Federated Residual-Element Optimization for Compliance- Aware Environmental Artificial Intelligence in Distributed Effluent Monitoring

Federated learning (FL) can support environmental monitoring when facilities cannot pool raw operational records, but ordinary FL does not encode permit direction, regulatory margins, censoring, missingness, or facility-specific compliance regimes. This study introduces Federated Residual-Element Optimization (FREO), a compliance-aware environmental artificial intelligence (AI) framework that converts effluent measurements into signed, unit-consistent regulatory residuals and communicates compact residual elements rather than raw samples. Ten de-identified Environmental Management Authority effluent workbooks, treated as workbook-level facility-category clients, produced 4036 assessable observations, 321 facility-month states, and 311 next-period prediction records. A boundary-purged temporal split removed train/test target-input overlap, leaving 204 training and 97 held-out records. On the within-facility next-period high-burden task, FREO achieved AUROC 0.966, AUPRC 0.923, F1 0.852, and Brier score 0.079, with facility-month bootstrap intervals of [0.924, 0.996], [0.810, 0.990], [0.727, 0.941], and [0.056, 0.104], respectively. Matched calibrated baselines indicate that residual features and training-only facility-prior calibration explain much of the gain; FedAvg-Cal slightly exceeded FREO on AUPRC, F1, and Brier. FREO is therefore positioned as an auditable residual-element workflow for raw-data-local regulatory screening, not as a universally superior optimizer.