Physics Structure-Informed Neural Networks in the TinyML Pipeline: Antisymmetry Preservation, Deployment Accounting, and Training-Budget Sensitivity
TL;DR
The results separate what physics structure preserves from what TinyML deployment must measure explicitly, as structure improves Burgers accuracy and antisymmetry at a given footprint rather than automatically shrinking hardware requirements.
Abstract
Physics structure-informed neural networks (Ψ-NN) promise to carry known physical relations into compact models, but tiny machine learning (TinyML) deployment adds compression, finite precision, compilation, and hardware constraints that can change how those benefits appear in practice. We study this end to end for Burgers odd-in-x antisymmetry. A Ψ-NN preserves the encoded relation through clustering, 8-bit integer (INT8) quantization, compilation, and Cortex-M target-instruction-set emulation, achieving 6.0% relative L2 error and an antisymmetry residual of 0.006; none of seven evaluated compression baselines matches both under the common protocol. Deployment accounting reveals a complementary result. Centroid count is not deployable memory because the relation/index table must also be stored, limiting 32-bit floating-point (FP32) weight-memory reduction to about 4× under one-byte indexing. At matched parameter count, structured and dense models have comparable flash and instruction requirements, so structure improves Burgers accuracy and antisymmetry at a given footprint rather than automatically shrinking hardware requirements. Under complete lossless checkpointing, interruption timing has no independent effect, while budget loss and checkpoint degradation govern robustness. In the eleven-problem dataset, none of four tested descriptors reaches statistical significance for budget sensitivity. These results separate what physics structure preserves from what TinyML deployment must measure explicitly.