arXiv subjects

Hongjie Jiang

Publications and source records attributed to Hongjie Jiang.

10 recordsLinked to original sources

arXiv2026

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with adequate accuracy, and limitations of the traditional solvers and specialized neural operators motivate the development of foundation models for solving PDEs. This paper introduces PDEformer-2, a versatile foundation model for two-dimensional PDEs. Based on our previous one-dimensional PDEformer-1 model, PDEformer-2 receives the PDE form as network input via computational graph representation, which has the flexibility to encode most common PDEs. The mesh-free predicted solutions can be directly queried at arbitrary spatio-temporal coordinates. A large (40TB) diverse dataset is employed to pretrain the current model, making it capable of simultaneously addressing PDEs with different symbolic forms, domain shapes, boundary conditions, number of variables, and time-dependency. Accurate zero-shot prediction is allowed for PDEs that resemble the pretraining ones. When adapted to new unseen PDEs, PDEformer-2 demonstrates faster learning than many specialized models, and has smaller errors given limited (less than 100) samples. Additionally, PDEformer-2 can be employed in the inverse problems thanks to its fast and differentiable nature and produces reasonable results in our experiments to recover coefficient scalars and fields of a PDE.

math.NA↗

arXiv2026

Foundation Neural Effective Hamiltonian for Strongly Correlated Quantum Materials

Simulating strongly correlated quantum materials often involves not a single Hamiltonian, but a family of Hamiltonians whose ground states evolve across experimentally tunable couplings. Foundation neural quantum states (FNQS) offer a promising route to amortizing many-body calculations across such families, but can lose accuracy near phase transitions and still incur non-negligible sampling costs that grow with the number of target couplings. We introduce the Foundation Neural Effective Hamiltonian (FNEH), which projects a Hamiltonian family onto a compact subspace spanned by FNQS sampled at selected couplings. By variationally combining FNQS across parameter space, FNEH systematically improves their ground-state approximation and can recover phase boundaries that the foundation model misidentifies. Once the required operator matrix elements are sampled, FNEH enables sweeps over couplings, observables, and phase boundaries at a cost governed by the small effective-Hamiltonian dimension, without repeated neural-network sampling at every target coupling. We demonstrate FNEH in strongly correlated moiré materials, where it accurately resolves competing phases, enables high-resolution multidimensional phase scans, and substantially reduces the computational cost of exploring many target Hamiltonians. The results open a new avenue for studying strongly correlated quantum materials with foundation models.

quant-ph↗

arXiv2026

Risk Awareness Injection: Calibrating Vision-Language Models for Safety without Compromising Utility

Vision language models (VLMs) extend the reasoning capabilities of large language models (LLMs) to cross-modal settings, yet remain highly vulnerable to multimodal jailbreak attacks. Existing defenses predominantly rely on safety fine-tuning or aggressive token manipulations, incurring substantial training costs or significantly degrading utility. Recent research shows that LLMs inherently recognize unsafe content in text, and the incorporation of visual inputs in VLMs frequently dilutes risk-related signals. Motivated by this, we propose Risk Awareness Injection (RAI), a lightweight and training-free framework for safety calibration that restores LLM-like risk recognition by amplifying unsafe signals in VLMs. Specifically, RAI constructs an Unsafe Prototype Subspace from language embeddings and performs targeted modulation on selected high-risk visual tokens, explicitly activating safety-critical signals within the cross-modal feature space. This modulation restores the model's LLM-like ability to detect unsafe content from visual inputs, while preserving the semantic integrity of original tokens for cross-modal reasoning. Extensive experiments across multiple jailbreak and utility benchmarks demonstrate that RAI substantially reduces attack success rate without compromising task performance.

cs.AI↗

arXiv2026

Neural Dynamics-Informed Pre-trained Framework for Personalized Brain Functional Network Construction

Brain activity is intrinsically a neural dynamic process constrained by anatomical space. This leads to significant variations in spatial distribution patterns and correlation patterns of neural activity across variable and heterogeneous scenarios. However, dominant brain functional network construction methods, which relies on pre-defined brain atlases and linear assumptions, fails to precisely capture varying neural activity patterns in heterogeneous scenarios. This limits the consistency and generalizability of the brain functional networks constructed by dominant methods. Here, a neural dynamics-informed pre-trained framework is proposed for personalized brain functional network construction. The proposed framework extracts personalized representations of neural activity patterns in heterogeneous scenarios. Personalized brain functional networks are obtained by utilizing these representations to guide brain parcellation and neural activity correlation estimation. Systematic evaluations were employed on 18 datasets across tasks, such as virtual neural modulation and abnormal neural circuit identification. Experimental results demonstrate that the proposed framework attains superior performance in heterogeneous scenarios. Overall, the proposed framework challenges the dominant brain functional network construction method.

