arXiv subjects

Longfei Gao

Publications and source records attributed to Longfei Gao.

11 recordsLinked to original sources

arXiv2026

Dekker's floating point number system and compensated summation algorithms

The recent hardware trend towards reduced precision computing has reignited the interest in numerical techniques that can be used to enhance the accuracy of floating point operations beyond what is natively supported for basic arithmetic operations on the hardware. In this work, we study the behavior of various compensated summation techniques, which can be used to enhance the accuracy for the summation operation, particularly in situations when the addends are not known a priori. Complete descriptions of the error behavior are provided for these techniques. In particular, the relationship between the intermediate results at two consecutive summing steps is provided, which is used to identify the operation that limits accuracy and guide the design of more nuanced techniques. The analysis relies on the work of Dekker [Numerische Mathematik, 1971], which uses a special floating point number system that does not require uniqueness in the number representation. Despite this seemingly strange attribute, Dekker's system is very convenient for the analysis here and allows general statements to be expressed succinctly compared to a number system that requires uniqueness. To prepare the foundation for discussion, we start by giving a thorough exhibition of Dekker's number system and supply the details that were omitted in Dekker [Numerische Mathematik, 1971]. Numerical examples are designed to explain the inner workings of these compensated summation techniques, illustrate their efficacy, and empirically verify the analytical results derived. Discussions are also given on application scenarios where these techniques can be beneficial.

math.NA↗

arXiv2025

Aurora: Architecting Argonne's First Exascale Supercomputer for Accelerated Scientific Discovery

Aurora is Argonne National Laboratory's pioneering Exascale supercomputer, designed to accelerate scientific discovery with cutting-edge architectural innovations. Key new technologies include the Intel(TM) Xeon(TM) Data Center GPU Max Series (code-named Sapphire Rapids) with support for High Bandwidth Memory (HBM), alongside the Intel(TM) Data Center GPU Max Series (code-named Ponte Vecchio) on each compute node. Aurora also integrates the Distributed Asynchronous Object Storage (DAOS), a novel exascale storage solution, and leverages Intel's oneAPI programming environment. This paper presents an in-depth exploration of Aurora's node architecture, the HPE Slingshot interconnect, the supporting software ecosystem, and DAOS. We provide insights into standard benchmark performance and applications readiness efforts via Aurora's Early Science Program and the Exascale Computing Project.

cs.DC↗

arXiv2025

TCM-Tongue: A Standardized Tongue Image Dataset with Pathological Annotations for AI-Assisted TCM Diagnosis

Traditional Chinese medicine (TCM) tongue diagnosis, while clinically valuable, faces standardization challenges due to subjective interpretation and inconsistent imaging protocols, compounded by the lack of large-scale, annotated datasets for AI development. To address this gap, we present the first specialized dataset for AI-driven TCM tongue diagnosis, comprising 6,719 high-quality images captured under standardized conditions and annotated with 20 pathological symptom categories (averaging 2.54 clinically validated labels per image, all verified by licensed TCM practitioners). The dataset supports multiple annotation formats (COCO, TXT, XML) for broad usability and has been benchmarked using nine deep learning models (YOLOv5/v7/v8 variants, SSD, and MobileNetV2) to demonstrate its utility for AI development. This resource provides a critical foundation for advancing reliable computational tools in TCM, bridging the data shortage that has hindered progress in the field, and facilitating the integration of AI into both research and clinical practice through standardized, high-quality diagnostic data.

eess.IV↗

arXiv2023

Half precision wave simulation

In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can significantly reduce the memory footprint comparing to operating at single or double precision. For memory bound applications such as time domain wave simulations, this is an attractive feature. However, the narrower width of the half precision data format can lead to degradation of the solution quality due to larger roundoff errors. In this work, we illustrate with carefully designed numerical experiments the negative impact caused by the accumulation of roundoff errors in wave simulations. Specifically, the energy-conserving property of the wave equations is employed as a convenient diagnosis tool. The corresponding remedy in the form of compensated sum is then provided, with its efficacy demonstrated using numerical examples with both acoustic and elastic wave equations on hardware that support half precision arithmetic natively.

