Yifan Du

Wayne Xin Zhao, Kun Zhou, Junyi Li et al.

Language is essentially a complex, intricate system of human expressions governed by grammatical rules. It poses a significant challenge to develop capable AI algorithms for comprehending and grasping a language. As a major approach, language modeling has been widely studied for language understanding and generation in the past two decades, evolving from statistical language models to neural language models. Recently, pre-trained language models (PLMs) have been proposed by pre-training Transformer models over large-scale corpora, showing strong capabilities in solving various NLP tasks. Since researchers have found that model scaling can lead to performance improvement, they further study the scaling effect by increasing the model size to an even larger size. Interestingly, when the parameter scale exceeds a certain level, these enlarged language models not only achieve a significant performance improvement but also show some special abilities that are not present in small-scale language models. To discriminate the difference in parameter scale, the research community has coined the term large language models (LLM) for the PLMs of significant size. Recently, the research on LLMs has been largely advanced by both academia and industry, and a remarkable progress is the launch of ChatGPT, which has attracted widespread attention from society. The technical evolution of LLMs has been making an important impact on the entire AI community, which would revolutionize the way how we develop and use AI algorithms. In this survey, we review the recent advances of LLMs by introducing the background, key findings, and mainstream techniques. In particular, we focus on four major aspects of LLMs, namely pre-training, adaptation tuning, utilization, and capacity evaluation. Besides, we also summarize the available resources for developing LLMs and discuss the remaining issues for future directions.

Wayne Xin Zhao, Kun Zhou, Junyi Li et al.

Language is essentially a complex, intricate system of human expressions governed by grammatical rules. It poses a significant challenge to develop capable AI algorithms for comprehending and grasping a language. As a major approach, language modeling has been widely studied for language understanding and generation in the past two decades, evolving from statistical language models to neural language models. Recently, pre-trained language models (PLMs) have been proposed by pre-training Transformer models over large-scale corpora, showing strong capabilities in solving various NLP tasks. Since researchers have found that model scaling can lead to performance improvement, they further study the scaling effect by increasing the model size to an even larger size. Interestingly, when the parameter scale exceeds a certain level, these enlarged language models not only achieve a significant performance improvement but also show some special abilities that are not present in small-scale language models. To discriminate the difference in parameter scale, the research community has coined the term large language models (LLM) for the PLMs of significant size. Recently, the research on LLMs has been largely advanced by both academia and industry, and a remarkable progress is the launch of ChatGPT, which has attracted widespread attention from society. The technical evolution of LLMs has been making an important impact on the entire AI community, which would revolutionize the way how we develop and use AI algorithms. In this survey, we review the recent advances of LLMs by introducing the background, key findings, and mainstream techniques. In particular, we focus on four major aspects of LLMs, namely pre-training, adaptation tuning, utilization, and capacity evaluation. Besides, we also summarize the available resources for developing LLMs and discuss the remaining issues for future directions.

Yifan Du, Hangyu Guo, Kun Zhou et al.

Visual instruction tuning is crucial for enhancing the zero-shot generalization capability of Multi-modal Large Language Models (MLLMs). In this paper, we aim to investigate a fundamental question: ''what makes for good visual instructions''. Through a comprehensive empirical study, we find that instructions focusing on complex visual reasoning tasks are particularly effective in improving the performance of MLLMs, with results correlating to instruction complexity. Based on this insight, we develop a systematic approach to automatically create high-quality complex visual reasoning instructions. Our approach employs a synthesize-complicate-reformulate paradigm, leveraging multiple stages to gradually increase the complexity of the instructions while guaranteeing quality. Based on this approach, we create the ComVint dataset with 32K examples, and fine-tune four MLLMs on it. Experimental results consistently demonstrate the enhanced performance of all compared MLLMs, such as a 27.86% and 27.60% improvement for LLaVA on MME-Perception and MME-Cognition, respectively. Our code and data are publicly available at the link: https://github.com/RUCAIBox/ComVint.

Yifan Du, Zikang Liu, Jinbiao Peng et al.

