Developing Chemical and Microbial Virtual Sensors with Cortical Gap Fusion Network in a Water Filtration System

Sparse-to-dense data reconstruction under extreme label sparsity presents a fundamental challenge in multi-fidelity data fusion. Environmental monitoring systems sometimes need to fuse expensive high-fidelity time series measurements with continuous low-fidelity sensor observations, creating a large supervision ratio that exceeds typical multi-fidelity applications by order of magnitude. Exploring a novel virtual sensor (soft sensor) can be a good solution to deal with this challenge. We develop the Cortical Gap Fusion Network (CGFN), a neuroscience-inspired architecture synthesizing spiking neural dynamics, unsupervised regime discovery, and discipline-informed constraints for sparse-to-dense data reconstruction. CGFN integrates four key innovations: (1) dual prediction heads implementing phasic burst-coded chemistry predictions and tonic neuromodulated microbial predictions with uncertainty quantified via Monte Carlo dropout; (2) a multiscale encoder combining dilated convolutions, self-attention, frequency analysis, and Leaky Integrate-and-Fire neurons for event-driven transient detection; (3) hierarchical cascade training exploiting discipline-informed causality to amplify effective supervision; and (4) curriculum-weighted temporal emphasis through Gaussian anchor diffusion concentrating learning near ground truth while maintaining interpolation stability. Validated was conducted based on a field-scale water filtration data set for microbial species population, revealing sub-weekly microbial dynamics for nitrogen removal in the water filtration process invisible to conventional monitoring.