Related papers: Machine learning and domain decomposition methods …
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…
Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…
This paper reviews machine learning applications and approaches to detection, classification and control of intelligent materials and structures with embedded distributed computation elements. The purpose of this survey is to identify…
Machine learning typically relies on the assumption that training and testing distributions are identical and that data is centrally stored for training and testing. However, in real-world scenarios, distributions may differ significantly…
While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…
We present a survey of ways in which existing scientific knowledge are included when constructing models with neural networks. The inclusion of domain-knowledge is of special interest not just to constructing scientific assistants, but…
In the era of deep learning (DL), convolutional neural networks (CNNs), and large language models (LLMs), machine learning (ML) models are becoming increasingly complex, demanding significant computational resources for both inference and…
With the advance of the powerful heterogeneous, parallel and distributed computing systems and ever increasing immense amount of data, machine learning has become an indispensable part of cutting-edge technology, scientific research and…
Learning across domains is challenging when data cannot be centralized due to privacy or heterogeneity, which limits the ability to train a single comprehensive model. Model merging provides an appealing alternative by consolidating…
There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML)…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
Artificial intelligence has made remarkable progress in handling complex tasks, thanks to advances in hardware acceleration and machine learning algorithms. However, to acquire more accurate outcomes and solve more complex issues,…
Machine unlearning (MU) is gaining increasing attention due to the need to remove or modify predictions made by machine learning (ML) models. While training models have become more efficient and accurate, the importance of unlearning…
Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains.…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods, and the integration with domain decomposition strategies…
Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these…
Automated machine learning (AutoML) aims to find optimal machine learning solutions automatically given a machine learning problem. It could release the burden of data scientists from the multifarious manual tuning process and enable the…