Multimodal deep search agents have shown great potential in solving complex tasks by iteratively collecting textual and visual evidence. However, managing the heterogeneous information and high token costs associated with multimodal inputs over long horizons remains a critical challenge, as existing methods often suffer from context explosion or the loss of crucial visual signals. To address this, we propose a novel Long-horizon MultiModal deep search framework, named LMM-Searcher, centered on a file-based visual representation mechanism. By offloading visual assets to an external file system and mapping them to lightweight textual identifiers (UIDs), our approach mitigates context overhead while preserving multimodal information for future access. We equip the agent with a tailored fetch-image tool, enabling a progressive, on-demand visual loading strategy for active perception. Furthermore, we introduce a data synthesis pipeline designed to generate queries requiring complex cross-modal multi-hop reasoning. Using this pipeline, we distill 12K high-quality trajectories to fine-tune Qwen3-VL-Thinking-30A3B into a specialized multimodal deep search agent. Extensive experiments across four benchmarks demonstrate that our method successfully scales to 100-turn search horizons, achieving state-of-the-art performance among open-source models on challenging long-horizon benchmarks like MM-BrowseComp and MMSearch-Plus, while also exhibiting strong generalizability across different base models. Our code will be released in https://github.com/RUCAIBox/LMM-Searcher.

Yifan Li, Yukai Gu, Yingqian Min et al.

Recent breakthroughs in video generation have demonstrated an emerging capability termed Chain-of-Frames (CoF) reasoning, where models resolve complex tasks through the generation of continuous frames. While these models show promise for Generative Video Reasoning (GVR), existing evaluation frameworks often rely on single-frame assessments, which can lead to outcome-hacking, where a model reaches a correct conclusion through an erroneous process. To address this, we propose a process-aware evaluation paradigm. We introduce VIPER, a comprehensive benchmark spanning 16 tasks across temporal, structural, symbolic, spatial, physics, and planning reasoning. Furthermore, we propose Process-outcome Consistency (POC@r), a new metric that utilizes VLM-as-Judge with a hierarchical rubric to evaluate both the validity of the intermediate steps and the final result. Our experiments reveal that state-of-the-art video models achieve POC@1.0 only about 20% and exhibit a significant outcome-hacking. We further explore the impact of test-time scaling and sampling robustness, highlighting a substantial gap between current video generation and true generalized visual reasoning. Our benchmark are released at https://github.com/RUCAIBox/VIPER.

Yifan Du, Guang Lin

This research presents a new turbulence generation method based on stochastic wavelets and tests its various properties in both homogeneous and inhomogeneous turbulence. Turbulence field can be generated with less basis compared to previous synthetic Fourier methods. Adaptive generation of inhomogeneous turbulence is achieved by scale reduction algorithm and lead to smaller computation cost. The generated turbulence shows good agreement with input data and theoretical results.

Yifan Du, Zikang Liu, Yifan Li et al.

Recently, slow-thinking reasoning systems, built upon large language models (LLMs), have garnered widespread attention by scaling the thinking time during inference. There is also growing interest in adapting this capability to multimodal large language models (MLLMs). Given that MLLMs handle more complex data semantics across different modalities, it is intuitively more challenging to implement multimodal slow-thinking systems. To address this issue, in this paper, we explore a straightforward approach by fine-tuning a capable MLLM with a small amount of textual long-form thought data, resulting in a multimodal slow-thinking system, Virgo (Visual reasoning with long thought). We find that these long-form reasoning processes, expressed in natural language, can be effectively transferred to MLLMs. Moreover, it seems that such textual reasoning data can be even more effective than visual reasoning data in eliciting the slow-thinking capacities of MLLMs. While this work is preliminary, it demonstrates that slow-thinking capacities are fundamentally associated with the language model component, which can be transferred across modalities or domains. This finding can be leveraged to guide the development of more powerful slow-thinking reasoning systems. We release our resources at https://github.com/RUCAIBox/Virgo.

GLM-V Team, Wenyi Hong, Wenmeng Yu et al.

We present GLM-4.1V-Thinking and GLM-4.5V, a family of vision-language models (VLMs) designed to advance general-purpose multimodal understanding and reasoning. In this report, we share our key findings in the development of the reasoning-centric training framework. We first develop a capable vision foundation model with significant potential through large-scale pre-training, which arguably sets the upper bound for the final performance. We then propose Reinforcement Learning with Curriculum Sampling (RLCS) to unlock the full potential of the model, leading to comprehensive capability enhancement across a diverse range of tasks, including STEM problem solving, video understanding, content recognition, coding, grounding, GUI-based agents, and long document interpretation. In a comprehensive evaluation across 42 public benchmarks, GLM-4.5V achieves state-of-the-art performance on nearly all tasks among open-source models of similar size, and demonstrates competitive or even superior results compared to closed-source models such as Gemini-2.5-Flash on challenging tasks including Coding and GUI Agents. Meanwhile, the smaller GLM-4.1V-9B-Thinking remains highly competitive-achieving superior results to the much larger Qwen2.5-VL-72B on 29 benchmarks. We open-source both GLM-4.1V-9B-Thinking and GLM-4.5V. Code, models and more information are released at https://github.com/zai-org/GLM-V.

