Related papers: Domain decomposition of large neural network surro…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Single Domain Generalization (SDG) aims to train models that maintain consistent performance across diverse scenarios using data from a single source. While latent diffusion models (LDMs) show promise for augmenting limited source data, our…
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…
Deep neural networks suffer from significant performance deterioration when there exists distribution shift between deployment and training. Domain Generalization (DG) aims to safely transfer a model to unseen target domains by only relying…
This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…
With the increasing utilization of deep learning in outdoor settings, its robustness needs to be enhanced to preserve accuracy in the face of distribution shifts, such as compression artifacts. Data augmentation is a widely used technique…
Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…
We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
Parallelization framework has become a necessity to speed up the training of deep neural networks (DNN) recently. Such framework typically employs the Model Average approach, denoted as MA-DNN, in which parallel workers conduct respective…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
Deep Neural Networks (DNNs) have improved the accuracy of classification problems in lots of applications. One of the challenges in training a DNN is its need to be fed by an enriched dataset to increase its accuracy and avoid it suffering…
This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition…
Deep neural networks with more parameters and FLOPs have higher capacity and generalize better to diverse domains. But to be deployed on edge devices, the model's complexity has to be constrained due to limited compute resource. In this…
Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. Fixed penalty methods, though common, lack adaptability and suffer from hyperparameter sensitivity. In this paper, we propose a…
For deep learning applications, the massive data development (e.g., collecting, labeling), which is an essential process in building practical applications, still incurs seriously high costs. In this work, we propose an effective data…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
We study in detail the two main algorithms which have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model. We show that the updates produced by the…
In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface…