Yuantong Gu

Jinshuai Bai, Gui-Rong Liu, Ashish Gupta et al.

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the local property throughout the entire training process. Compared to deep neural networks, a PIRBN comprises of only one hidden layer and a radial basis "activation" function. Under appropriate conditions, we demonstrated that the training of PIRBNs using gradient descendent methods can converge to Gaussian processes. Besides, we studied the training dynamics of PIRBN via the neural tangent kernel (NTK) theory. In addition, comprehensive investigations regarding the initialisation strategies of PIRBN were conducted. Based on numerical examples, PIRBN has been demonstrated to be more effective and efficient than PINN in solving PDEs with high-frequency features and ill-posed computational domains. Moreover, the existing PINN numerical techniques, such as adaptive learning, decomposition and different types of loss functions, are applicable to PIRBN. The programs that can regenerate all numerical results can be found at https://github.com/JinshuaiBai/PIRBN.

Shusheng Xiao, Jinshuai Bai, Hyogu Jeong et al.

Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions. Generative TO offers a route to rapid design exploration, but existing models may rely on adversarial training, long reverse-diffusion sampling, or external guidance to maintain structural feasibility and physical consistency. This study develops a flow matching-based topology optimisation (FMTO) framework for conditional topology generation. Linear FMTO is first formulated as an endpoint-based baseline by interpolating between a Gaussian source field and the BESO reference topology. To introduce mechanically meaningful intermediate states, a trajectory-aware FMTO formulation is proposed, where volume-fraction-indexed BESO states are used to construct the probability path and target velocity field. This incorporates physics-guided optimisation history into generative flow learning without adding inference-time optimisation. A path--velocity mismatch analysis explains why moderate trajectory weighting can improve generation stability, whereas excessive guidance may over-constrain the learned transport. Numerical examples show that FMTO generates diverse topology candidates with improved compliance-related performance, volume-fraction satisfaction, topology fidelity, and substantially fewer sampling steps than a diffusion-based baseline. Under limited training data, trajectory-aware FMTO achieves the best overall performance with a moderate trajectory weight. Studies on trajectory-anchor density and three-dimensional topology generation further demonstrate the influence of path design and the applicability of the proposed framework beyond two-dimensional problems.

Zijian Wu, Lingkai Kong, Wenwei Zhang et al.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out OPV-Bench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2% to 73.3% on AIME2025 as the compute budget scales.

Jinshuai Bai, Laith Alzubaidi, Qingxia Wang et al.

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications, such as structural risk estimation and medical diagnosis. This presents a significant barrier to the practical implementation of DL in these fields. Physics-guided deep learning (PGDL) is a novel type of DL that can integrate physics laws to train neural networks. This can be applied to any systems that are controlled or governed by physics laws, such as mechanics, finance and medical applications. It has been demonstrated that, with the additional information provided by physics laws, PGDL achieves great accuracy and generalisation in the presence of data scarcity. This review provides a detailed examination of PGDL and offers a structured overview of its use in addressing data scarcity across various fields, including physics, engineering and medical applications. Moreover, the review identifies the current limitations and opportunities for PGDL in relation to data scarcity and offers a thorough discussion on the future prospects of PGDL.

Sabah Abdulazeez Jebur, Khalid A. Hussein, Haider Kadhim Hoomod et al.

Anomaly detection in videos is challenging due to the complexity, noise, and diverse nature of activities such as violence, shoplifting, and vandalism. While deep learning (DL) has shown excellent performance in this area, existing approaches have struggled to apply DL models across different anomaly tasks without extensive retraining. This repeated retraining is time-consuming, computationally intensive, and unfair. To address this limitation, a new DL framework is introduced in this study, consisting of three key components: transfer learning to enhance feature generalization, model fusion to improve feature representation, and multi-task classification to generalize the classifier across multiple tasks without training from scratch when new task is introduced. The framework's main advantage is its ability to generalize without requiring retraining from scratch for each new task. Empirical evaluations demonstrate the framework's effectiveness, achieving an accuracy of 97.99% on the RLVS dataset (violence detection), 83.59% on the UCF dataset (shoplifting detection), and 88.37% across both datasets using a single classifier without retraining. Additionally, when tested on an unseen dataset, the framework achieved an accuracy of 87.25%. The study also utilizes two explainability tools to identify potential biases, ensuring robustness and fairness. This research represents the first successful resolution of the generalization issue in anomaly detection, marking a significant advancement in the field.

