Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and W-cycles. We use grammar rules to generate arbitrary-shaped cycles, wherein the smoothers and their relaxation weights are chosen independently at each step within the cycle. We call this a flexible multigrid cycle. These flexible cycles are used in Algebraic Multigrid (AMG) methods with the help of grammar rules and optimized using genetic programming. The flexible AMG methods are implemented in the software library of hypre, and the programs are optimized separately for two cases: a standalone AMG solver for a 3D anisotropic problem and an AMG preconditioner with conjugate gradient for a multiphysics code. We observe that the optimized flexible cycles provide higher efficiency and better performance than the standard cycle types.

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most severe limitation of AMG methods is the dependence on parameters that require to be fine-tuned. In particular, the strong threshold parameter is the most relevant since it stands at the basis of the construction of successively coarser grids needed by the AMG methods. We introduce a novel Deep Learning algorithm that minimizes the computational cost of the AMG method when used as a finite element solver. We show that our algorithm requires minimal changes to any existing code. The proposed Artificial Neural Network (ANN) tunes the value of the strong threshold parameter by interpreting the sparse matrix of the linear system as a black-and-white image and exploiting a pooling operator to transform it into a small multi-channel image. We experimentally prove that the pooling successfully reduces the computational cost of processing a large sparse matrix and preserves the features needed for the regression task at hand. We train the proposed algorithm on a large dataset containing problems with a highly heterogeneous diffusion coefficient defined in different three-dimensional geometries and discretized with unstructured grids and linear elasticity problems with a highly heterogeneous Young's modulus. When tested on problems with coefficients or geometries not present in the training dataset, our approach reduces the computational time by up to 30%.

We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on spectrally equivalent coarse-grid operators, we have developed novel ML algorithms that utilize neural networks (NNs) combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall AMG convergence for solving parametric partial differential equation (PDE) problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and compare with existing methods for computing non-Galerkin coarse-grid operators.

Deep learning-based adversarial malware detectors have yielded promising results in detecting never-before-seen malware executables without relying on expensive dynamic behavior analysis and sandbox. Despite their abilities, these detectors have been shown to be vulnerable to adversarial malware variants - meticulously modified, functionality-preserving versions of original malware executables generated by machine learning. Due to the nature of these adversarial modifications, these adversarial methods often use a \textit{single view} of malware executables (i.e., the binary/hexadecimal view) to generate adversarial malware variants. This provides an opportunity for the defenders (i.e., malware detectors) to detect the adversarial variants by utilizing more than one view of a malware file (e.g., source code view in addition to the binary view). The rationale behind this idea is that while the adversary focuses on the binary view, certain characteristics of the malware file in the source code view remain untouched which leads to the detection of the adversarial malware variants. To capitalize on this opportunity, we propose Adversarially Robust Multiview Malware Defense (ARMD), a novel multi-view learning framework to improve the robustness of DL-based malware detectors against adversarial variants. Our experiments on three renowned open-source deep learning-based malware detectors across six common malware categories show that ARMD is able to improve the adversarial robustness by up to seven times on these malware detectors.

Deep Learning (DL)-based malware detectors are increasingly adopted for early detection of malicious behavior in cybersecurity. However, their sensitivity to adversarial malware variants has raised immense security concerns. Generating such adversarial variants by the defender is crucial to improving the resistance of DL-based malware detectors against them. This necessity has given rise to an emerging stream of machine learning research, Adversarial Malware example Generation (AMG), which aims to generate evasive adversarial malware variants that preserve the malicious functionality of a given malware. Within AMG research, black-box method has gained more attention than white-box methods. However, most black-box AMG methods require numerous interactions with the malware detectors to generate adversarial malware examples. Given that most malware detectors enforce a query limit, this could result in generating non-realistic adversarial examples that are likely to be detected in practice due to lack of stealth. In this study, we show that a novel DL-based causal language model enables single-shot evasion (i.e., with only one query to malware detector) by treating the content of the malware executable as a byte sequence and training a Generative Pre-Trained Transformer (GPT). Our proposed method, MalGPT, significantly outperformed the leading benchmark methods on a real-world malware dataset obtained from VirusTotal, achieving over 24.51\% evasion rate. MalGPT enables cybersecurity researchers to develop advanced defense capabilities by emulating large-scale realistic AMG.

In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods are numerical methods used to solve large linear systems of equations efficiently. One of the main differences between AMG methods is how the coarser grid is constructed from a given fine grid. There are two main classes of AMG methods; graph and aggregation based coarsening methods. Here we propose an aggregation-based coarsening framework leveraging graph representation learning and clustering algorithms. Our method introduces the power of machine learning into the AMG research field and opens a new perspective for future researches. The proposed method uses graph representation learning techniques to learn latent features of the graph obtained from the underlying matrix of coefficients. Using these extracted features, we generated a coarser grid from the fine grid. The proposed method is highly capable of parallel computations. Our experiments show that the proposed method's efficiency in solving large systems is closely comparable with other aggregation-based methods, demonstrating the high capability of graph representation learning in designing multi-grid solvers.