arXiv subjects

Jingtao Ding

Publications and source records attributed to Jingtao Ding.

At least 37 records · Page 2Linked to original sources

arXiv2026

Beyond Accuracy and Complexity: The Effective Information Criterion for Structurally Stable Symbolic Regression

Symbolic regression (SR) traditionally balances accuracy and complexity, implicitly assuming that simpler formulas are structurally more rational. We argue that this assumption is insufficient: existing algorithms often exploit this metric to discover accurate and compact but structurally irrational formulas that are numerically ill-conditioned and physically inexplicable. Inspired by the structural stability of real physical laws, we propose the Effective Information Criterion (EIC) to quantify formula rationality. EIC models formulas as information channels and measures the amplification of inherent rounding noise during recursive calculation, effectively distinguishing physically plausible structures from pathological ones without relying on ground truth. Our analysis reveals a stark structural stability gap between human-derived equations and SR-discovered results. By integrating EIC into SR workflows, we provide explicit structural guidance: for heuristic search, EIC steers algorithms toward stable regions to yield superior Pareto frontiers; for generative models, EIC-based filtering improves pre-training sample efficiency by 2-4 times and boosts generalization R2 by 22.4%. Finally, an extensive study with 108 human experts shows that EIC aligns with human preferences in 70% of cases, validating structural stability as a critical prerequisite for human-perceived interpretability.

cs.LG↗

arXiv2026

ChaosNexus: A Foundation Model for ODE-based Chaotic System Forecasting with Hierarchical Multi-scale Awareness

Foundation models have shown great promise in achieving zero-shot or few-shot forecasting for ODE-based chaotic systems via large-scale pretraining. However, existing architectures often fail to capture the multi-scale temporal structures and distinct spectral characteristics of chaotic dynamics. To address this, we introduce ChaosNexus, a foundation model for chaotic system forecasting underpinned by the proposed ScaleFormer architecture. By processing temporal contexts across hierarchically varying patch sizes, ChaosNexus effectively captures long-range dependencies and preserves high-frequency fluctuations. To address heterogeneity across distinct systems, we integrate Mixture-of-Experts (MoE) layers into each ScaleFormer block and explicitly condition the final forecasts on a learned frequency fingerprint, providing the model with a global spectral view of the system. Extensive evaluations on over 9,000 synthetic systems demonstrate that ChaosNexus achieves superior fidelity in long-term attractor statistics while maintaining competitive point-wise accuracy. Furthermore, in real-world applications, it achieves a remarkable zero-shot mean error below 1°C for 5-day station-based weather forecasting. Codes are available at https://github.com/TomXaxaxa/ChaosNexus.

cs.LG↗

arXiv2026

Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions

Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be assessed during training. Moreover, the straight flow assumption suffers from some inherent limitations. To address this, we propose to fine-tune FM via Maximum Likelihood Estimation (MLE) of reconstructions -- enabled by FM's smooth ODE formulation, unlike the stochastic differential equations (SDEs) in diffusion models. We first theoretically analyze the relationship between training loss and inference error in FM under numerical precision constraints. We then propose an easy-to-implement fine-tuning framework based on MLE of reconstructions, with flexibility for sophisticated extensions. Building on this, we incorporate a generalized artificial viscosity term that enhances flow stability and robustness, accompanied by a direct parameterization method and rigorous theoretical guarantees. Experiments demonstrate our method's effectiveness across diverse settings: a toy example provides mechanistic insights into the fine-tuning process, while large-scale evaluations on meteorological forecasting and robotic manipulation policies validate reliable performance improvements.

cs.LG↗

arXiv2026

Inferring Network Evolutionary History via Structure-State Coupled Learning

Inferring a network's evolutionary history from a single final snapshot with limited temporal annotations is fundamental yet challenging. Existing approaches predominantly rely on topology alone, which often provides insufficient and noisy cues. This paper leverages network steady-state dynamics -- converged node states under a given dynamical process -- as an additional and widely accessible observation for network evolution history inference. We propose CS$^2$, which explicitly models structure-state coupling to capture how topology modulates steady states and how the two signals jointly improve edge discrimination for formation-order recovery. Experiments on six real temporal networks, evaluated under multiple dynamical processes, show that CS$^2$ consistently outperforms strong baselines, improving pairwise edge precedence accuracy by 4.0% on average and global ordering consistency (Spearman-$ρ$) by 7.7% on average. CS$^2$ also more faithfully recovers macroscopic evolution trajectories such as clustering formation, degree heterogeneity, and hub growth. Moreover, a steady-state-only variant remains competitive when reliable topology is limited, highlighting steady states as an independent signal for evolution inference.

