Neuroscience Inspired Graph Operators Towards Edge-Deployable Virtual Sensing for Irregular Geometries

Spiking neural operators are appealing for neuromorphic edge computing because event-driven substrates can, in principle, translate sparse activity into lower latency and energy. Whether that advantage survives deployment on commodity edge-GPU software stacks, however, remains unclear. We study this question on a Jetson Orin Nano 8 GB using five pretrained variable-spiking wavelet neural operator (VS-WNO) checkpoints and five matched dense wavelet neural operator (WNO) checkpoints on the Darcy rectangular benchmark. On a reference-aligned path, VS-WNO exhibits substantial algorithmic sparsity, with mean spike rates decreasing from 54.26% at the first spiking layer to 18.15% at the fourth. On a deployment-style request path, however, this sparsity does not reduce deployed cost: VS-WNO reaches 59.6 ms latency and 228.0 mJ dynamic energy per inference, whereas dense WNO reaches 53.2 ms and 180.7 mJ, while also achieving slightly lower reference-path error (1.77% versus 1.81%). Nsight Systems indicates that the request path remains launch-dominated and dense rather than sparsity-aware: for VS-WNO, cudaLaunchKernel accounts for 81.6% of CUDA API time within the latency window, and dense convolution kernels account for 53.8% of GPU kernel time; dense WNO shows the same pattern. On this Jetson-class GPU stack, spike sparsity is measurable but does not reduce deployed cost because the runtime does not suppress dense work as spike activity decreases.

We propose EdgeSpike, a co-designed spiking neural network (SNN) framework for autonomous low-power sensing in edge Internet of Things (IoT) architectures. EdgeSpike unifies (i) a hybrid surrogate-gradient and direct-encoding training pipeline, (ii) a hardware-aware neural architecture search (NAS) bounded by per-inference energy and memory budgets, (iii) an event-driven runtime targeting Intel Loihi 2, SpiNNaker 2, and commodity ARM Cortex-M microcontrollers with custom spike-sparse SIMD kernels, and (iv) a lightweight local plasticity rule enabling continual on-device adaptation without backpropagation. The framework is evaluated across five sensing tasks (keyword spotting, vibration-based machine fault detection, surface electromyography gesture recognition, 77 GHz radar human-activity classification, and structural-health acoustic-emission monitoring) on three hardware targets. EdgeSpike achieves a mean classification accuracy of 91.4%, within 1.2 percentage points (pp) of strong INT8 convolutional neural network (CNN) baselines (mean 92.6%), while reducing energy per inference by 18x to 47x on neuromorphic hardware (mean 31x) and by 4.6x to 7.9x on Cortex-M (mean 6.1x). End-to-end latency remains at or below 9.4 ms across all 15 task-hardware configurations. A seven-month, 64-node wireless field deployment confirms a 6.3x extension in projected battery lifetime (from 312 to 1978 days at 2 Wh per node) and bounded accuracy degradation under seasonal drift (0.7 pp with on-device adaptation versus 2.1 pp without). Hardware-aware NAS evaluates 8400 candidates and yields a 12-point Pareto front. EdgeSpike will be released as open source with reproducible training pipelines, hardware-portable runtimes, and benchmark suites.

Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scientific machine learning. While spectral methods provide strong inductive biases for modeling global interactions, they are typically limited to regular domains, and existing neural approaches often require domain warping, interpolation, or costly geometric embeddings. We introduce the \textbf{Graph Spectral Neural Operator (GSNO)}, a neural operator that combines spatial graph spectral decompositions with temporal Fourier transforms through a unified space--time spectral kernel. This formulation enables globally coherent operator learning on non-Cartesian discretizations without domain warping or autoregressive rollouts. By replacing learned geometric embeddings with a graph Laplacian spectral basis, GSNO provides geometry-aware spectral learning with low parameter complexity. Across steady and unsteady PDE benchmarks on irregular and geometry-dependent domains, GSNO achieves strong accuracy with reduced runtime and parameter counts, while demonstrating robust zero-shot generalization across mesh resolutions and geometry families.