Related papers: A machine learning accelerated FE$^2$ homogenizati…
The authors have shown in previous contributions that reduced order modeling with optimal cubature applied to finite element square (FE2) techniques results in a reliable and affordable multiscale approach, the HPR-FE2 technique. Such…
Federated learning involves training machine learning models over devices or data silos, such as edge processors or data warehouses, while keeping the data local. Training in heterogeneous and potentially massive networks introduces bias…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm:…
The future of machine learning lies in moving data collection along with training to the edge. Federated Learning, for short FL, has been recently proposed to achieve this goal. The principle of this approach is to aggregate models learned…
In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…
Multi-view Feature Extraction (MvFE) has wide applications in machine learning, image processing and other fields. When dealing with massive high-dimensional data, the performance of classical computer faces severe challenges due to MvFE…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
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…
Mixture-of-Experts (MoE) has emerged as a promising approach to scale up deep learning models due to its significant reduction in computational resources. However, the dynamic nature of MoE leads to load imbalance among experts, severely…
As a promising approach to deal with distributed data, Federated Learning (FL) achieves major advancements in recent years. FL enables collaborative model training by exploiting the raw data dispersed in multiple edge devices. However, the…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The sensitivity of heterogeneous energetic (HE) materials (propellants, explosives, and pyrotechnics) is critically dependent on their microstructure. Initiation of chemical reactions occurs at hot spots due to energy localization at sites…
Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Machine learning methods for estimating heterogeneous treatment effects (HTE) facilitate large-scale personalized decision-making across various domains such as healthcare, policy making, education, and more. Current machine learning…