cs.SI↗

arXiv2025

WorldMove, a global open data for human mobility

High-quality human mobility data is crucial for applications such as urban planning, transportation management, and public health, yet its collection is often hindered by privacy concerns and data scarcity-particularly in less-developed regions. To address this challenge, we introduce WorldMove, a large-scale synthetic mobility dataset covering over 1,600 cities across 179 countries and 6 continents. Our method leverages publicly available multi-source data, including gridded population distribution, point-of-interest (POI) maps, and commuting origin-destination (OD) flows-to generate realistic city-scale mobility trajectories using a diffusion-based generative model. The generation process involves defining city boundaries, collecting multi-source input features, and simulating individual-level movements that reflect plausible daily mobility behavior. Comprehensive validation demonstrates that the generated data closely aligns with real-world observations, both in terms of fine-grained individual mobility behavior and city-scale population flows. Alongside the pre-generated datasets, we release the trained model and a complete open-source pipeline, enabling researchers and practitioners to generate custom synthetic mobility data for any city worldwide. This work not only fills critical data gaps, but also lays a global foundation for scalable, privacy-preserving, and inclusive mobility research-empowering data-scarce regions and enabling universal access to human mobility insights.

cs.SI↗

arXiv2025

Understanding World or Predicting Future? A Comprehensive Survey of World Models

The concept of world models has garnered significant attention due to advancements in multimodal large language models such as GPT-4 and video generation models such as Sora, which are central to the pursuit of artificial general intelligence. This survey offers a comprehensive review of the literature on world models. Generally, world models are regarded as tools for either understanding the present state of the world or predicting its future dynamics. This review presents a systematic categorization of world models, emphasizing two primary functions: (1) constructing internal representations to understand the mechanisms of the world, and (2) predicting future states to simulate and guide decision-making. Initially, we examine the current progress in these two categories. We then explore the application of world models in key domains, including generative games, autonomous driving, robotics, and social simulacra, with a focus on how each domain utilizes these aspects. Finally, we outline key challenges and provide insights into potential future research directions. We summarize the representative papers along with their code repositories in https://github.com/tsinghua-fib-lab/World-Model.

cs.CL↗

arXiv2025

MoveGPT: Scaling Mobility Foundation Models with Spatially-Aware Mixture of Experts

The success of foundation models in language has inspired a new wave of general-purpose models for human mobility. However, existing approaches struggle to scale effectively due to two fundamental limitations: a failure to use meaningful basic units to represent movement, and an inability to capture the vast diversity of patterns found in large-scale data. In this work, we develop MoveGPT, a large-scale foundation model specifically architected to overcome these barriers. MoveGPT is built upon two key innovations: (1) a unified location encoder that maps geographically disjoint locations into a shared semantic space, enabling pre-training on a global scale; and (2) a Spatially-Aware Mixture-of-Experts Transformer that develops specialized experts to efficiently capture diverse mobility patterns. Pre-trained on billion-scale datasets, MoveGPT establishes a new state-of-the-art across a wide range of downstream tasks, achieving performance gains of up to 35% on average. It also demonstrates strong generalization capabilities to unseen cities. Crucially, our work provides empirical evidence of scaling ability in human mobility, validating a clear path toward building increasingly capable foundation models in this domain.

cs.AI↗

arXiv2025

PID-controlled Langevin Dynamics for Faster Sampling of Generative Models

Langevin dynamics sampling suffers from extremely low generation speed, fundamentally limited by numerous fine-grained iterations to converge to the target distribution. We introduce PID-controlled Langevin Dynamics (PIDLD), a novel sampling acceleration algorithm that reinterprets the sampling process using control-theoretic principles. By treating energy gradients as feedback signals, PIDLD combines historical gradients (the integral term) and gradient trends (the derivative term) to efficiently traverse energy landscapes and adaptively stabilize, thereby significantly reducing the number of iterations required to produce high-quality samples. Our approach requires no additional training, datasets, or prior information, making it immediately integrable with any Langevin-based method. Extensive experiments across image generation and reasoning tasks demonstrate that PIDLD achieves higher quality with fewer steps, making Langevin-based generative models more practical for efficiency-critical applications. The implementation can be found at \href{https://github.com/tsinghua-fib-lab/PIDLD}{https://github.com/tsinghua-fib-lab/PIDLD}.

