arXiv subjects

Jiacheng Cen

Publications and source records attributed to Jiacheng Cen.

11 recordsLinked to original sources

arXiv2026

Planar Symmetric Pattern Generation

Generating objects with specific symmetries is essential in various real-world scenarios. However, adapting existing 2D continuous representations to enforce planar group symmetry remains a challenge, as the transformation of non-reflective group elements may disrupt continuity. To overcome this limitation, we propose a symmetrization framework for arbitrary planar groups. Our method transforms any 2D continuous representation into a symmetric one while preserving continuity. We provide the mathematical formulation of this representation, demonstrate its approximation capability for symmetric functions, and detail the construction methodology. We validate our approach through three visual design tasks (pattern design, paper-cutting design and stylized topology design) and one material design task. Experiments confirm that our representation enables effective symmetry control and demonstrate its broader applicability.

cs.LG↗

arXiv2026

Reducing Symmetry Increase in Equivariant Neural Networks

Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries. The mathematical essence of this phenomenon is that a symmetric input, after being processed by an equivariant map, experiences an increase in symmetry. While prior research has documented symmetry increase in specific cases, a rigorous understanding of its underlying causes and general reduction strategies remains lacking. In this paper, we provide a detailed and in-depth characterization of symmetry increase together with a principled framework for its reduction: (i) For any given feature space and input symmetry group, we prove that the increased symmetry admits an infimum determined by the structure of the feature space; (ii) Building on this foundation, we develop a computable algorithm to derive this infimum, and propose practical guidelines for feature design to prevent harmful symmetry increases. (iii) Under standard regularity assumptions, we demonstrate that for most equivariant maps, our guidelines effectively reduce symmetry increase. To complement our theoretical findings, we provide visualizations and experiments on both synthetic datasets and the real-world QM9 dataset. The results validate our theoretical predictions.

cs.LG↗

arXiv2026

Optimization and Generation in Aerodynamics Inverse Design

Aerodynamic inverse design can improve vehicle and aircraft efficiency, but practical design rarely seeks performance alone: vehicle refinement must reduce drag while preserving visual features linked to design language, brand recognition and user perception. Traditional CFD-driven optimization is accurate but slow for broad exploration, and current learning-based methods are still largely performance-driven and lack a coherent target linking optimization, generation and visual consistency. Here we formulate visual preservation and aerodynamic improvement as one probability target. Designs consistent with a reference shape or view define a learned visual design distribution, which is reweighted by aerodynamic cost. Optimization then refines an initial geometry toward a low-cost, high-probability design, whereas guided generation samples lower-cost 3D candidates from the same input view. OpenFOAM evaluation shows that visual-feature-preserving optimization reduces vehicle drag by 5.8\% relative to the initial vehicle and reduces the best valid aircraft drag-to-lift objective by 28.8\% relative to the initial aircraft while preserving input visual features. For view-based generation, guidance reduces vehicle drag by 3.0\% and the aircraft drag-to-lift objective by 68.6\% relative to direct generation from the same view, while maintaining visual consistency. Wind-tunnel tests with 3D-printed vehicle prototypes provide an independent wake-level check, and controlled analyses explain the distributional mechanisms behind these results. This work provides a probabilistic foundation and practical route for visual-feature-preserving aerodynamic refinement and early-stage 3D design exploration.

cs.LG↗

arXiv2026

Agentic Fusion of Large Atomic and Language Models to Accelerate Superconductor Discovery

