Related papers: Efficient Exascale Discretizations: High-Order Fin…
Neural architectures and hardware accelerators have been two driving forces for the progress in deep learning. Previous works typically attempt to optimize hardware given a fixed model architecture or model architecture given fixed…
Recent feature matching methods have achieved remarkable performance but lack efficiency consideration. In this paper, we revisit the mainstream detector-free matching pipeline and improve all its stages considering both accuracy and…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
Verification of solutions is crucial for establishing the reliability of simulations. A central challenge is to find an accurate and reliable estimate of the discretization error. Current approaches to this estimation rely on the observed…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations. We extended the code generation infrastructure in Firedrake…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Modern GPUs are equipped with tensor cores (TCs) that are commonly used for matrix multiplication in artificial intelligence workloads. However, because they have high computational throughput, they can lead to significant performance gains…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
High performance grid computing is a key enabler of large scale collaborative computational science. With the promise of exascale computing, high performance grid systems are expected to incur electricity bills that grow super-linearly over…
To enable the pre-trained models to be fine-tuned with local data on edge devices without sharing data with the cloud, we design an efficient split fine-tuning (SFT) framework for edge and cloud collaborative learning. We propose three…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…