Tufan Kumbasar

Murat Furkan Mansur, Tufan Kumbasar

Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Informed Neural Networks (PINNs) sit between these extremes, but inverse PINNs typically assume a known governing equation with fixed coefficients, leading to identifiability failures when the true dynamics are unknown or state-dependent. We propose \textbf{SOLIS}, which models unknown dynamics via a \emph{state-conditioned second-order surrogate model} and recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, recovering interpretable natural frequency, damping, and gain without presupposing a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and stabilizes training with a cyclic curriculum and \textbf{Local Physics Hints} windowed ridge-regression anchors that mitigate optimization collapse. Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.

Ertugrul Kececi, Tufan Kumbasar

Recent advances in Deep Learning (DL) have strengthened data-driven System Identification (SysID), with Neural and Fuzzy Ordinary Differential Equation (NODE/FODE) models achieving high accuracy in nonlinear dynamic modeling. Yet, system states in these frameworks are often reconstructed without clear physical meaning, and input contributions to the state derivatives remain difficult to interpret. To address these limitations, we propose Explainable FODE (xFODE), an interpretable SysID framework with integrated DL-based training. In xFODE, we define states in an incremental form to provide them with physical meanings. We employ fuzzy additive models to approximate the state derivative, thereby enhancing interpretability per input. To provide further interpretability, Partitioning Strategies (PSs) are developed, enabling the training of fuzzy additive models with explainability. By structuring the antecedent space during training so that only two consecutive rules are activated for any given input, PSs not only yield lower complexity for local inference but also enhance the interpretability of the antecedent space. To train xFODE, we present a DL framework with parameterized membership function learning that supports end-to-end optimization. Across benchmark SysID datasets, xFODE matches the accuracy of NODE, FODE, and NLARX models while providing interpretable insights.

Ertugrul Kececi, Tufan Kumbasar

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.

Mehmet Ali Ferah, Tufan Kumbasar

System identification (SysID) is critical for modeling dynamical systems from experimental data, yet traditional approaches often fail to capture nonlinear behaviors. While deep learning offers powerful tools for modeling such dynamics, incorporating uncertainty quantification is essential to ensure reliable predictions. This paper presents a systematic framework for constructing and training interval Neural Networks (INNs) for uncertainty-aware SysID. By extending crisp neural networks into interval counterparts, we develop Interval LSTM and NODE models that propagate uncertainty through interval arithmetic without probabilistic assumptions. This design allows them to represent uncertainty and produce prediction intervals. For training, we propose two strategies: Cascade INN (C-INN), a two-stage approach converting a trained crisp NN into an INN, and Joint INN (J-INN), a one-stage framework jointly optimizing prediction accuracy and interval precision. Both strategies employ uncertainty-aware loss functions and parameterization tricks to ensure reliable learning. Comprehensive experiments on multiple SysID datasets demonstrate the effectiveness of both approaches and benchmark their performance against well-established uncertainty-aware baselines: C-INN achieves superior point prediction accuracy, whereas J-INN yields more accurate and better-calibrated prediction intervals. Furthermore, to reveal how uncertainty is represented across model parameters, the concept of channel-wise elasticity is introduced, which is used to identify distinct patterns across the two training strategies. The results of this study demonstrate that the proposed framework effectively integrates deep learning with uncertainty-aware modeling.

Batuhan Cengiz, Halil Faruk Karagoz, Tufan Kumbasar

Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification frameworks can capture high-density prediction regions and bypass convex quantile constraints, they are restricted by quantization errors and the curse of dimensionality due to a constant number of bins per dimension. To address these limitations, we introduce a conformalized high-density quantile regression approach with a dynamically adaptive set of prototypes. Our method optimizes the set of prototypes by adaptively adding, deleting, and relocating quantization bins throughout the training process. Moreover, our conformal scheme provides valid coverage guarantees, focusing on regions with the highest probability density. Experiments across diverse datasets and dimensionalities confirm that our method consistently achieves high-quality prediction regions with enhanced coverage and robustness, all while utilizing fewer prototypes and memory, ensuring scalability to higher dimensions. The code is available at https://github.com/batuceng/max_quantile .

Ata Koklu, Yusuf Guven, Tufan Kumbasar

In this paper, we tackle the task of generating Prediction Intervals (PIs) in high-risk scenarios by proposing enhancements for learning Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) to address their learning challenges. In this context, we first provide extra design flexibility to the Karnik-Mendel (KM) and Nie-Tan (NT) center of sets calculation methods to increase their flexibility for generating PIs. These enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. To address the large-scale learning challenge, we transform the IT2-FLS's constraint learning problem into an unconstrained form via parameterization tricks, enabling the direct application of deep learning optimizers. To address the curse of dimensionality issue, we expand the High-Dimensional Takagi-Sugeno-Kang (HTSK) method proposed for type-1 FLS to IT2-FLSs, resulting in the HTSK2 approach. Additionally, we introduce a framework to learn the enhanced IT2-FLS with a dual focus, aiming for high precision and PI generation. Through exhaustive statistical results, we reveal that HTSK2 effectively addresses the dimensionality challenge, while the enhanced KM and NT methods improved learning and enhanced uncertainty quantification performances of IT2-FLSs.