cs.LG↗

arXiv2026

TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions

Accurately solving time-dependent partial differential equations (PDEs) with neural networks remains challenging due to long-time error accumulation and the difficulty of enforcing general boundary conditions. We introduce TENG-BC, a high-precision neural PDE solver based on the Time-Evolving Natural Gradient, designed to perform under general boundary constraints. At each time step, TENG-BC performs a boundary-aware optimization that jointly enforces interior dynamics and boundary conditions, accommodating Dirichlet, Neumann, Robin, and mixed types within a unified framework. This formulation admits a natural-gradient interpretation, enabling stable time evolution without delicate penalty tuning. Across benchmarks over diffusion, transport, and nonlinear PDEs with various boundary conditions, TENG-BC achieves solver-level accuracy under comparable sampling budgets, outperforming conventional solvers and physics-informed neural network (PINN) baselines.

cs.LG↗

arXiv2025

Brain Network Analysis Based on Fine-tuned Self-supervised Model for Brain Disease Diagnosis

Functional brain network analysis has become an indispensable tool for brain disease analysis. It is profoundly impacted by deep learning methods, which can characterize complex connections between ROIs. However, the research on foundation models of brain network is limited and constrained to a single dimension, which restricts their extensive application in neuroscience. In this study, we propose a fine-tuned brain network model for brain disease diagnosis. It expands brain region representations across multiple dimensions based on the original brain network model, thereby enhancing its generalizability. Our model consists of two key modules: (1)an adapter module that expands brain region features across different dimensions. (2)a fine-tuned foundation brain network model, based on self-supervised learning and pre-trained on fMRI data from thousands of participants. Specifically, its transformer block is able to effectively extract brain region features and compute the inter-region associations. Moreover, we derive a compact latent representation of the brain network for brain disease diagnosis. Our downstream experiments in this study demonstrate that the proposed model achieves superior performance in brain disease diagnosis, which potentially offers a promising approach in brain network analysis research.

eess.IV↗

arXiv2024

The generalized inverses of tensors via the C-Product

This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the C-Product. Moreover, the inverse along a tensor is also introduced. Secondly, this paper gives some other expressions of the generalized inverses of tensors by using several decomposition forms of tensors. Finally, the algorithms for the Moore-Penrose inverse, Drazin inverse of tensors and the inverse along a tensor are established.

math.RA↗

arXiv2024

A Pilot Study on the Comparison of Prefrontal Cortex Activities of Robotic Therapies on Elderly with Mild Cognitive Impairment

Demographic shifts have led to an increase in mild cognitive impairment (MCI), and this study investigates the effects of cognitive training (CT) and reminiscence therapy (RT) conducted by humans or socially assistive robots (SARs) on prefrontal cortex activation in elderly individuals with MCI, aiming to determine the most effective therapy-modality combination for promoting cognitive function. This pilot study employs a randomized control trial (RCT) design. Additionally, the study explores the efficacy of Reminiscence Therapy (RT) in comparison to Cognitive Training (CT). Eight MCI subjects, with a mean age of 70.125 years, were randomly assigned to ``human-led'' or ``SAR-led'' groups. Utilizing Functional Near-infrared Spectroscopy (fNIRS) to measure oxy-hemoglobin concentration changes in the dorsolateral prefrontal cortex (DLPFC), the study found no significant differences in the effects of human-led and SAR-led cognitive training on DLPFC activation. However, distinct patterns emerged in memory encoding and retrieval phases between RT and CT, shedding light on the impacts of these interventions on brain activation in the context of MCI.

cs.RO↗

arXiv2022

The generalized inverses of the quaternion tensor via the T-product

In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and properties of the defined inverses are investigated. Moreover, algorithms are established for computing the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors, respectively.

math.RA↗

arXiv2022

Dynamic Ensemble Bayesian Filter for Robust Control of a Human Brain-machine Interface

Objective: Brain-machine interfaces (BMIs) aim to provide direct brain control of devices such as prostheses and computer cursors, which have demonstrated great potential for mobility restoration. One major limitation of current BMIs lies in the unstable performance in online control due to the variability of neural signals, which seriously hinders the clinical availability of BMIs. Method: To deal with the neural variability in online BMI control, we propose a dynamic ensemble Bayesian filter (DyEnsemble). DyEnsemble extends Bayesian filters with a dynamic measurement model, which adjusts its parameters in time adaptively with neural changes. This is achieved by learning a pool of candidate functions and dynamically weighting and assembling them according to neural signals. In this way, DyEnsemble copes with variability in signals and improves the robustness of online control. Results: Online BMI experiments with a human participant demonstrate that, compared with the velocity Kalman filter, DyEnsemble significantly improves the control accuracy (increases the success rate by 13.9% and reduces the reach time by 13.5% in the random target pursuit task) and robustness (performs more stably over different experiment days). Conclusion: Our results demonstrate the superiority of DyEnsemble in online BMI control. Significance: DyEnsemble frames a novel and flexible framework for robust neural decoding, which is beneficial to different neural decoding applications.

cs.LG↗