Artificial intelligence has accelerated materials discovery through high-throughput prediction and generation, yet the decision problem remains a formidable bottleneck. While current AI systems readily propose millions of candidates, navigating the decision regarding a viable experimental target requires resolving multi-dimensional judgments across atomic-scale numerical computation and high-level semantic reasoning. Here we present ElementsClaw, an agentic framework for materials discovery that orchestrates a suite of Large Atomic Model (LAM) tools finetuned from our proposed 1-billion-parameter model Elements for numerical computation, while leveraging Large Language Models (LLMs) for semantic reasoning. Applied to superconductors, ElementsClaw rediscovers 66 experimentally verified superconductors that are absent from the standard SuperCon3D database. Scaling to 2.4 million equilibrium crystals, ElementsClaw identifies 68,000 high-confidence candidates in just 28 GPU hours (https://developer.damo-academy.com/material), expanding known superconducting space by orders of magnitude compared to datasets curated over decades. Guided by the agent's reasoning, we experimentally synthesize and verify four novel superconductors: the motif-guided Zr$_3$ScRe$_8$ ($T_c$ = 6.5 K), the de novo generated HfZrRe$_4$ ($T_c$ = 5.9 K), the structurally reinterpreted Zr$_4$VRe$_7$ ($T_c$ = 3.5 K), and the database-latent Hf$_{21}$Re$_{25}$ ($T_c$ = 2.5 K). Together, our results establish a knowledge integrated, autonomously orchestrated, and experimentally grounded paradigm for materials discovery.

cs.LG↗

arXiv2025

Geometric Mixture Models for Electrolyte Conductivity Prediction

Accurate prediction of ionic conductivity in electrolyte systems is crucial for advancing numerous scientific and technological applications. While significant progress has been made, current research faces two fundamental challenges: (1) the lack of high-quality standardized benchmarks, and (2) inadequate modeling of geometric structure and intermolecular interactions in mixture systems. To address these limitations, we first reorganize and enhance the CALiSol and DiffMix electrolyte datasets by incorporating geometric graph representations of molecules. We then propose GeoMix, a novel geometry-aware framework that preserves Set-SE(3) equivariance-an essential but challenging property for mixture systems. At the heart of GeoMix lies the Geometric Interaction Network (GIN), an equivariant module specifically designed for intermolecular geometric message passing. Comprehensive experiments demonstrate that GeoMix consistently outperforms diverse baselines (including MLPs, GNNs, and geometric GNNs) across both datasets, validating the importance of cross-molecular geometric interactions and equivariant message passing for accurate property prediction. This work not only establishes new benchmarks for electrolyte research but also provides a general geometric learning framework that advances modeling of mixture systems in energy materials, pharmaceutical development, and beyond.

cs.LG↗

arXiv2025

Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?

Equivariant Graph Neural Networks (GNNs) that incorporate E(3) symmetry have achieved significant success in various scientific applications. As one of the most successful models, EGNN leverages a simple scalarization technique to perform equivariant message passing over only Cartesian vectors (i.e., 1st-degree steerable vectors), enjoying greater efficiency and efficacy compared to equivariant GNNs using higher-degree steerable vectors. This success suggests that higher-degree representations might be unnecessary. In this paper, we disprove this hypothesis by exploring the expressivity of equivariant GNNs on symmetric structures, including $k$-fold rotations and regular polyhedra. We theoretically demonstrate that equivariant GNNs will always degenerate to a zero function if the degree of the output representations is fixed to 1 or other specific values. Based on this theoretical insight, we propose HEGNN, a high-degree version of EGNN to increase the expressivity by incorporating high-degree steerable vectors while maintaining EGNN's efficiency through the scalarization trick. Our extensive experiments demonstrate that HEGNN not only aligns with our theoretical analyses on toy datasets consisting of symmetric structures, but also shows substantial improvements on more complicated datasets such as $N$-body and MD17. Our theoretical findings and empirical results potentially open up new possibilities for the research of equivariant GNNs.

cs.LG↗

arXiv2025

Universally Invariant Learning in Equivariant GNNs

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must effectively capture the intricate multi-body interactions among different nodes. Prior methods attain this via deeper architectures, augmented body orders, or increased degrees of steerable features, often at high computational cost and without polynomial-time solutions. In this work, we present a theoretically grounded framework for constructing complete equivariant GNNs that is both efficient and practical. We prove that a complete equivariant GNN can be achieved through two key components: 1) a complete scalar function, referred to as the canonical form of the geometric graph; and 2) a full-rank steerable basis set. Leveraging this finding, we propose an efficient algorithm for constructing complete equivariant GNNs based on two common models: EGNN and TFN. Empirical results demonstrate that our model demonstrates superior completeness and excellent performance with only a few layers, thereby significantly reducing computational overhead while maintaining strong practical efficacy.