Omer Bahadir Gokmen, Yusuf Guven, Tufan Kumbasar

In this study, we introduce the Fuzzy Additive Model (FAM) and FAM with Explainability (FAME) as a solution for Explainable Artificial Intelligence (XAI). The family consists of three layers: (1) a Projection Layer that compresses the input space, (2) a Fuzzy Layer built upon Single Input-Single Output Fuzzy Logic Systems (SFLS), where SFLS functions as subnetworks within an additive index model, and (3) an Aggregation Layer. This architecture integrates the interpretability of SFLS, which uses human-understandable if-then rules, with the explainability of input-output relationships, leveraging the additive model structure. Furthermore, using SFLS inherently addresses issues such as the curse of dimensionality and rule explosion. To further improve interpretability, we propose a method for sculpting antecedent space within FAM, transforming it into FAME. We show that FAME captures the input-output relationships with fewer active rules, thus improving clarity. To learn the FAM family, we present a deep learning framework. Through the presented comparative results, we demonstrate the promising potential of FAME in reducing model complexity while retaining interpretability, positioning it as a valuable tool for XAI.

Yusuf Guven, Ata Koklu, Tufan Kumbasar

General Type-2 (GT2) Fuzzy Logic Systems (FLSs) are perfect candidates to quantify uncertainty, which is crucial for informed decisions in high-risk tasks, as they are powerful tools in representing uncertainty. In this paper, we travel back in time to provide a new look at GT2-FLSs by adopting Zadeh's (Z) GT2 Fuzzy Set (FS) definition, intending to learn GT2-FLSs that are capable of achieving reliable High-Quality Prediction Intervals (HQ-PI) alongside precision. By integrating Z-GT2-FS with the \(α\)-plane representation, we show that the design flexibility of GT2-FLS is increased as it takes away the dependency of the secondary membership function from the primary membership function. After detailing the construction of Z-GT2-FLSs, we provide solutions to challenges while learning from high-dimensional data: the curse of dimensionality, and integrating Deep Learning (DL) optimizers. We develop a DL framework for learning dual-focused Z-GT2-FLSs with high performances. Our study includes statistical analyses, highlighting that the Z-GT2-FLS not only exhibits high-precision performance but also produces HQ-PIs in comparison to its GT2 and IT2 fuzzy counterparts which have more learnable parameters. The results show that the Z-GT2-FLS has a huge potential in uncertainty quantification.

Ertuğrul Keçeci, Müjde Güzelkaya, Tufan Kumbasar

This paper addresses the System Identification (SYSID) problem within the framework of federated learning. We introduce a novel algorithm, Incremental Clustering-based federated learning method for SYSID (IC-SYSID), designed to tackle SYSID challenges across multiple data sources without prior knowledge. IC-SYSID utilizes an incremental clustering method, ClusterCraft (CC), to eliminate the dependency on the prior knowledge of the dataset. CC starts with a single cluster model and assigns similar local workers to the same clusters by dynamically increasing the number of clusters. To reduce the number of clusters generated by CC, we introduce ClusterMerge, where similar cluster models are merged. We also introduce enhanced ClusterCraft to reduce the generation of similar cluster models during the training. Moreover, IC-SYSID addresses cluster model instability by integrating a regularization term into the loss function and initializing cluster models with scaled Glorot initialization. It also utilizes a mini-batch deep learning approach to manage large SYSID datasets during local training. Through the experiments conducted on a real-world representing SYSID problem, where a fleet of vehicles collaboratively learns vehicle dynamics, we show that IC-SYSID achieves a high SYSID performance while preventing the learning of unstable clusters.

Ata Koklu, Yusuf Guven, Tufan Kumbasar

Type-1 and Interval Type-2 (IT2) Fuzzy Logic Systems (FLS) excel in handling uncertainty alongside their parsimonious rule-based structure. Yet, in learning large-scale data challenges arise, such as the curse of dimensionality and training complexity of FLSs. The complexity is due mainly to the constraints to be satisfied as the learnable parameters define FSs and the complexity of the center of the sets calculation method, especially of IT2-FLSs. This paper explicitly focuses on the learning problem of FLSs and presents a computationally efficient learning method embedded within the realm of Deep Learning (DL). The proposed method tackles the learning challenges of FLSs by presenting computationally efficient implementations of FLSs, thereby minimizing training time while leveraging mini-batched DL optimizers and automatic differentiation provided within the DL frameworks. We illustrate the efficiency of the DL framework for FLSs on benchmark datasets.

