Problem
Research questions and friction points this paper is trying to address.
numerical precision
scientific computing
mixed-precision
PDE simulations
low-precision formats
What Bloats Your Floats? Right-Sizing Numerical Precision for Scientific Computing
🤖 AI Summary
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.
📝 Abstract
While FP64 (binary64) remains the standard representation of real numbers in scientific computing, hardware trends increasingly favor low-precision formats optimized for AI workloads. This shift prioritizes throughput and energy efficiency over full-precision capabilities. We challenge the necessity of high-precision arithmetic in PDE-governed simulations, where spatial and temporal discretization errors introduce a physical noise floor that masks the lower-order bits of the FP64 format, rendering them irrelevant. We propose a criterion based on the Signal-to-Noise Ratio (SNR) with respect to spatial and temporal refinements to evaluate the impact of safe precision reduction on scientific computations. Finally, we present an automated dataflow-centric workflow for targeted lowering within mixed-precision subgraphs in complex scientific applications. Large-scale evaluations of weather and climate applications show that strategic precision reduction on GPUs achieves up to 1.8x speedup without compromising physical fidelity.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Mixed-Precision
Signal-to-Noise Ratio
Automated Workflow
Scientific Computing
PDE Simulations
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