Fuzzy-based input method for uncertainty quantification in a deterministic model comparison with ChatGPT for peak flow prediction

• Compared model performance of PCSWMM and GPT models for peak-flow prediction under varying data-split approaches using comprehensive evaluation metrics. • Developed a novel integration of fuzzy methods for quantifying uncertainty in rainfall and peak-flow observations. • Quantified the uncertainty in model prediction (peak flow), enhancing real-world plausibility and interpretability of predictions, and effectively conveying this uncertainty to stakeholders for informed decision-making. ChatGPT, a generative AI, is applied and compared to the PCSWMM hydrological model for modelling peak flow in a small watershed in the runoff period of April to September. A new approach for fuzzy mathematical representation of rainfall and peak-flow errors was developed to lead to a fuzzy based GPT model and fuzzy based PCSWMM model. This led to fuzzy output for both models and a more appropriate application of both models given data errors and large language model structure. Training and validation were conducted with an approximately 25/75 split of the data and again using a 75/25 data split. Evaluation metrics were used to compare model performance under the different data-split scenarios. Calibrated and validated PCSWMM outperformed GPT in the 25/75 data split but ChatGPT 4o mini’s generation outperformed PCSWMM in the 75/25 split and with comparable validation metrics and an application that was less onerous than when using PCSWMM. The fuzzy-based error analysis showed that for both models, a fuzzy-based approach produced more interpretable and reasonable results than either original model. Moreover, the trade-off between coverage (uncertainty range) and precision for GPT‑4o mini model’s fuzzy output at high membership levels demonstrated enhanced predictive performance under data‑scarce conditions.