Yingqian Min, Kun Zhou, Yifan Li et al.

Recent advancements in reinforcement learning with verifiable rewards (RLVR) have significantly improved the complex reasoning ability of vision-language models (VLMs). However, its outcome-level supervision is too coarse to diagnose and correct errors within the reasoning chain. To this end, we propose Perceval, a process reward model (PRM) that enables token-level error grounding, which can extract image-related claims from the response and compare them one by one with the visual evidence in the image, ultimately returning claims that contain perceptual errors. Perceval is trained with perception-intensive supervised training data. We then integrate Perceval into the RL training process to train the policy models. Specifically, compared to traditional GRPO, which applies sequence-level advantages, we apply token-level advantages by targeting penalties on hallucinated spans identified by Perceval, thus enabling fine-grained supervision signals. In addition to augmenting the training process, Perceval can also assist VLMs during the inference stage. Using Perceval, we can truncate the erroneous portions of the model's response, and then either have the model regenerate the response directly or induce the model to reflect on its previous output. This process can be repeated multiple times to achieve test-time scaling. Experiments show significant improvements on benchmarks from various domains across multiple reasoning VLMs trained with RL, highlighting the promise of perception-centric supervision as a general-purpose strategy. For test-time scaling, it also demonstrates consistent performance gains over other strategies, such as major voting. Our code and data will be publicly released at https://github.com/RUCAIBox/Perceval.

Yifan Du, Yuqi Huo, Kun Zhou et al.

Video Multimodal Large Language Models (MLLMs) have shown remarkable capability of understanding the video semantics on various downstream tasks. Despite the advancements, there is still a lack of systematic research on visual context representation, which refers to the scheme to select frames from a video and further select the tokens from a frame. In this paper, we explore the design space for visual context representation, and aim to improve the performance of video MLLMs by finding more effective representation schemes. Firstly, we formulate the task of visual context representation as a constrained optimization problem, and model the language modeling loss as a function of the number of frames and the number of embeddings (or tokens) per frame, given the maximum visual context window size. Then, we explore the scaling effects in frame selection and token selection respectively, and fit the corresponding function curve by conducting extensive empirical experiments. We examine the effectiveness of typical selection strategies and present empirical findings to determine the two factors. Furthermore, we study the joint effect of frame selection and token selection, and derive the optimal formula for determining the two factors. We demonstrate that the derived optimal settings show alignment with the best-performed results of empirical experiments. Our code and model are available at: https://github.com/RUCAIBox/Opt-Visor.

Chengwei Zhang, Yifan Du, Siyu Liao

Neural channel decoder, as a data-driven channel decoding strategy, has shown very promising improvement on error-correcting capability over the classical methods. However, the success of those deep learning-based decoder comes at the cost of drastically increased model storage and computational complexity, hindering their practical adoptions in real-world time-sensitive resource-sensitive communication and storage systems. To address this challenge, we propose an efficient variational diffusion model-based channel decoder, which effectively integrates the domain-specific belief propagation process to the modern diffusion model. By reaping the low-cost benefits of belief propagation and strong learning capability of diffusion model, our proposed neural decoder simultaneously achieves very low cost and high error-correcting performance. Experimental results show that, compared with the state-of-the-art neural channel decoders, our model provides a feasible solution for practical deployment via achieving the best decoding performance with significantly reduced computational cost and model size.

Yifan Du, Chengwei Zhang, Siyu Liao et al.

Ground robot navigation in complex 3D environments is often hindered by geometric ambiguity, where non-traversable structures such as furniture share local geometric properties with navigable ground. Furthermore, the computational cost of searching massive voxel spaces remains a significant challenge. To address these issues, we present a surface extraction framework that constructs a reduced state space of physically reachable standing positions by enforcing ground support, overhead clearance, and seed-based connectivity constraints. Evaluation across five Matterport3D indoor scenes and three PCT benchmark scenes demonstrates over 80\% state space reduction and sub-millisecond A* search on the Matterport3D scenes, with 100\% planning success across all 300 tested queries.

