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High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

In this work we employ data-driven homogenization approaches to predict the particular mechanical evolution of polycrystalline aggregates with tens of individual crystals. In these oligocrystals the differences in stress response due to…

Standard physics-informed neural networks (PINNs) struggle to simulate highly oscillatory Helmholtz solutions in heterogeneous media because pointwise minimization of second-order PDE residuals is computationally expensive, biased toward…

The growing demand for computational resources in machine learning has made efficient resource allocation a critical challenge, especially in heterogeneous hardware clusters where devices vary in capability, age, and energy efficiency.…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding…

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…

Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for…

Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the…

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…

Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle…

Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…

Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative…

Real-world graph data environments intrinsically exist noise (e.g., link and structure errors) that inevitably disturb the effectiveness of graph representation and downstream learning tasks. For homogeneous graphs, the latest works use…

The speed of deep neural networks training has become a big bottleneck of deep learning research and development. For example, training GoogleNet by ImageNet dataset on one Nvidia K20 GPU needs 21 days. To speed up the training process, the…