Neural Networks for Solving PDEs on Edge Computing Platforms: A Comprehensive Analysis

Solving elliptic partial differential equations (PDEs) with traditional methods is challenging on edge devices due to their reliance on fine meshes. This study evaluates neural networks as an efficient alternative, comparing 60 architectures and five optimizers on three single-board computers. Our methodology uniquely tested spatial interpolation by training on 900 points and verifying on 6,400, demonstrating robustness to mesh density. Deeper architectures (4–5 layers, 30–50 neurons) achieved errors of 10−4, with Adamax consistently proving the best-performing optimizer. Hardware benchmarks revealed critical trade-offs. The NVIDIA Jetson Nano offered optimal overall performance (8–12 ms inference, ≈ 1<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> power consumption, temperatures < 32°C), while the TPU-accelerated ASUS Tinker Edge T provided superior linear scalability, essential for varying problem sizes. However, this finding highlights that specialized hardware requires software co-optimization, as unoptimized TPU inference was unexpectedly slow. The Raspberry Pi required active cooling due to significant overheating (up to < 80°C). Across all platforms, neural networks maintained high solution accuracy (< 0.05% error deviation), overcoming the limitations of traditional mesh refinement. We conclude that neural networks are a compelling alternative for solving PDEs on edge devices.