scientific computing

This work addresses the challenges of integrating sparse linear algebra libraries into scientific computing applications—such as computational fluid dynamics (CFD), power grid simulation, and cardiac electrophysiology—including poor maintainability, high cross-platform adaptation costs, and tight coupling between application code and low-level implementations. We propose a modular integration framework built upon Ginkgo, which achieves loose coupling via a unified abstract interface, explicit decoupling of algorithms from hardware backends, and runtime backend selection. From a software engineering perspective, the framework significantly reduces integration complexity while enhancing portability, testability, and long-term maintainability. Experimental evaluation demonstrates that the framework sustains high performance across heterogeneous platforms (CPU/GPU), shortens the hardware adaptation cycle, and enables efficient, sustainable multi-domain simulation.

Scientific software selection frequently suffers from non-reproducible benchmarks due to multi-library, multi-metric evaluation and dynamic evolution—such as the introduction of new algorithms or modifications to test cases and evaluation criteria. This paper addresses numerical integration over arbitrary 2D/3D domains with implicit or parameterized boundaries (cut-cell quadrature), proposing the first automated benchmarking framework that systematically integrates CI/CD engineering practices into scientific computing workflows. The framework unifies GitHub Actions, Docker, Python-based scheduling, Jupyter-based report generation, and semantically versioned result archiving. It supports automated configuration, execution, visualization, and historical result comparison. It achieves >90% automation for benchmark tasks and regression detection; reduces integration time for new libraries or algorithms by 70%; and enables precise attribution of performance deviations to specific code commits. The framework significantly enhances reliability, reproducibility, and evolutionary adaptability in scientific software evaluation.

This study addresses the lack of quantitative evidence on the educational impact of federally funded computational science graduate internships at U.S. national laboratories. To fill this gap, the project developed the first multidimensional learning outcomes assessment framework specifically for computational science internships, employing a mixed-methods design integrating structured pre-post surveys, qualitative coding, and inferential statistical testing. Results demonstrate statistically significant improvements in interns’ computational competencies (p < 0.01), domain-specific knowledge in sustainable energy (+32%), and intent to pursue careers at national laboratories (+41%). Furthermore, 78% of participants advanced into related doctoral programs or industry positions. This work provides the first empirically grounded evaluation of national laboratory internship efficacy, establishing both a methodological foundation and evidence-based insights to inform STEM workforce development policy and the design of industry–academia partnership programs.

This work addresses the absence of a standardized benchmark for evaluating code generation targeting partial differential equation (PDE) solvers, particularly with respect to numerical accuracy, computational efficiency, and compatibility with mainstream finite element libraries. To bridge this gap, the authors introduce the first multi-metric, multi-library benchmark for PDE solver generation, comprising 645 structured instances spanning six mathematical problem types and eleven PDE classes. The benchmark supports three major finite element frameworks—DOLFINx, Firedrake, and deal.II—and incorporates a staged evaluation framework that holistically assesses code executability, numerical correctness, and performance. Experimental results demonstrate that while current large language models can produce executable code, their success rate drops substantially when stringent accuracy and efficiency requirements are imposed, thereby underscoring the necessity and effectiveness of the proposed benchmark in advancing reliable and efficient automated PDE solver generation.

This work addresses the absence of a systematic, traceable, and reproducible framework for reporting the performance of mathematical libraries—a gap that hinders accurate performance evaluation and resource planning for scientific applications on high-performance computing (HPC) systems. To this end, the paper introduces LAAB, the first framework explicitly designed around four core principles: traceability, compatibility, reliability, and accessibility. LAAB establishes an end-to-end reproducible performance evaluation pipeline through standardized benchmarking protocols, comprehensive metadata management, execution environment tracking, and advanced performance analysis techniques. The framework substantially enhances the accuracy and interoperability of mathematical library performance reporting, thereby providing a robust foundation for performance prediction and resource scheduling in scientific computing.

Modern computational fluid dynamics (CFD) urgently requires seamless integration of simulation into design, optimization, and data-driven workflows, confronting challenges in the co-design of physical models, numerical methods, heterogeneous hardware, and automatic differentiation. This work systematically evaluates the suitability of the Julia programming language for CFD, leveraging its unified language ecosystem, multiple dispatch, and type specialization to deeply integrate high performance, differentiability, and software composability. Empirical validation through distributed CPU/multi-GPU parallelism, performance-portable frameworks, and open-source CFD projects demonstrates the feasibility of native Julia-based CFD at scale and its advantages in differentiable workflows. Nevertheless, the maturity of Julia’s industrial toolchain still lags behind that of conventional languages.

This work proposes an end-to-end scientific workflow framework for partial differential equations (PDEs) based on large language models (LLMs), aiming to bridge the gap between simulation and real-world systems. The framework systematically integrates LLMs across the entire PDE pipeline—spanning discovery of governing equations, automated generation and iterative refinement of numerical solvers, and simulation-informed decision-making—thereby establishing an intelligent interface that connects natural language, symbolic mathematics, executable code, and physical constraints. Experimental results demonstrate the framework’s significant potential in automating PDE-centric scientific workflows, while also highlighting critical challenges such as the scarcity of high-quality data and difficulties in transferring learned capabilities to real-world scenarios.

This project addresses the energy efficiency constraints and precision challenges introduced by heterogeneous accelerators in scientific computing. With "energy consumption per trusted solution" as its core objective, it establishes a mixed-precision computing framework. This work innovatively proposes a "reckless yet responsible" computing paradigm that integrates novel number formats, floating-point emulation, hardware-software co-design, and multi-level resource management to effectively balance aggressive low-precision arithmetic with system-level detection and verification. Furthermore, the project systematically reviews the technological landscape and development trajectories of this field, distills a list of open problems, and provides comprehensive design guidelines. Ultimately, it offers both a theoretical foundation and practical reference for next-generation energy-efficient scientific computing.

This study addresses the loss of precision caused by rounding errors in finite element computations, which remains difficult to analyze a priori. We propose the first automated a posteriori rounding error estimation framework that leverages running error analysis to track numerical and error propagation in real time. Built upon the FEniCS Form Compiler, this method achieves the first automated error estimation within finite element kernels through a C++ backend, custom arithmetic types, and templated kernel generation techniques. Experimental results demonstrate that the framework successfully detects catastrophic cancellation with only a 2–4× performance overhead. By effectively supporting mixed-precision design and numerical debugging, this work establishes a new paradigm for ensuring reliability in scientific computing.

This study addresses the contradiction between high-precision floating-point redundancy in scientific computing and the hardware trend toward lower precision. By revealing that numerical discretization errors can mask low-order bit information, this work proposes a signal-to-noise ratio (SNR)-based criterion for safe precision reduction. Building upon this principle, a dataflow-driven automated mixed-precision workflow is developed, integrating subgraph optimization and GPU acceleration to achieve adaptive precision allocation for partial differential equation simulations. When applied to meteorological and climate modeling, the proposed method attains up to a 1.8× speedup while strictly preserving physical fidelity. Overall, this research provides a systematic solution for energy efficiency optimization in scientific computing.