Dong Guo, Faming Wu, Feida Zhu et al. · pku

We present Seed1.5-VL, a vision-language foundation model designed to advance general-purpose multimodal understanding and reasoning. Seed1.5-VL is composed with a 532M-parameter vision encoder and a Mixture-of-Experts (MoE) LLM of 20B active parameters. Despite its relatively compact architecture, it delivers strong performance across a wide spectrum of public VLM benchmarks and internal evaluation suites, achieving the state-of-the-art performance on 38 out of 60 public benchmarks. Moreover, in agent-centric tasks such as GUI control and gameplay, Seed1.5-VL outperforms leading multimodal systems, including OpenAI CUA and Claude 3.7. Beyond visual and video understanding, it also demonstrates strong reasoning abilities, making it particularly effective for multimodal reasoning challenges such as visual puzzles. We believe these capabilities will empower broader applications across diverse tasks. In this report, we mainly provide a comprehensive review of our experiences in building Seed1.5-VL across model design, data construction, and training at various stages, hoping that this report can inspire further research. Seed1.5-VL is now accessible at https://www.volcengine.com/ (Volcano Engine Model ID: doubao-1-5-thinking-vision-pro-250428)

Yifan Du, Kun Zhou, Yuqi Huo et al.

With the rapid development of video Multimodal Large Language Models (MLLMs), numerous benchmarks have been proposed to assess their video understanding capability. However, due to the lack of rich events in the videos, these datasets may suffer from the short-cut bias that the answers can be deduced from a few frames, without the need to watch the entire video. To address this issue, we introduce Event-Bench, an event-oriented long video understanding benchmark built on existing datasets and human annotations. Event-Bench includes six event-related tasks and 2,190 test instances to comprehensively evaluate video event understanding ability. Additionally, we propose Video Instruction Merging~(VIM), a cost-effective method that enhances video MLLMs using merged, event-intensive video instructions, addressing the scarcity of human-annotated, event-intensive data. Extensive experiments show that the best-performing model, GPT-4o, achieves an overall accuracy of 53.33, significantly outperforming the best open-source model by 41.42%. Leveraging an effective instruction synthesis method and an adaptive model architecture, VIM surpasses both state-of-the-art open-source models and GPT-4V on the Event-Bench. All code, data, and models are publicly available at https://github.com/RUCAIBox/Event-Bench.

Zijia Zhao, Haoyu Lu, Yuqi Huo et al.

Video understanding is a crucial next step for multimodal large language models (MLLMs). Various benchmarks are introduced for better evaluating the MLLMs. Nevertheless, current video benchmarks are still inefficient for evaluating video models during iterative development due to the high cost of constructing datasets and the difficulty in isolating specific skills. In this paper, we propose VideoNIAH (Video Needle In A Haystack), a benchmark construction framework through synthetic video generation. VideoNIAH decouples video content from their query-responses by inserting unrelated visual 'needles' into original videos. The framework automates the generation of query-response pairs using predefined rules, minimizing manual labor. The queries focus on specific aspects of video understanding, enabling more skill-specific evaluations. The separation between video content and the queries also allow for increased video variety and evaluations across different lengths. Utilizing VideoNIAH, we compile a video benchmark VNBench, which includes tasks such as retrieval, ordering, and counting to evaluate three key aspects of video understanding: temporal perception, chronological ordering, and spatio-temporal coherence. We conduct a comprehensive evaluation of both proprietary and open-source models, uncovering significant differences in their video understanding capabilities across various tasks. Additionally, we perform an in-depth analysis of the test results and model configurations. Based on these findings, we provide some advice for improving video MLLM training, offering valuable insights to guide future research and model development. The code and data are available at https://github.com/joez17/VideoNIAH.

Yifan Du, Junyi Li, Tianyi Tang et al.

In this paper, we propose a novel language model guided captioning approach, LAMOC, for knowledge-based visual question answering (VQA). Our approach employs the generated captions by a captioning model as the context of an answer prediction model, which is a Pre-trained Language model (PLM). As the major contribution, we leverage the guidance and feedback of the prediction model to improve the capability of the captioning model. In this way, the captioning model can become aware of the task goal and information need from the PLM. To develop our approach, we design two specific training stages, where the first stage adapts the captioning model to the prediction model (selecting more suitable caption propositions for training) and the second stage tunes the captioning model according to the task goal (learning from feedback of the PLM). Extensive experiments demonstrate the effectiveness of the proposed approach on the knowledge-based VQA task. Specifically, on the challenging A-OKVQA dataset, LAMOC outperforms several competitive zero-shot methods and even achieves comparable results to a fine-tuned VLP model. Our code is publicly available at https://github.com/RUCAIBox/LAMOC.

