A　method　is　proposed　for　recognizing　and　predicting　non-linear　systems　employing　a　radial　basis　function　neural　network　(RBFNN)　and　robust　hybrid　particle　swarm　optimization　(HPSO)　approach.　A　PSO　is　coupled　with　a　spiral-shaped　mechanism　(HPSO-SSM)　to　optimize　the　PSO　performance　by　mitigating　its　constraints,　such　as　sluggish　convergence　and　the　local　minimum　dilemma.　Three　advancements　are　incorporated　into　the　hypothesized　HPSO-SSM　algorithms　to　achieve　remarkable　results.　First,　the　diversity　of　the　search　process　is　promoted　to　update　the　inertial　weight　w　based　on　the　logistic　map　sequence.　Then,　two　distinct　parameters　are　trained　in　the　original　position　update　algorithm　to　enhance　the　work　efficiency　of　the　successive　generation.　Finally,　the　proposed　approach　employs　a　spiral-shaped　mechanism　as　a　local　search　operator　inside　the　optimum　solution　space.　Moreover,　the　HPSO-SSM　method　concurrently　improves　the　RBFNN　parameters　and　network　size,　building　a　model　with　a　compact　configuration　and　higher　precision.　Two　non-linear　benchmark　functions　and　the　total　phosphorus　(TP)　modelling　issue　in　a　waste　water　treatment　process　(WWTP)　are　utilized　to　assess　the　overall　efficacy　of　the　creative　technique.　The　results　of　testing　indicate　that　the　projected　HPSO-SSM-RBFNN　algorithm　performed　very　effectively.