arXiv subjects

Guojie Li

Publications and source records attributed to Guojie Li.

7 recordsLinked to original sources

arXiv2026

Incorporating Continuous Dependence Qualifies Physics-Informed Neural Networks for Operator Learning

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real applications are highly restricted by their poor generalization performance. Inspired by the rigorous mathematical statements on the well-posedness of PDEs, we develop a novel extension of PINNs by incorporating the additional information on the continuous dependence of PDE solutions with respect to parameters and initial/boundary values (abbreviated as cd-PINN). Extensive numerical experiments demonstrate that, with limited labeled data, cd-PINN achieves 1-3 orders of magnitude lower in test MSE than DeepONet and FNO. Therefore, incorporating the continuous dependence of PDE solutions provides a simple way for qualifying PINNs for operator learning.

math.DS↗

arXiv2026

A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of different thermodynamic structure-informed neural networks by incorporating various thermodynamics formulations, including Newtonian, Lagrangian, and Hamiltonian mechanics for conservative systems, as well as the Onsager variational principle and extended irreversible thermodynamics for dissipative systems. Through comprehensive numerical experiments on representative ordinary and partial differential equations, we quantitatively evaluate the impact of these formulations on accuracy, physical consistency, noise robustness, and interpretability. The results show that Newtonian-residual-based PINNs can reconstruct system states but fail to reliably recover key physical and thermodynamic quantities, whereas structure-preserving formulation significantly enhances parameter identification, thermodynamic consistency, and robustness. These findings provide practical guidance for principled design of thermodynamics-consistency model, and lay the groundwork for integrating more general nonequilibrium thermodynamic structures into physics-informed machine learning.

cs.LG↗

arXiv2025

GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling

Medical image segmentation demands models that achieve high accuracy while maintaining computational efficiency and clinical interpretability. While recent Kolmogorov-Arnold Networks (KANs) offer powerful adaptive non-linearities, their full-channel spline transformations incur a quadratic parameter growth of $\mathcal{O}(C^{2}(G+k))$ with respect to the channel dimension $C$, where $G$ and $k$ denote the number of grid intervals and spline polynomial order, respectively. Moreover, unconstrained spline mappings lack structural constraints, leading to excessive functional freedom, which may cause overfitting under limited medical annotations. To address these challenges, we propose GroupKAN (Grouped Kolmogorov-Arnold Networks), an efficient architecture driven by group-structured spline modeling. Specifically, we introduce: (1) Grouped KAN Transform (GKT), which restricts spline interactions to intra-group channel mappings across $g$ groups, effectively reducing the spline-induced quadratic expansion to \textbf{$\mathcal{O}(C^2(\frac{G+k}{g} + 1))$}, thereby significantly lowering the effective quadratic coefficient; and (2) Grouped KAN Activation (GKA), which applies shared spline functions within each group to enable efficient token-wise non-linearities. By imposing structured constraints on channel interactions, GroupKAN achieves a substantial reduction in parameter redundancy without sacrificing expressive capacity.Extensive evaluations on three medical benchmarks (BUSI, GlaS, and CVC) demonstrate that GroupKAN achieves an average IoU of 79.80\%, outperforming the strong U-KAN baseline by +1.11\% while requiring only 47.6\% of the parameters (3.02M vs. 6.35M). Qualitative results further reveal that GroupKAN produces sharply localized activation maps that better align with the ground truth than MLPs and KANs, significantly enhancing clinical interpretability.

cs.CV↗

arXiv2025

Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model

We present Ring-1T, the first open-source, state-of-the-art thinking model with a trillion-scale parameter. It features 1 trillion total parameters and activates approximately 50 billion per token. Training such models at a trillion-parameter scale introduces unprecedented challenges, including train-inference misalignment, inefficiencies in rollout processing, and bottlenecks in the RL system. To address these, we pioneer three interconnected innovations: (1) IcePop stabilizes RL training via token-level discrepancy masking and clipping, resolving instability from training-inference mismatches; (2) C3PO++ improves resource utilization for long rollouts under a token budget by dynamically partitioning them, thereby obtaining high time efficiency; and (3) ASystem, a high-performance RL framework designed to overcome the systemic bottlenecks that impede trillion-parameter model training. Ring-1T delivers breakthrough results across critical benchmarks: 93.4 on AIME-2025, 86.72 on HMMT-2025, 2088 on CodeForces, and 55.94 on ARC-AGI-1. Notably, it attains a silver medal-level result on the IMO-2025, underscoring its exceptional reasoning capabilities. By releasing the complete 1T parameter MoE model to the community, we provide the research community with direct access to cutting-edge reasoning capabilities. This contribution marks a significant milestone in democratizing large-scale reasoning intelligence and establishes a new baseline for open-source model performance.

cs.CL↗

arXiv2024

MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions from data. This paper proposes a novel neural network architecture, the MEP-Net, which combines the MEP with neural networks to generate probability distributions from moment constraints. We also provide a comprehensive overview of the fundamentals of the maximum entropy principle, its mathematical formulations, and a rigorous justification for its applicability for non-equilibrium systems based on the large deviations principle. Through fruitful numerical experiments, we demonstrate that the MEP-Net can be particularly useful in modeling the evolution of probability distributions in biochemical reaction networks and in generating complex distributions from data.

stat.ML↗

arXiv2024

Decentralized Collaborative Pricing and Shunting for Multiple EV Charging Stations Based on Multi-Agent Reinforcement Learning

The extraordinary electric vehicle (EV) popularization in the recent years has facilitated research studies in alleviating EV energy charging demand. Previous studies primarily focused on the optimizations over charging stations (CS) profit and EV users cost savings through charge/discharge scheduling events. In this work, the random behaviors of EVs are considered, with EV users preferences over multi-CS characteristics modelled to imitate the potential CS selection disequilibrium. A price scheduling strategy under decentralized collaborative framework is proposed to achieve EV shunting in a multi-CS environment, while minimizing the charging cost through multi agent reinforcement learning. The proposed problem is formulated as a Markov Decision Process (MDP) with uncertain transition probability.

cs.MA↗

arXiv2014

Temporal scaling in information propagation

For the study of information propagation, one fundamental problem is uncovering universal laws governing the dynamics of information propagation. This problem, from the microscopic perspective, is formulated as estimating the propagation probability that a piece of information propagates from one individual to another. Such a propagation probability generally depends on two major classes of factors: the intrinsic attractiveness of information and the interactions between individuals. Despite the fact that the temporal effect of attractiveness is widely studied, temporal laws underlying individual interactions remain unclear, causing inaccurate prediction of information propagation on evolving social networks. In this report, we empirically study the dynamics of information propagation, using the dataset from a population-scale social media website. We discover a temporal scaling in information propagation: the probability a message propagates between two individuals decays with the length of time latency since their latest interaction, obeying a power-law rule. Leveraging the scaling law, we further propose a temporal model to estimate future propagation probabilities between individuals, reducing the error rate of information propagation prediction from 6.7% to 2.6% and improving viral marketing with 9.7% incremental customers.

cs.SI↗