Tianyi Tang, Yushuo Chen, Yifan Du et al.

People often imagine relevant scenes to aid in the writing process. In this work, we aim to utilize visual information for composition in the same manner as humans. We propose a method, LIVE, that makes pre-trained language models (PLMs) Learn to Imagine for Visuallyaugmented natural language gEneration. First, we imagine the scene based on the text: we use a diffusion model to synthesize high-quality images conditioned on the input texts. Second, we use CLIP to determine whether the text can evoke the imagination in a posterior way. Finally, our imagination is dynamic, and we conduct synthesis for each sentence rather than generate only one image for an entire paragraph. Technically, we propose a novel plug-and-play fusion layer to obtain visually-augmented representations for each text. Our vision-text fusion layer is compatible with Transformerbased architecture. We have conducted extensive experiments on four generation tasks using BART and T5, and the automatic results and human evaluation demonstrate the effectiveness of our proposed method. We will release the code, model, and data at the link: https://github.com/RUCAIBox/LIVE.

Yifan Li, Yifan Du, Kun Zhou et al.

Inspired by the superior language abilities of large language models (LLM), large vision-language models (LVLM) have been recently explored by integrating powerful LLMs for improving the performance on complex multimodal tasks. Despite the promising progress on LVLMs, we find that LVLMs suffer from the hallucination problem, i.e. they tend to generate objects that are inconsistent with the target images in the descriptions. To investigate it, this work presents the first systematic study on object hallucination of LVLMs. We conduct the evaluation experiments on several representative LVLMs, and show that they mostly suffer from severe object hallucination issue. We further discuss that the visual instructions may influence the hallucination, and find that: objects that frequently occur in the visual instructions or co-occur with the image objects, are obviously prone to be hallucinated by LVLMs. Besides, we find that existing evaluation methods might be affected by the input instructions and generation styles of LVLMs. Thus, we further design an improved evaluation method for object hallucination by proposing a polling-based query method called POPE. Experiment results demonstrate that our POPE can evaluate the object hallucination in a more stable and flexible way. Our codes and data are publicly available at https://github.com/RUCAIBox/POPE.

Yujie Li, Zezhi Shao, Chengqing Yu et al.

Spatio-temporal tasks often encounter incomplete data arising from missing or inaccessible sensors, making spatio-temporal kriging crucial for inferring the completely missing temporal information. However, current models struggle with ensuring the validity and generalizability of inferred spatio-temporal patterns, especially in capturing dynamic spatial dependencies and temporal shifts, and optimizing the generalizability of unknown sensors. To overcome these limitations, we propose Spatio-Temporal Aware Graph Adversarial Neural Network (STA-GANN), a novel GNN-based kriging framework that improves spatio-temporal pattern validity and generalization. STA-GANN integrates (i) Decoupled Phase Module that senses and adjusts for timestamp shifts. (ii) Dynamic Data-Driven Metadata Graph Modeling to update spatial relationships using temporal data and metadata; (iii) An adversarial transfer learning strategy to ensure generalizability. Extensive validation across nine datasets from four fields and theoretical evidence both demonstrate the superior performance of STA-GANN.

Yifan Du, Kun Zhou, Yingqian Min et al.

We study how different Chain-of-Thought (CoT) designs affect the acquisition of the generalizable visual reasoning ability in vision-language models (VLMs). While CoT data, especially long or visual CoT such as "think with image", has been widely used to supervise intermediate reasoning, it remains unclear why specific CoT designs help and which ones truly support generalizable reasoning. To systematically evaluate this, we focus on a controlled maze-solving benchmark where reasoning rules are fully visual, difficulty can be tuned by grid size, and all the intermediate steps can be automatically generated. Using Qwen2.5-VL-7B under a standard SFT-then-RL pipeline, we compare three representative CoT formats: Language CoT, Grounding CoT (with spatial coordinate trajectories), and Visual CoT (with image manipulations). Our experiments reveal that visual and longer CoT mainly accelerate convergence but do not lift the final performance ceiling; concise CoT containing only essential grounding steps outperforms longer traces; and, strikingly, CoT retaining only the minimal grounding results generalizes best across different maze sizes. We further validate these insights on other vision-centric tasks. These findings highlight a "short is long" effect and provide practical guidance for constructing more generalizable SFT datasets for visual reasoning.