Zehui Zhao, Laith Alzubaidi, Jinglan Zhang et al.

Deep learning has significantly advanced automatic medical diagnostics and released the occupation of human resources to reduce clinical pressure, yet the persistent challenge of data scarcity in this area hampers its further improvements and applications. To address this gap, we introduce a novel ensemble framework called `Efficient Transfer and Self-supervised Learning based Ensemble Framework' (ETSEF). ETSEF leverages features from multiple pre-trained deep learning models to efficiently learn powerful representations from a limited number of data samples. To the best of our knowledge, ETSEF is the first strategy that combines two pre-training methodologies (Transfer Learning and Self-supervised Learning) with ensemble learning approaches. Various data enhancement techniques, including data augmentation, feature fusion, feature selection, and decision fusion, have also been deployed to maximise the efficiency and robustness of the ETSEF model. Five independent medical imaging tasks, including endoscopy, breast cancer, monkeypox, brain tumour, and glaucoma detection, were tested to demonstrate ETSEF's effectiveness and robustness. Facing limited sample numbers and challenging medical tasks, ETSEF has proved its effectiveness by improving diagnostics accuracies from 10\% to 13.3\% when compared to strong ensemble baseline models and up to 14.4\% improvements compared with published state-of-the-art methods. Moreover, we emphasise the robustness and trustworthiness of the ETSEF method through various vision-explainable artificial intelligence techniques, including Grad-CAM, SHAP, and t-SNE. Compared to those large-scale deep learning models, ETSEF can be deployed flexibly and maintain superior performance for challenging medical imaging tasks, showing the potential to be applied to more areas that lack training data

Zehui Zhao, Laith Alzubaidi, Jinglan Zhang et al.

Recently, transfer learning and self-supervised learning have gained significant attention within the medical field due to their ability to mitigate the challenges posed by limited data availability, improve model generalisation, and reduce computational expenses. Transfer learning and self-supervised learning hold immense potential for advancing medical research. However, it is crucial to recognise that transfer learning and self-supervised learning architectures exhibit distinct advantages and limitations, manifesting variations in accuracy, training speed, and robustness. This paper compares the performance and robustness of transfer learning and self-supervised learning in the medical field. Specifically, we pre-trained two models using the same source domain datasets with different pre-training methods and evaluated them on small-sized medical datasets to identify the factors influencing their final performance. We tested data with several common issues in medical domains, such as data imbalance, data scarcity, and domain mismatch, through comparison experiments to understand their impact on specific pre-trained models. Finally, we provide recommendations to help users apply transfer learning and self-supervised learning methods in medical areas, and build more convenient and efficient deployment strategies.

Jinshuai Bai, Zhongya Lin, Yizheng Wang et al.

Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINNs) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINNs framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINNs framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINNs framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at https://github.com/JinshuaiBai/energy_PINN_Contact.(The code will be available after acceptance)

Junhao Shen, Haiteng Zhao, Yuzhe Gu et al.

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes SOPHIA, a simple and scalable Semi-Off-Policy RL for vision-language slow-tHInking reAsoning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms. Extensive experiments with InternVL2.5 and InternVL3.0 with 8B and 38B sizes show the effectiveness of SOPHIA. Notably, SOPHIA improves InternVL3.0-38B by 8.50% in average, reaching state-of-the-art performance among open-source LVLMs on multiple multimodal reasoning benchmarks, and even outperforms some closed-source models (e.g., GPT-4.1) on the challenging MathVision and OlympiadBench, achieving 49.08% and 49.95% pass@1 accuracy, respectively. Analysis shows SOPHIA outperforms supervised fine-tuning and direct on-policy RL methods, offering a better policy initialization for further on-policy training.

