arXiv subjects

Zhihan Lyu

Publications and source records attributed to Zhihan Lyu.

5 recordsLinked to original sources

arXiv2026

HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators

Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate. Existing rollout-training strategies reduce the mismatch between training inputs and self-generated states, yet their supervision still measures only the absolute discrepancy from the ground-truth trajectory. Such supervision is therefore uninformative about whether the operator has overcome the long-horizon failure behaviors it exhibited earlier during optimization. We propose history-enriched rollout training (HERO), which augments conventional absolute trajectory supervision with relative supervision derived from the model's optimization history. HERO ranks detached candidate rollouts from a periodically refreshed lagged operator, the current model, and a perturbed input by rollout error, spectral discrepancy, energy drift, and error growth, and selects the strongest failure trajectory as reference. This reference enters a margin-based objective as a fixed comparison baseline, inducing a bounded, sample-dependent reweighting of the ground-truth rollout gradient rather than an independent gradient direction, which we further analyze theoretically. Experiments on nine PDE benchmarks with spectral and attention-based backbones show that HERO consistently improves long-horizon accuracy, stable rollout length, and out-of-distribution robustness at no inference-time cost. These results indicate that history-enriched relative supervision is effective for stabilizing long-horizon autoregressive prediction.

cs.LG↗

arXiv2026

Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction

Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs). However, long-horizon autoregressive prediction remains challenging: local errors accumulate as spectral inconsistency, phase misalignment, or mean drift. Existing methods mainly improve state representations and operator backbones, while leaving the repeatedly applied latent transition increment weakly structured, allowing spectral errors and unstable channel couplings to accumulate during rollout. To address these issues, we propose a geometry-aware incremental neural operator (GeoIncNO) for stable long-horizon PDE prediction. GeoIncNO predicts latent increments for residual advancement and uses lightweight low-rank projectors to regulate channel coupling within active frequency bands derived from the increment spectral energy distribution. To reduce physical-space reconstruction errors, GeoIncNO further introduces a mean--fluctuation decoupled reconstruction mechanism, where stable mean structures and dynamic fluctuations are fused separately, and phase correction is applied only to the zero-mean fluctuation component. Extensive experiments on six PDE benchmarks, covering 1D, 2D, and 3D dynamical systems, show that GeoIncNO achieves consistently strong prediction accuracy, improved rollout stability, and better spectral fidelity compared with competitive neural-operator baselines.

cs.AI↗

arXiv2025

Efficient MRI Parallel Imaging Reconstruction by K-Space Rendering via Generalized Implicit Neural Representation

High-resolution magnetic resonance imaging (MRI) is essential in clinical diagnosis. However, its long acquisition time remains a critical issue. Parallel imaging (PI) is a common approach to reduce acquisition time by periodically skipping specific k-space lines and reconstructing images from undersampled data. This study presents a generalized implicit neural representation (INR)-based framework for MRI PI reconstruction, addressing limitations commonly encountered in conventional methods, such as subject-specific or undersampling scale-specific requirements and long reconstruction time. The proposed method overcomes these limitations by leveraging prior knowledge of voxel-specific features and integrating a novel scale-embedded encoder module. This encoder generates scale-independent voxel-specific features from undersampled images, enabling robust reconstruction across various undersampling scales without requiring retraining for each specific scale or subject. The INR model treats MR signal intensities and phase values as continuous functions of spatial coordinates and prior knowledge to render fully sampled k-space, efficiently reconstructing high-quality MR images from undersampled data. Extensive experiments on publicly available MRI datasets demonstrate the superior performance of the proposed method in reconstructing images at multiple acceleration factors (4x, 5x, and 6x), achieving higher evaluation metrics and visual fidelity compared to state-of-the-art methods. In terms of efficiency, this INR-based approach exhibits notable advantages, including reduced floating point operations and GPU usage, allowing for accelerated processing times while maintaining high reconstruction quality. The generalized design of the model significantly reduces computational resources and time consumption, making it more suitable for real-time clinical applications.

eess.IV↗

arXiv2025

CATD: Unified Representation Learning for EEG-to-fMRI Cross-Modal Generation

Multi-modal neuroimaging analysis is crucial for a comprehensive understanding of brain function and pathology, as it allows for the integration of different imaging techniques, thus overcoming the limitations of individual modalities. However, the high costs and limited availability of certain modalities pose significant challenges. To address these issues, this paper proposes the Condition-Aligned Temporal Diffusion (CATD) framework for end-to-end cross-modal synthesis of neuroimaging, enabling the generation of functional magnetic resonance imaging (fMRI)-detected Blood Oxygen Level Dependent (BOLD) signals from more accessible Electroencephalography (EEG) signals. By constructing Conditionally Aligned Block (CAB), heterogeneous neuroimages are aligned into a latent space, achieving a unified representation that provides the foundation for cross-modal transformation in neuroimaging. The combination with the constructed Dynamic Time-Frequency Segmentation (DTFS) module also enables the use of EEG signals to improve the temporal resolution of BOLD signals, thus augmenting the capture of the dynamic details of the brain. Experimental validation demonstrates that the framework improves the accuracy of brain activity state prediction by 9.13% (reaching 69.8%), enhances the diagnostic accuracy of brain disorders by 4.10% (reaching 99.55%), effectively identifies abnormal brain regions, enhancing the temporal resolution of BOLD signals. The proposed framework establishes a new paradigm for cross-modal synthesis of neuroimaging by unifying heterogeneous neuroimaging data into a latent representation space, showing promise in medical applications such as improving Parkinson's disease prediction and identifying abnormal brain regions.

cs.CV↗

arXiv2025

BG-GAN: Generative AI Enable Representing Brain Structure-Function Connections for Alzheimer's Disease

The relationship between brain structure and function is critical for revealing the pathogenesis of brain disorders, including Alzheimer's disease (AD). However, mapping brain structure to function connections is a very challenging task. In this work, a bidirectional graph generative adversarial network (BG-GAN) is proposed to represent brain structure-function connections. Specifically, by designing a module incorporating inner graph convolution network (InnerGCN), the generators of BG-GAN can employ features of direct and indirect brain regions to learn the mapping function between the structural domain and the functional domain. Besides, a new module named Balancer is designed to counterpoise the optimization between generators and discriminators. By introducing the Balancer into BG-GAN, both the structural generator and functional generator can not only alleviate the issue of mode collapse but also learn complementarity of structural and functional features. Experimental results using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset show that both generated structure and function connections can improve the identification accuracy of AD. The experimental findings suggest that the relationship between brain structure and function is not a complete one-to-one correspondence. They also suggest that brain structure is the basis of brain function, and the strong structural connections are majorly accompanied by strong functional connections.

cs.AI↗