cs.LG↗

arXiv2025

UniMove: A Unified Model for Multi-city Human Mobility Prediction

Human mobility prediction is vital for urban planning, transportation optimization, and personalized services. However, the inherent randomness, non-uniform time intervals, and complex patterns of human mobility, compounded by the heterogeneity introduced by varying city structures, infrastructure, and population densities, present significant challenges in modeling. Existing solutions often require training separate models for each city due to distinct spatial representations and geographic coverage. In this paper, we propose UniMove, a unified model for multi-city human mobility prediction, addressing two challenges: (1) constructing universal spatial representations for effective token sharing across cities, and (2) modeling heterogeneous mobility patterns from varying city characteristics. We propose a trajectory-location dual-tower architecture, with a location tower for universal spatial encoding and a trajectory tower for sequential mobility modeling. We also design MoE Transformer blocks to adaptively select experts to handle diverse movement patterns. Extensive experiments across multiple datasets from diverse cities demonstrate that UniMove truly embodies the essence of a unified model. By enabling joint training on multi-city data with mutual data enhancement, it significantly improves mobility prediction accuracy by over 10.2\%. UniMove represents a key advancement toward realizing a true foundational model with a unified architecture for human mobility. We release the implementation at https://github.com/tsinghua-fib-lab/UniMove/.

cs.LG↗

arXiv2025

Diffusion Transformers as Open-World Spatiotemporal Foundation Models

The urban environment is characterized by complex spatio-temporal dynamics arising from diverse human activities and interactions. Effectively modeling these dynamics is essential for understanding and optimizing urban systems. In this work, we introduce UrbanDiT, a foundation model for open-world urban spatio-temporal learning that successfully scales up diffusion transformers in this field. UrbanDiT pioneers a unified model that integrates diverse data sources and types while learning universal spatio-temporal patterns across different cities and scenarios. This allows the model to unify both multi-data and multi-task learning, and effectively support a wide range of spatio-temporal applications. Its key innovation lies in the elaborated prompt learning framework, which adaptively generates both data-driven and task-specific prompts, guiding the model to deliver superior performance across various urban applications. UrbanDiT offers three advantages: 1) It unifies diverse data types, such as grid-based and graph-based data, into a sequential format; 2) With task-specific prompts, it supports a wide range of tasks, including bi-directional spatio-temporal prediction, temporal interpolation, spatial extrapolation, and spatio-temporal imputation; and 3) It generalizes effectively to open-world scenarios, with its powerful zero-shot capabilities outperforming nearly all baselines with training data. UrbanDiT sets up a new benchmark for foundation models in the urban spatio-temporal domain. Code and datasets are publicly available at https://github.com/tsinghua-fib-lab/UrbanDiT.

cs.LG↗

arXiv2025

Collaborative Deterministic-Probabilistic Forecasting for Diverse Spatiotemporal Systems

Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have shown promise in capturing complex data distributions, their application to spatiotemporal forecasting remains limited due to complex spatiotemporal dynamics and high computational demands. we propose CoST, a general forecasting framework that collaborates deterministic and diffusion models for diverse spatiotemporal systems. CoST formulates a mean-residual decomposition strategy: it leverages a powerful deterministic model to capture the conditional mean and a lightweight diffusion model to learn residual uncertainties. This collaborative formulation simplifies learning objectives, improves accuracy and efficiency, and generalizes across diverse spatiotemporal systems. To address spatial heterogeneity, we further design a scale-aware diffusion mechanism to guide the diffusion process. Extensive experiments across ten real-world datasets from climate, energy, communication, and urban systems show that CoST achieves 25\% performance gains over state-of-the-art baselines, while significantly reducing computational cost.

cs.LG↗

arXiv2025

Structure-prior Informed Diffusion Model for Graph Source Localization with Limited Data