Mehmet Ali Ferah, Tufan Kumbasar

System Identification (SysID) is crucial for modeling and understanding dynamical systems using experimental data. While traditional SysID methods emphasize linear models, their inability to fully capture nonlinear dynamics has driven the adoption of Deep Learning (DL) as a more powerful alternative. However, the lack of uncertainty quantification (UQ) in DL-based models poses challenges for reliability and safety, highlighting the necessity of incorporating UQ. This paper introduces a systematic framework for constructing and learning Interval Neural Networks (INNs) to perform UQ in SysID tasks. INNs are derived by transforming the learnable parameters (LPs) of pre-trained neural networks into interval-valued LPs without relying on probabilistic assumptions. By employing interval arithmetic throughout the network, INNs can generate Prediction Intervals (PIs) that capture target coverage effectively. We extend Long Short-Term Memory (LSTM) and Neural Ordinary Differential Equations (Neural ODEs) into Interval LSTM (ILSTM) and Interval NODE (INODE) architectures, providing the mathematical foundations for their application in SysID. To train INNs, we propose a DL framework that integrates a UQ loss function and parameterization tricks to handle constraints arising from interval LPs. We introduce novel concept "elasticity" for underlying uncertainty causes and validate ILSTM and INODE in SysID experiments, demonstrating their effectiveness.

Ahmet Eren Sertbaş, Tufan Kumbasar

Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a \textit{stable-by-design LPV neural network-based state-space} (NN-SS) model that simultaneously learns latent states and internal scheduling variables directly from data. The state-transition matrix, generated by a neural network using the learned scheduling variables, is guaranteed to be stable through a Schur-based parameterization. The architecture combines an encoder for initial state estimation with a state-space representer network that constructs the full set of scheduling-dependent system matrices. For training the NN-SS, we develop a framework that integrates multi-step prediction losses with a state-consistency regularization term, ensuring robustness against drift and improving long-horizon prediction accuracy. The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods and recent gradient-based approaches. These findings highlight the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear systems.

Mert Can Kurucu, Tufan Kumbasar, İbrahim Eksin et al.

Robust loss functions are crucial for training deep neural networks in the presence of label noise, yet existing approaches require extensive, dataset-specific hyperparameter tuning. In this work, we introduce Fractional Classification Loss (FCL), an adaptive robust loss that automatically calibrates its robustness to label noise during training. Built within the active-passive loss framework, FCL employs the fractional derivative of the Cross-Entropy (CE) loss as its active component and the Mean Absolute Error (MAE) as its passive loss component. With this formulation, we demonstrate that the fractional derivative order $μ$ spans a family of loss functions that interpolate between MAE-like robustness and CE-like fast convergence. Furthermore, we integrate $μ$ into the gradient-based optimization as a learnable parameter and automatically adjust it to optimize the trade-off between robustness and convergence speed. We reveal that FCL's unique property establishes a critical trade-off that enables the stable learning of $μ$: lower log penalties on difficult or mislabeled examples improve robustness but impose higher penalties on easy or clean data, reducing model confidence in them. Consequently, FCL can dynamically reshape its loss landscape to achieve effective classification performance under label noise. Extensive experiments on benchmark datasets show that FCL achieves state-of-the-art results without the need for manual hyperparameter tuning.

Aydoğan Soylu, Tufan Kumbasar

Accurate modeling of aerodynamic coefficients is crucial for understanding and optimizing the performance of modern aircraft systems. This paper presents the novel deployment of an Evolving Type-2 Quantum Fuzzy Neural Network (eT2QFNN) for modeling the aerodynamic coefficients of the ATTAS aircraft to express the aerodynamic characteristics. eT2QFNN can represent the nonlinear aircraft model by creating multiple linear submodels with its rule-based structure through an incremental learning strategy rather than a traditional batch learning approach. Moreover, it enhances robustness to uncertainties and data noise through its quantum membership functions, as well as its automatic rule-learning and parameter-tuning capabilities. During the estimation of the aerodynamic coefficients via the flight data of the ATTAS, two different studies are conducted in the training phase: one with a large amount of data and the other with a limited amount of data. The results show that the modeling performance of the eT2QFNN is superior in comparison to baseline counterparts. Furthermore, eT2QFNN estimated the aerodynamic model with fewer rules compared to Type-1 fuzzy counterparts. In addition, by applying the Delta method to the proposed approach, the stability and control derivatives of the aircraft are analyzed. The results prove the superiority of the proposed eT2QFNN in representing aerodynamic coefficients.

