Related papers: A Unified Phase-Field Fourier Neural Network Frame…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…
This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…
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,…
Fundus image segmentation on unseen domains is challenging, especially for the over-parameterized deep models trained on the small medical datasets. To address this challenge, we propose a method named Adaptive Feature-fusion Neural Network…
Solving optimal power flow (OPF) problems for large distribution networks incurs high computational complexity. We consider a large multi-phase distribution network of tree topology with a deep penetration of active devices. We divide the…
This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…
Integration of machine learning (ML) into the topology optimization (TO) framework is attracting increasing attention, but data acquisition in data-driven models is prohibitive. Compared with popular ML methods, the physics-informed neural…
In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…
Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial…
Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the…
In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural…
Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is…
Automated design methods for convolutional neural networks (CNNs) have recently been developed in order to increase the design productivity. We propose a neuroevolution method capable of evolving and optimizing CNNs with respect to the…
The idea of embedding optimization problems into deep neural networks as optimization layers to encode constraints and inductive priors has taken hold in recent years. Most existing methods focus on implicitly differentiating…
While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized…
We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…