Exponential Function-Based Neural Tangent Kernels for SECM Signal Reconstruction

Scanning electrochemical microscopy (SECM) provides spatially resolved electrochemical information but is constrained by long acquisition times arising from dense spatial sampling requirements. This work investigates whether physics-informed signal representations can improve neural reconstruction of SECM approach curve signals from sparse measurements. We propose an exponential function-based Neural Tangent Kernel (NTK) framework in which SECM signals are encoded using deterministic exponential feature mappings aligned with diffusion-controlled electrochemical dynamics. A layer-wise NTK checkpointing mechanism is employed to filter covariantly insignificant components during training, reducing redundancy while preserving dominant signal modes. The method is evaluated on synthetically generated SECM signals designed to replicate characteristic approach curve behavior. Quantitative performance is assessed using root mean square error (RMSE), mean absolute error (MAE), relative error (%), and the coefficient of determination (R2). Compared to a random Gaussian (Fourier feature) baseline (RMSE = 0.0952, MAE = 0.0547, Rel.Err = 17.68%), the proposed exponential mappings achieve consistently lower reconstruction error, with the best configuration yielding RMSE = 0.0858, MAE = 0.0375, and relative error = 11.10% under identical training conditions. Results demonstrate that incorporating physically motivated exponential feature representations into NTK-aware learning improves reconstruction fidelity and stability for low-dimensional electrochemical signals, highlighting the potential of physics-informed kernel methods for accelerated SECM data acquisition.