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Custom Floating-Point Computations for the Optimization of ODE Solvers on FPGA

Authors Serena Curzel , Marco Gribaudo

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Author Details

Serena Curzel
  • Politecnico di Milano, Italy
Marco Gribaudo
  • Politecnico di Milano, Italy

Funding

Funded by the European Union - NextGenerationEU - PNRR - M4 - C2 - I1.3 - SERICS PE00000014 - Cascade Funding SPOKE 8 - (MAM-CYD) - CUP J33C22002810001.

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Serena Curzel and Marco Gribaudo. Custom Floating-Point Computations for the Optimization of ODE Solvers on FPGA. In 16th Workshop on Parallel Programming and Run-Time Management Techniques for Many-Core Architectures and 14th Workshop on Design Tools and Architectures for Multicore Embedded Computing Platforms (PARMA-DITAM 2025). Open Access Series in Informatics (OASIcs), Volume 127, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.PARMA-DITAM.2025.2

Abstract

Mean Field Analysis and Markovian Agents are powerful techniques for modeling complex systems of distributed interacting objects, for which efficient analytical and numerical solution algorithms can be implemented through linear systems of ordinary differential equations (ODEs). Solving such ODE systems on Field Programmable Gate Arrays (FPGAs) is a promising alternative to traditional CPU- and GPU-based approaches, especially in terms of energy consumption; however, the floating-point computations required are generally thought to be slow and inefficient when implemented on FPGA. In this paper, we demonstrate the use of High-Level Synthesis with automated customization of low-precision floating-point calculations, obtaining hardware accelerators for ODE solvers with improved quality of results and minimal output error. The proposed methodology does not require any manual rewriting of the solver code, but it remains prohibitively slow to evaluate any possible floating-point configuration through logic synthesis; in the future, we will thus implement automated design space exploration methods able to suggest promising configurations under user-defined accuracy and performance constraints.

Subject Classification

ACM Subject Classification
  • Hardware → Methodologies for EDA
  • Hardware → High-level and register-transfer level synthesis
  • Computer systems organization → Architectures
  • Hardware → Very large scale integration design
  • Hardware → Reconfigurable logic and FPGAs
Keywords
  • Differential Equations
  • High-Level Synthesis
  • FPGA
  • floating-point

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Supplementary Materials

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