and…

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs).…

Owing to the increasing need for massive data analysis and model training at the network edge, as well as the rising concerns about the data privacy, a new distributed training framework called federated learning (FL) has emerged. In each…

Federated Learning (FL) has garnered significant attention in manufacturing for its robust model development and privacy-preserving capabilities. This paper contributes to research focused on the robustness of FL models in object detection,…

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…

The acoustic scattering problem is modeled by the exterior Helmholtz equation, which is challenging to solve due to both the unboundedness of the domain and the high dispersion error, known as the pollution effect. We develop high-order…

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…

Federated learning (FL) enables collaborative model training across distributed devices without sharing raw data, but applying FL to multi-modal settings introduces significant challenges. Clients typically possess heterogeneous modalities…

The optimization with orthogonality has been shown useful in training deep neural networks (DNNs). To impose orthogonality on DNNs, both computational efficiency and stability are important. However, existing methods utilizing Riemannian…

Low-dose CT (LDCT) denoising remains an important yet challenging problem in medical imaging. Although recent learning-based methods have shown promising performance, those optimized using classical pixel-level objectives often produce…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…