math.NA↗

arXiv2023

LiDAR-NeRF: Novel LiDAR View Synthesis via Neural Radiance Fields

We introduce a new task, novel view synthesis for LiDAR sensors. While traditional model-based LiDAR simulators with style-transfer neural networks can be applied to render novel views, they fall short of producing accurate and realistic LiDAR patterns because the renderers rely on explicit 3D reconstruction and exploit game engines, that ignore important attributes of LiDAR points. We address this challenge by formulating, to the best of our knowledge, the first differentiable end-to-end LiDAR rendering framework, LiDAR-NeRF, leveraging a neural radiance field (NeRF) to facilitate the joint learning of geometry and the attributes of 3D points. However, simply employing NeRF cannot achieve satisfactory results, as it only focuses on learning individual pixels while ignoring local information, especially at low texture areas, resulting in poor geometry. To this end, we have taken steps to address this issue by introducing a structural regularization method to preserve local structural details. To evaluate the effectiveness of our approach, we establish an object-centric multi-view LiDAR dataset, dubbed NeRF-MVL. It contains observations of objects from 9 categories seen from 360-degree viewpoints captured with multiple LiDAR sensors. Our extensive experiments on the scene-level KITTI-360 dataset, and on our object-level NeRF-MVL show that our LiDAR-NeRF surpasses the model-based algorithms significantly.

cs.CV↗

arXiv2022

Nonuniform 3D finite difference elastic wave simulation on staggered grids

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by nonconforming interfaces. We demonstrate that this layer-wise finite difference discretization has the potential to significantly reduce the simulation cost, compared to its fully uniform counterpart. Stability of such a discretization is achieved by using specially designed difference operators, which are variants of the standard difference operators with adaptations near boundaries or interfaces, and penalty terms, which are appended to the discretized wave system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized wave system is shown to preserve the energy conserving property of the continuous elastic wave equation, and $\textit{a fortiori}$ ensure the stability of the simulation. Numerical examples are presented to demonstrate the efficacy of the proposed simulation approach.

math.NA↗

arXiv2022

Strongly imposing the free surface boundary condition for wave equations with finite difference operators

Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive structural evaluation, etc. Finite difference methods remain popular choices for these simulations due to their simplicity and efficiency. In particular, the family of finite difference methods based on the summation-by-parts operators and the simultaneous-approximation-terms technique have been proposed for these simulations, which offers great flexibility in addressing boundary and interface conditions. For the applications mentioned above, surface of the earth is usually associated with the free surface boundary condition. In this study, we demonstrate that the weakly imposed free surface boundary condition through the simultaneous-approximation-terms technique can have issue when the source terms, which introduces abrupt disturbances to the wave field, are placed too close to the surface. In response, we propose to build the free surface boundary condition into the summation-by-parts finite difference operators and hence strongly and automatically impose the free surface boundary condition to address this issue. The procedure is very simple for acoustic wave equation, requiring resetting a few rows and columns in the existing difference operators only. For the elastic wave equation, the procedure is more involved and requires special design of the grid layout and summation-by-parts operators that satisfy additional requirements, as revealed by the discrete energy analysis. In both cases, the energy conserving property is preserved. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.

math.NA↗

arXiv2022

Simultaneous approximation terms for elastic wave equations on nonuniform grids

We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations on uniform grids. To address this issue, we demonstrate how to properly couple two non-overlapping neighboring subdomains that are discretized uniformly, but with different grid spacings. Specifically, a numerical procedure is presented to impose the interface conditions weakly through carefully designed penalty terms, such that the overall semi-discretization conserves a discrete energy resembling the continuous energy possessed by the elastic wave system.

math.NA↗

arXiv2021

Explicit coupling of acoustic and elastic wave propagation in finite difference simulations

We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), while with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretization with carefully designed penalty terms.

physics.comp-ph↗

arXiv2018

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

math.NA↗

arXiv2018

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

math.NA↗