Related papers: Shifting the Sweet Spot: High-Performance Matrix-F…
In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying…
Developing kernels for Processing-In-Memory (PIM) platforms poses unique challenges in data management and parallel programming on limited processing units. Although software development kits (SDKs) for PIM, such as the UPMEM SDK, provide…
We present a sequence of optimizations to the performance-critical compute kernels of the high-order discontinuous Galerkin solver of the hyperbolic PDE engine ExaHyPE -- successively tackling bottlenecks due to SIMD operations, cache…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
Fully Homomorphic Encryption (FHE) is a technique that allows arbitrary computations to be performed on encrypted data without the need for decryption, making it ideal for securing many emerging applications. However, FHE computation is…
Computing on encrypted data is a promising approach to reduce data security and privacy risks, with homomorphic encryption serving as a facilitator in achieving this goal. In this work, we accelerate homomorphic operations using the…
Faster explicit elastic wavefield simulations are required for large and complex three-dimensional media using a structured finite element method. Such wavefield simulations are suitable for GPUs, which have exhibited improved computational…
Parameter-efficient tuning (PET) aims to transfer pre-trained foundation models to downstream tasks by learning a small number of parameters. Compared to traditional fine-tuning, which updates the entire model, PET significantly reduces…
In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H-Matrices) with ACA (Adaptive Cross Approximation).…
Current FP8 grouped GEMM implementations require padding each group to a fixed alignment (e.g., 128), incurring memory and computational overhead. We propose \textit{TMA-Adaptive FP8 Grouped GEMM}, which eliminates padding by dynamically…
The growing scale of deep learning models has rendered standard hyperparameter (HP) optimization prohibitively expensive. A promising solution is the use of scale-aware hyperparameters, which can enable direct transfer of optimal HPs from…
Finite element simulations play a critical role in a wide range of applications, from automotive design to tsunami modeling and computational electromagnetics. Performing these simulations efficiently at the high resolutions needed for…
Modern Machine Learning (ML) training on large-scale datasets is a very time-consuming workload. It relies on the optimization algorithm Stochastic Gradient Descent (SGD) due to its effectiveness, simplicity, and generalization performance.…
The widespread adoption of cloud-based solutions introduces privacy and security concerns. Techniques such as homomorphic encryption (HE) mitigate this problem by allowing computation over encrypted data without the need for decryption.…
In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type…
For over a decade, explicit memory architectures like the Neural Turing Machine have remained theoretically appealing yet practically intractable for language modeling due to catastrophic gradient instability during Backpropagation Through…
Mixture-of-Experts (MoE) architectures are evolving towards finer granularity to improve parameter efficiency. However, existing MoE designs face an inherent trade-off between the granularity of expert specialization and hardware execution…