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Wenjun Cui

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4 papers

1 author row

AAAI Conference 2025 Conference Paper

Efficient Training of Neural Fractional-Order Differential Equation via Adjoint Backpropagation

Qiyu Kang
Xuhao Li
Kai Zhao
Wenjun Cui
Yanan Zhao
Weihua Deng
Wee Peng Tay

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamic systems with nonlocal characteristics. Recent progress at the intersection of FDEs and deep learning has catalyzed a new wave of innovative models, demonstrating the potential to address challenges such as graph representation learning. However, training neural FDEs has primarily relied on direct differentiation through forward-pass operations in FDE numerical solvers, leading to increased memory usage and computational complexity, particularly in large-scale applications. To address these challenges, we propose a scalable adjoint backpropagation method for training neural FDEs by solving an augmented FDE backward in time, which substantially reduces memory requirements. This approach provides a practical neural FDE toolbox and holds considerable promise for diverse applications. We demonstrate the effectiveness of our method in several tasks, achieving performance comparable to baseline models while significantly reducing computational overhead.

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NeurIPS Conference 2025 Conference Paper

Neural Fractional Attention Differential Equations

Qiyu Kang
Wenjun Cui
Xuhao Li
Yuxin Ma
Xueyang Fu
Wee Peng Tay
Yidong Li
Zheng-Jun Zha

The integration of differential equations with neural networks has created powerful tools for modeling complex dynamics effectively across diverse machine learning applications. While standard integer-order neural ordinary differential equations (ODEs) have shown considerable success, they are limited in their capacity to model systems with memory effects and historical dependencies. Fractional calculus offers a mathematical framework capable of addressing this limitation, yet most current fractional neural networks use static memory weightings that cannot adapt to input-specific contextual requirements. This paper proposes a generalized neural Fractional Attention Differential Equation (FADE), which combines the memory-retention capabilities of fractional calculus with contextual learnable attention mechanisms. Our approach replaces fixed kernel functions in fractional operators with neural attention kernels that adaptively weight historical states based on their contextual relevance to current predictions. This allows our framework to selectively emphasize important temporal dependencies while filtering less relevant historical information. Our theoretical analysis establishes solution boundedness, problem well-posedness, and numerical equation solver convergence properties of the proposed model. Furthermore, through extensive evaluation on tasks such as fluid flow, graph learning problems and spatio-temporal traffic flow forecasting, we demonstrate that our adaptive attention-based fractional framework outperforms both integer-order neural ODE models and existing fractional approaches. The results confirm that our framework provides superior modeling capacity for complex dynamics with varying temporal dependencies. The code is available at \url{https: //github. com/cuiwjTech/NeurIPS2025_FADE}.

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AAAI Conference 2025 Conference Paper

Neural Variable-Order Fractional Differential Equation Networks

Wenjun Cui
Qiyu Kang
Xuhao Li
Kai Zhao
Wee Peng Tay
Weihua Deng
Yidong Li

The use of neural differential equation models in machine learning applications has gained significant traction in recent years. In particular, fractional differential equations (FDEs) have emerged as a powerful tool for capturing complex dynamics in various domains. While existing models have primarily focused on constant-order fractional derivatives, variable-order fractional operators offer a more flexible and expressive framework for modeling complex memory patterns. In this work, we introduce the Neural Variable-Order Fractional Differential Equation network (NvoFDE), a novel neural network framework that integrates variable-order fractional derivatives with learnable neural networks. Our framework allows for the modeling of adaptive derivative orders dependent on hidden features, capturing more complex feature-updating dynamics and providing enhanced flexibility. We conduct extensive experiments across multiple graph datasets to validate the effectiveness of our approach. Our results demonstrate that NvoFDE outperforms traditional constant-order fractional and integer models across a range of tasks, showcasing its superior adaptability and performance.

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IJCAI Conference 2024 Conference Paper

Structure-Preserving Physics-Informed Neural Networks with Energy or Lyapunov Structure

Haoyu Chu
Yuto Miyatake
Wenjun Cui
Shikui Wei
Daisuke Furihata

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be established. This limitation could be a potential reason why the learning process for PINNs is not always efficient and the numerical results may suggest nonphysical behavior. Besides, there is little research on their applications on downstream tasks. To address these issues, we propose structure-preserving PINNs to improve their performance and broaden their applications for downstream tasks. Firstly, by leveraging prior knowledge about the physical system, a structure‐preserving loss function is designed to assist the PINN in learning the underlying structure. Secondly, a framework that utilizes structure-preserving PINN for robust image recognition is proposed. Here, preserving the Lyapunov structure of the underlying system ensures the stability of the system. Experimental results demonstrate that the proposed method improves the numerical accuracy of PINNs for partial differential equations (PDEs). Furthermore, the robustness of the model against adversarial perturbations in image data is enhanced.

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