Source localization in graph information propagation is essential for mitigating network disruptions, including misinformation spread, cyber threats, and infrastructure failures. Existing deep generative approaches face significant challenges in real-world applications due to limited propagation data availability. We present SIDSL (\textbf{S}tructure-prior \textbf{I}nformed \textbf{D}iffusion model for \textbf{S}ource \textbf{L}ocalization), a generative diffusion framework that leverages topology-aware priors to enable robust source localization with limited data. SIDSL addresses three key challenges: unknown propagation patterns through structure-based source estimations via graph label propagation, complex topology-propagation relationships via a propagation-enhanced conditional denoiser with GNN-parameterized label propagation module, and class imbalance through structure-prior biased diffusion initialization. By learning pattern-invariant features from synthetic data generated by established propagation models, SIDSL enables effective knowledge transfer to real-world scenarios. Experimental evaluation on four real-world datasets demonstrates superior performance with 7.5-13.3\% F1 score improvements over baselines, including over 19\% improvement in few-shot and 40\% in zero-shot settings, validating the framework's effectiveness for practical source localization. Our code can be found \href{https://github.com/tsinghua-fib-lab/SIDSL}{here}.

cs.SI↗

arXiv2025

Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length

Symbolic regression, a task discovering the formula best fitting the given data, is typically based on the heuristical search. These methods usually update candidate formulas to obtain new ones with lower prediction errors iteratively. However, since formulas with similar function shapes may have completely different symbolic forms, the prediction error does not decrease monotonously as the search approaches the target formula, causing the low recovery rate of existing methods. To solve this problem, we propose a novel search objective based on the minimum description length, which reflects the distance from the target and decreases monotonically as the search approaches the correct form of the target formula. To estimate the minimum description length of any input data, we design a neural network, MDLformer, which enables robust and scalable estimation through large-scale training. With the MDLformer's output as the search objective, we implement a symbolic regression method, SR4MDL, that can effectively recover the correct mathematical form of the formula. Extensive experiments illustrate its excellent performance in recovering formulas from data. Our method successfully recovers around 50 formulas across two benchmark datasets comprising 133 problems, outperforming state-of-the-art methods by 43.92%. Experiments on 122 unseen black-box problems further demonstrate its generalization performance. We release our code at https://github.com/tsinghua-fib-lab/SR4MDL .

cs.LG↗

arXiv2025

Advancing network resilience theories with symbolized reinforcement learning

Many complex networks display remarkable resilience under external perturbations, internal failures and environmental changes, yet they can swiftly deteriorate into dysfunction upon the removal of a few keystone nodes. Discovering theories that measure network resilience offers the potential to prevent catastrophic collapses--from species extinctions to financial crise--with profound implications for real-world systems. Current resilience theories address the problem from a single perspective of topology, neglecting the crucial role of system dynamics, due to the intrinsic complexity of the coupling between topology and dynamics which exceeds the capabilities of human analytical methods. Here, we report an automatic method for resilience theory discovery, which learns from how AI solves a complicated network dismantling problem and symbolizes its network attack strategies into theoretical formulas. This proposed self-inductive approach discovers the first resilience theory that accounts for both topology and dynamics, highlighting how the correlation between node degree and state shapes overall network resilience, and offering insights for designing early warning signals of systematic collapses. Additionally, our approach discovers formulas that refine existing well-established resilience theories with over 37.5% improvement in accuracy, significantly advancing human understanding of complex networks with AI.

physics.soc-ph↗

arXiv2025

Unveiling the Power of Noise Priors: Enhancing Diffusion Models for Mobile Traffic Prediction

Accurate prediction of mobile traffic, i.e., network traffic from cellular base stations, is crucial for optimizing network performance and supporting urban development. However, the non-stationary nature of mobile traffic, driven by human activity and environmental changes, leads to both regular patterns and abrupt variations. Diffusion models excel in capturing such complex temporal dynamics due to their ability to capture the inherent uncertainties. Most existing approaches prioritize designing novel denoising networks but often neglect the critical role of noise itself, potentially leading to sub-optimal performance. In this paper, we introduce a novel perspective by emphasizing the role of noise in the denoising process. Our analysis reveals that noise fundamentally shapes mobile traffic predictions, exhibiting distinct and consistent patterns. We propose NPDiff, a framework that decomposes noise into prior and residual components, with the prior} derived from data dynamics, enhancing the model's ability to capture both regular and abrupt variations. NPDiff can seamlessly integrate with various diffusion-based prediction models, delivering predictions that are effective, efficient, and robust. Extensive experiments demonstrate that it achieves superior performance with an improvement over 30\%, offering a new perspective on leveraging diffusion models in this domain. We provide code and data at https://github.com/tsinghua-fib-lab/NPDiff.

