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Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
Geological carbon and energy storage are pivotal for achieving net-zero carbon emissions and addressing climate change. However, they face uncertainties due to geological factors and operational limitations, resulting in possibilities of…
In order to reduce the computational complexity of large language models, great efforts have been made to to improve the efficiency of transformer models such as linear attention and flash-attention. However, the model size and…
Dynamic-shape deep neural networks (DNNs) are rapidly evolving, attracting attention for their ability to handle variable input sizes in real-time applications. However, existing compilation optimization methods for such networks often rely…
Scientific simulation leveraging high-performance computing (HPC) systems is crucial for modeling complex systems and phenomena in fields such as astrophysics, climate science, and fluid dynamics, generating massive datasets that often…
Modern scientific simulations and instruments generate data volumes that overwhelm memory and storage, throttling scalability. Lossy compression mitigates this by trading controlled error for reduced footprint and throughput gains, yet…
In modern generative-AI workloads, matrix-vector/matrix-matrix multiplications (\emph{MatMul}) dominate the compute and energy cost. Achieving dramatic reductions in energy per token therefore requires a novel, specialized hardware that is…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…
Large language models (LLMs) have achieved state-of-the-art performance in natural language processing; however, their high computational cost remains a major bottleneck. In this study, we target computational efficiency by focusing on a…
Ensemble simulations of high-dimensional flow models (e.g., Navier Stokes type PDEs) are computationally prohibitive for real time applications. Neural operators enable fast inference but are limited by costly data requirements and poor…
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic…
As the landscape of deep neural networks evolves, heterogeneous dataflow accelerators, in the form of multi-core architectures or chiplet-based designs, promise more flexibility and higher inference performance through scalability. So far,…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
The computational and memory challenges of large language models (LLMs) have sparked several optimization approaches towards their efficient implementation. While prior LLM-targeted quantization, and prior works on sparse acceleration have…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
Dynamic voltage and frequency scaling (DVFS) and task-to-core allocation are critical for thermal management and balancing energy and performance in embedded systems. Existing approaches either rely on utilization-based heuristics that…