探索和利用科学计算中的运行时可重构浮点精度：求解偏微分方程的案例研究.pdf

1、Exploring and Exploiting Runtime ReconfigurableFloating-Point Precision in Scientific Computing:a Case Study for Solving PDEsCong“Callie”Hao,Georgia Institute of TechnologyASP-DAC 2025 Tokyo,JapanCong“Callie”Hao|Sharc-lab Georgia Institute of Technology Definition:solving complex real-world problems

2、 using mathematical models and computational algorithms Core Techniques:numerical methodsoPartial Differential Equations(PDE)ApplicationsoPhysics:Simulations of fluid dynamics and heat transferoEngineering:Structural analysis and optimizationoClimate Science:Weather prediction and environmental mode

3、lingoBiology:Protein folding and genome analysis2Scientific ComputingCong“Callie”Hao|Sharc-lab Georgia Institute of Technology Simulate heat diffusion along a 1D rod over timeo(,):temperature at position and time o:time(in seconds)o:position along the length of the rod Finite difference approximatio

4、n:oDiscretize space into points and time into steps oCompute step by step3Example of Heat Equation=22+1=+2(+1 2+1)Cong“Callie”Hao|Sharc-lab Georgia Institute of Technology4Scientific Computing v.s.Machine LearningVery sensitive in data precisionComputationally intensiveSupercomputers in HPC centersS

5、cientific Computing Machine LearningLow-precision is prevailingComputationally intensiveClouds and edges32-bit floating point64-bit floating point8-bit floating point8-bit or 16-bit fixed point8-bit or 4-bit integerApproximate Computing(AxC)Cong“Callie”Hao|Sharc-lab Georgia Institute of TechnologySc

6、ientific Computing Challenges010002000300016-bit FP32-bit FP64-bit FP4858412,667Area of floating-point multipliers(Synthesized on FPGA)Massive computation power Long simulation latencyoCan take weeks or months More bandwidth Large memory requirement Can we reduce precision?oEven reducing by half wou