cs.LG↗

arXiv2025

Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning

Equivariant Graph Neural Networks (GNNs) have achieved remarkable success across diverse scientific applications. However, existing approaches face critical efficiency challenges when scaling to large geometric graphs and suffer significant performance degradation when the input graphs are sparsified for computational tractability. To address these limitations, we introduce FastEGNN and DistEGNN, two novel enhancements to equivariant GNNs for large-scale geometric graphs. FastEGNN employs a key innovation: a small ordered set of virtual nodes that effectively approximates the large unordered graph of real nodes. Specifically, we implement distinct message passing and aggregation mechanisms for different virtual nodes to ensure mutual distinctiveness, and minimize Maximum Mean Discrepancy (MMD) between virtual and real coordinates to achieve global distributedness. This design enables FastEGNN to maintain high accuracy while efficiently processing large-scale sparse graphs. For extremely large-scale geometric graphs, we present DistEGNN, a distributed extension where virtual nodes act as global bridges between subgraphs in different devices, maintaining consistency while dramatically reducing memory and computational overhead. We comprehensively evaluate our models across four challenging domains: N-body systems (100 nodes), protein dynamics (800 nodes), Water-3D (8,000 nodes), and our new Fluid113K benchmark (113,000 nodes). Results demonstrate superior efficiency and performance, establishing new capabilities in large-scale equivariant graph learning. Code is available at https://github.com/GLAD-RUC/DistEGNN.

cs.LG↗

arXiv2025

STORM-BORN: A Challenging Mathematical Derivations Dataset Curated via a Human-in-the-Loop Multi-Agent Framework

High-quality math datasets are crucial for advancing the reasoning abilities of large language models (LLMs). However, existing datasets often suffer from three key issues: outdated and insufficient challenging content, neglecting human-like reasoning, and limited reliability due to single-LLM generation. To address these, we introduce STORM-BORN, an ultra-challenging dataset of mathematical derivations sourced from cutting-edge academic papers, which includes dense human-like approximations and heuristic cues. To ensure the reliability and quality, we propose a novel human-in-the-loop, multi-agent data generation framework, integrating reasoning-dense filters, multi-agent collaboration, and human mathematicians' evaluations. We curated a set of 2,000 synthetic samples and deliberately selected the 100 most difficult problems. Even most advanced models like GPT-o1 solved fewer than 5% of them. Fine-tuning on STORM-BORN boosts accuracy by 7.84% (LLaMA3-8B) and 9.12% (Qwen2.5-7B). As AI approaches mathematician-level reasoning, STORM-BORN provides both a high-difficulty benchmark and a human-like reasoning training resource. Our code and dataset are publicly available at https://github.com/lwhere/STORM-BORN.

cs.CL↗

arXiv2025

A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To address this issue, researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we formalize geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey.

cs.LG↗

arXiv2025

Large Language-Geometry Model: When LLM meets Equivariance

Accurately predicting 3D structures and dynamics of physical systems is crucial in scientific applications. Existing approaches that rely on geometric Graph Neural Networks (GNNs) effectively enforce $\mathrm{E}(3)$-equivariance, but they often fall in leveraging extensive broader information. While direct application of Large Language Models (LLMs) can incorporate external knowledge, they lack the capability for spatial reasoning with guaranteed equivariance. In this paper, we propose EquiLLM, a novel framework for representing 3D physical systems that seamlessly integrates E(3)-equivariance with LLM capabilities. Specifically, EquiLLM comprises four key components: geometry-aware prompting, an equivariant encoder, an LLM, and an equivariant adaptor. Essentially, the LLM guided by the instructive prompt serves as a sophisticated invariant feature processor, while 3D directional information is exclusively handled by the equivariant encoder and adaptor modules. Experimental results demonstrate that EquiLLM delivers significant improvements over previous methods across molecular dynamics simulation, human motion simulation, and antibody design, highlighting its promising generalizability.

cs.LG↗