cs.LG↗

arXiv2025

A Comprehensive Survey on Artificial Intelligence for Complex Network: Potential, Methodology and Application

Complex networks pervade various real-world systems, from the natural environment to human societies. The essence of these networks is in their ability to transition and evolve from microscopic disorder-where network topology and node dynamics intertwine-to a macroscopic order characterized by certain collective behaviors. Over the past two decades, complex network science has significantly enhanced our understanding of the statistical mechanics, structures, and dynamics underlying real-world networks. Despite these advancements, there remain considerable challenges in exploring more realistic systems and enhancing practical applications. The emergence of artificial intelligence (AI) technologies, coupled with the abundance of diverse real-world network data, has heralded a new era in complex network science research. This survey aims to systematically address the potential advantages of AI in overcoming the lingering challenges of complex network research. It endeavors to summarize the pivotal research problems and provide an exhaustive review of the corresponding methodologies and applications. Through this comprehensive survey-the first of its kind on AI for complex networks-we expect to provide valuable insights that will drive further research and advancement in this interdisciplinary field.

cs.SI↗

arXiv2025

A Survey of Physics-Informed AI for Complex Urban Systems

Urban systems are typical examples of complex systems, where the integration of physics-based modeling with artificial intelligence (AI) presents a promising paradigm for enhancing predictive accuracy, interpretability, and decision-making. In this context, AI excels at capturing complex, nonlinear relationships, while physics-based models ensure consistency with real-world laws and provide interpretable insights. We provide a comprehensive review of physics-informed AI methods in urban applications. The proposed taxonomy categorizes existing approaches into three paradigms - Physics-Integrated AI, Physics-AI Hybrid Ensemble, and AI-Integrated Physics - and further details seven representative methods. This classification clarifies the varying degrees and directions of physics-AI integration, guiding the selection and development of appropriate methods based on application needs and data availability. We systematically examine their applications across eight key urban domains: energy, environment, economy, transportation, information, public services, emergency management, and the urban system as a whole. Our analysis highlights how these methodologies leverage physical laws and data-driven models to address urban challenges, enhancing system reliability, efficiency, and adaptability. By synthesizing existing methodologies and their urban applications, we identify critical gaps and outline future research directions, paving the way toward next-generation intelligent urban system modeling.

physics.soc-ph↗

arXiv2025

OpenCarbon: A Contrastive Learning-based Cross-Modality Neural Approach for High-Resolution Carbon Emission Prediction Using Open Data

Accurately estimating high-resolution carbon emissions is crucial for effective emission governance and mitigation planning. While conventional methods for precise carbon accounting are hindered by substantial data collection efforts, the rise of open data and advanced learning techniques offers a promising solution. Once an open data-based prediction model is developed and trained, it can easily infer emissions for new areas based on available open data. To address this, we incorporate two modalities of open data, satellite images and point-of-interest (POI) data, to predict high-resolution urban carbon emissions, with satellite images providing macroscopic and static and POI data offering fine-grained and relatively dynamic functionality information. However, estimating high-resolution carbon emissions presents two significant challenges: the intertwined and implicit effects of various functionalities on carbon emissions, and the complex spatial contiguity correlations that give rise to the agglomeration effect. Our model, OpenCarbon, features two major designs that target the challenges: a cross-modality information extraction and fusion module to extract complementary functionality information from two modules and model their interactions, and a neighborhood-informed aggregation module to capture the spatial contiguity correlations. Extensive experiments demonstrate our model's superiority, with a significant performance gain of 26.6\% on R2. Further generalizability tests and case studies also show OpenCarbon's capacity to capture the intrinsic relation between urban functionalities and carbon emissions, validating its potential to empower efficient carbon governance and targeted carbon mitigation planning. Codes and data are available: https://github.com/JinweiZzz/OpenCarbon.

cs.CV↗