Hidayet Ersin Dursun, Yusuf Güven, Tufan Kumbasar

This work focuses on the design of a deep learning-based autonomous driving system deployed and tested on the real-world MIT Racecar to assess its effectiveness in driving scenarios. The Deep Neural Network (DNN) translates raw image inputs into real-time steering commands in an end-to-end learning fashion, following the imitation learning framework. The key design challenge is to ensure that DNN predictions are accurate and fast enough, at a high sampling frequency, and result in smooth vehicle operation under different operating conditions. In this study, we design and compare various DNNs, to identify the most effective approach for real-time autonomous driving. In designing the DNNs, we adopted an incremental design approach that involved enhancing the model capacity and dataset to address the challenges of real-world driving scenarios. We designed a PD system, CNN, CNN-LSTM, and CNN-NODE, and evaluated their performance on the real-world MIT Racecar. While the PD system handled basic lane following, it struggled with sharp turns and lighting variations. The CNN improved steering but lacked temporal awareness, which the CNN-LSTM addressed as it resulted in smooth driving performance. The CNN-NODE performed similarly to the CNN-LSTM in handling driving dynamics, yet with slightly better driving performance. The findings of this research highlight the importance of iterative design processes in developing robust DNNs for autonomous driving applications. The experimental video is available at https://www.youtube.com/watch?v=FNNYgU--iaY.

Yusuf Guven, Tufan Kumbasar

Uncertainty Quantification (UQ) is crucial for deploying reliable Deep Learning (DL) models in high-stakes applications. Recently, General Type-2 Fuzzy Logic Systems (GT2-FLSs) have been proven to be effective for UQ, offering Prediction Intervals (PIs) to capture uncertainty. However, existing methods often struggle with computational efficiency and adaptability, as generating PIs for new coverage levels $(φ_d)$ typically requires retraining the model. Moreover, methods that directly estimate the entire conditional distribution for UQ are computationally expensive, limiting their scalability in real-world scenarios. This study addresses these challenges by proposing a blueprint calibration strategy for GT2-FLSs, enabling efficient adaptation to any desired $φ_d$ without retraining. By exploring the relationship between $α$-plane type reduced sets and uncertainty coverage, we develop two calibration methods: a lookup table-based approach and a derivative-free optimization algorithm. These methods allow GT2-FLSs to produce accurate and reliable PIs while significantly reducing computational overhead. Experimental results on high-dimensional datasets demonstrate that the calibrated GT2-FLS achieves superior performance in UQ, highlighting its potential for scalable and practical applications.

Ertuğrul Keçeci, Müjde Güzelkaya, Tufan Kumbasar

This paper presents FedAlign, a Federated Learning (FL) framework particularly designed for System Identification (SYSID) tasks by aligning state representations. Local workers can learn State-Space Models (SSMs) with equivalent representations but different dynamics. We demonstrate that directly aggregating these local SSMs via FedAvg results in a global model with altered system dynamics. FedAlign overcomes this problem by employing similarity transformation matrices to align state representations of local SSMs, thereby establishing a common parameter basin that retains the dynamics of local SSMs. FedAlign computes similarity transformation matrices via two distinct approaches: FedAlign-A and FedAlign-O. In FedAlign-A, we represent the global SSM in controllable canonical form (CCF). We apply control theory to analytically derive similarity transformation matrices that convert each local SSM into this form. Yet, establishing global SSM in CCF brings additional alignment challenges in multi input - multi output SYSID as CCF representation is not unique, unlike in single input - single output SYSID. In FedAlign-O, we address these alignment challenges by reformulating the local parameter basin alignment problem as an optimization task. We determine the parameter basin of a local worker as the common parameter basin and solve least square problems to obtain similarity transformation matrices needed to align the remaining local SSMs. Through the experiments conducted on synthetic and real-world datasets, we show that FedAlign outperforms FedAvg, converges faster, and provides improved stability of the global SSM thanks to the efficient alignment of local parameter basins.

M. Ugur Yavas, N. Kemal Ure, Tufan Kumbasar

Automated lane change is one of the most challenging task to be solved of highly automated vehicles due to its safety-critical, uncertain and multi-agent nature. This paper presents the novel deployment of the state of art Q learning method, namely Rainbow DQN, that uses a new safety driven rewarding scheme to tackle the issues in an dynamic and uncertain simulation environment. We present various comparative results to show that our novel approach of having reward feedback from the safety layer dramatically increases both the agent's performance and sample efficiency. Furthermore, through the novel deployment of Rainbow DQN, it is shown that more intuition about the agent's actions is extracted by examining the distributions of generated Q values of the agents. The proposed algorithm shows superior performance to the baseline algorithm in the challenging scenarios with only 200000 training steps (i.e. equivalent to 55 hours driving).