xFODE+: Explainable Type-2 Fuzzy Additive ODEs for Uncertainty Quantification

• URL: http://arxiv.org/abs/2604.14880v1
• Date: Thu, 16 Apr 2026 11:16:34 GMT
• Title: xFODE+: Explainable Type-2 Fuzzy Additive ODEs for Uncertainty Quantification
• Abstract summary: We introduce Explainable Type-2 Fuzzy Additive ODEs for UQ (xFODE+), an interpretable SysID model.<n>xFODE+ produces PIs alongside point predictions while retaining physically meaningful incremental states.<n>Results on benchmark SysID datasets show that xFODE+ matches FODE in PI quality and achieves comparable accuracy.
• Score: 6.5745172279769255
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recent advances in Deep Learning (DL) have boosted data-driven System Identification (SysID), but reliable use requires Uncertainty Quantification (UQ) alongside accurate predictions. Although UQ-capable models such as Fuzzy ODE (FODE) can produce Prediction Intervals (PIs), they offer limited interpretability. We introduce Explainable Type-2 Fuzzy Additive ODEs for UQ (xFODE+), an interpretable SysID model which produces PIs alongside point predictions while retaining physically meaningful incremental states. xFODE+ implements each fuzzy additive model with Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) and constraints membership functions to the activation of two neighboring rules, limiting overlap and keeping inference locally transparent. The type-reduced sets produced by the IT2-FLSs are aggregated to construct the state update together with the PIs. The model is trained in a DL framework via a composite loss that jointly optimizes prediction accuracy and PI quality. Results on benchmark SysID datasets show that xFODE+ matches FODE in PI quality and achieves comparable accuracy, while providing interpretability.

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