Yizheng Wang, Jinshuai Bai, Zhongya Lin et al.

In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.

Yuzhe Gu, Xiyu Liang, Jiaojiao Zhao et al.

Large language models (LLMs) with extended context windows enable powerful downstream applications but impose significant memory overhead, as caching all key-value (KV) states scales linearly with sequence length and batch size. Existing cache eviction methods address this by exploiting attention sparsity, yet they typically rank tokens heuristically using accumulated attention weights without considering their true impact on attention outputs. We propose Optimal Brain Cache (OBCache), a principled framework that formulates cache eviction as a layer-wise structured pruning problem. Building upon the Optimal Brain Damage (OBD) theory, OBCache quantifies token saliency by measuring the perturbation in attention outputs induced by pruning tokens, with closed-form scores derived for isolated keys, isolated values, and joint key-value pairs. Our scores account not only for attention weights but also for information from value states and attention outputs, thereby enhancing existing eviction strategies with output-aware signals. Experiments on LLaMA and Qwen models demonstrate that replacing the heuristic scores in existing works, which estimate token saliency across different query positions, with OBCache's output-aware scores consistently improves long-context accuracy.

Mohammadreza Sadeghi, Mahsa Ghazvini Nejad, MirHamed Jafarzadeh Asl et al.

Parameter-efficient fine-tuning (PEFT) is essential for reducing the computational overhead of large language models (LLMs). Low-rank family adapters are commonly used to control the parameter size efficiently while maintaining the generative power of LLMs. However, their limited expressiveness due to the rank constraint often restricts their performance on complex tasks. We propose Mixture of Kronecker Adapters (MoKA), a new generation of Kronecker adapters that addresses this limitation by modeling weight updates as a mixture of Kronecker products. Our proposed adapter leverages a gating mechanism that measures the importance of each Kronecker factor, enabling more expressive adaptation. Moreover, MoKA enables a rank flexibility that provides a better trade-off between parameter efficiency and accuracy. To ensure hardware efficiency, we reformulate Kronecker computations using standard matrix operations, allowing seamless deployment on GPU-optimized hardware. We conduct extensive experiments on instruction-tuning and commonsense reasoning tasks using low-bit quantized versions of LLaMA2-7B and LLaMA3-8B models. MoKA not only outperforms PEFT baselines, but also reduces the number of trainable parameters up to 27x, achieving state-of-the-art trade-offs between performance and parameter efficiency.

Zehui Zhao, Laith Alzubaidi, Haider A. Alwzwazy et al.

In recent years, advanced deep learning architectures have shown strong performance in medical imaging tasks. However, the traditional centralized learning paradigm poses serious privacy risks as all data is collected and trained on a single server. To mitigate this challenge, decentralized approaches such as federated learning and swarm learning have emerged, allowing model training on local nodes while sharing only model weights. While these methods enhance privacy, they struggle with heterogeneous and imbalanced data and suffer from inefficiencies due to frequent communication and the aggregation of weights. More critically, the dynamic and complex nature of clinical environments demands scalable AI systems capable of continuously learning from diverse modalities and multilabels. Yet, both centralized and decentralized models are prone to catastrophic forgetting during system expansion, often requiring full model retraining to incorporate new data. To address these limitations, we propose VGS-ATD, a novel distributed learning framework. To validate VGS-ATD, we evaluate it in experiments spanning 30 datasets and 80 independent labels across distributed nodes, VGS-ATD achieved an overall accuracy of 92.7%, outperforming centralized learning (84.9%) and swarm learning (72.99%), while federated learning failed under these conditions due to high requirements on computational resources. VGS-ATD also demonstrated strong scalability, with only a 1% drop in accuracy on existing nodes after expansion, compared to a 20% drop in centralized learning, highlighting its resilience to catastrophic forgetting. Additionally, it reduced computational costs by up to 50% relative to both centralized and swarm learning, confirming its superior efficiency and scalability.