Jiyang Tang, Hengyi Li, Yifan Du et al.

Although video multimodal large language models (video MLLMs) have achieved substantial progress in video captioning tasks, it remains challenging to adjust the focal emphasis of video captions according to human preferences. To address this limitation, we propose Aligned Video Captioning via Direct Preference Optimization (AVC-DPO), a post-training framework designed to enhance captioning capabilities in video MLLMs through preference alignment. Our approach designs enhanced prompts that specifically target temporal dynamics and spatial information-two key factors that humans care about when watching a video-thereby incorporating human-centric preferences. AVC-DPO leverages the same foundation model's caption generation responses under varied prompt conditions to conduct preference-aware training and caption alignment. Using this framework, we have achieved exceptional performance in the LOVE@CVPR'25 Workshop Track 1A: Video Detailed Captioning Challenge, achieving first place on the Video Detailed Captioning (VDC) benchmark according to the VDCSCORE evaluation metric.

Yifan Du, Zikang Liu, Junyi Li et al.

As transformer evolves, pre-trained models have advanced at a breakneck pace in recent years. They have dominated the mainstream techniques in natural language processing (NLP) and computer vision (CV). How to adapt pre-training to the field of Vision-and-Language (V-L) learning and improve downstream task performance becomes a focus of multimodal learning. In this paper, we review the recent progress in Vision-Language Pre-Trained Models (VL-PTMs). As the core content, we first briefly introduce several ways to encode raw images and texts to single-modal embeddings before pre-training. Then, we dive into the mainstream architectures of VL-PTMs in modeling the interaction between text and image representations. We further present widely-used pre-training tasks, and then we introduce some common downstream tasks. We finally conclude this paper and present some promising research directions. Our survey aims to provide researchers with synthesis and pointer to related research.

Yifan Du, Tamer A. Zaki

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. In this framework, the network parameters are treated as functions with respect to the appropriate coordinate and are numerically updated using the governing equations. By marching the neural network weights in the parameter space, EDNN can predict state-space trajectories that are indefinitely long, which is difficult for other neural network approaches. Boundary conditions of the PDEs are treated as hard constraints, are embedded into the neural network, and are therefore exactly satisfied throughout the entire solution trajectory. Several applications including the heat equation, the advection equation, the Burgers equation, the Kuramoto Sivashinsky equation and the Navier-Stokes equations are solved to demonstrate the versatility and accuracy of EDNN. The application of EDNN to the incompressible Navier-Stokes equation embeds the divergence-free constraint into the network design so that the projection of the momentum equation to solenoidal space is implicitly achieved. The numerical results verify the accuracy of EDNN solutions relative to analytical and benchmark numerical solutions, both for the transient dynamics and statistics of the system.

Aoxue Chen, Yifan Du, Liyao Mars Gao et al.

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered equation to noise and the complexities of model selection. In this work, we propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients, predominantly when the coefficients are spatially or temporally dependent. Specifically, we apply threshold Bayesian group Lasso regression with a spike-and-slab prior (tBGL-SS) and leverage a Gibbs sampler for Bayesian posterior estimation of PDE coefficients. This approach not only enhances the robustness of point estimation with valid uncertainty quantification but also relaxes the computational burden from Bayesian inference through the integration of coefficient thresholds as an approximate MCMC method. Moreover, from the quantified uncertainties, we propose a Bayesian total error bar criteria for model selection, which outperforms classic metrics including the root mean square and the Akaike information criterion. The capability of this method is illustrated by the discovery of several classical benchmark PDEs with spatially or temporally varying coefficients from solution data obtained from the reference simulations. In the experiments, we show that the tBGL-SS method is more robust than the baseline methods under noisy environments and provides better model selection criteria along the regularization path.

Liyao Gao, Yifan Du, Hongshan Li et al.

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in general, current machine learning methods have no theoretical way to guarantee rotational symmetry. By observing an important property of contraction and rotation operation on high-order symmetric tensors, we prove that the rotation operation is preserved via tensor contraction. Based on this theoretical justification, in this paper, we introduce Rotation-Equivariant Network (RotEqNet) to guarantee the property of rotation-equivariance for high-order tensors in fluid systems. We implement RotEqNet and evaluate our claims through four case studies on various fluid systems. The property of error reduction and rotation-equivariance is verified in these case studies. Results from the comparative study show that our method outperforms conventional methods, which rely on data augmentation.