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Xiaofeng Qian

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9 papers

2 author rows

TMLR Journal 2026 Journal Article

Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials

Cong Fu
Yuchao Lin
Zachary Krueger
Haiyang Yu
Maho Nakata
Jianwen Xie
Emine Kucukbenli
Xiaofeng Qian

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/.

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NeurIPS Conference 2025 Conference Paper

Graph-based Symbolic Regression with Invariance and Constraint Encoding

Ziyu Xiang
Kenna Ashen
Xiaofeng Qian
Xiaoning Qian

Symbolic regression (SR) seeks interpretable analytical expressions that uncover the governing relationships within data, providing mechanistic insight beyond 'black-box' models. However, existing SR methods often suffer from two key limitations: (1) *redundant representations* that fail to capture mathematical equivalences and higher-order operand relations, breaking permutation invariance and hindering efficient learning; and (2) *sparse rewards* caused by incomplete incorporation of constraints that can only be evaluated on full expressions, such as constant fitting or physical-law verification. To address these challenges, we propose a unified framework, **Graph-based Symbolic Regression (GSR)**, which compresses the search space through the permutation-invariant representations, expression graphs (EGs), that intrinsically encode expression equivalences via a term-rewriting system (TRS) and a directed acyclic graph (DAG) structure. GSR mitigates reward sparsity by employing a hybrid neural-guided Monte Carlo tree search (hnMCTS) on EGs, where constraint-informed neural guidance enables the direct incorporation of expression-level constraint priors, and an adaptive $\epsilon$-UCB policy balances exploration and exploitation. Theoretical analyses establish the uniqueness of our proposed EG representation and the convergence of the hnMCTS algorithm. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of GSR in discovering underlying expressions and adhering to physical laws, offering practical solutions for scientific discovery.

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NeurIPS Conference 2025 Conference Paper

Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations

Yuchao Lin
Cong Fu
Zachary Krueger
Haiyang Yu
Maho Nakata
Jianwen Xie
Emine Kucukbenli
Xiaofeng Qian

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks whose CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https: //github. com/divelab/AIRS).

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ICML Conference 2024 Conference Paper

A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

Keqiang Yan
Alexandra Saxton
Xiaofeng Qian
Xiaoning Qian
Shuiwang Ji

We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to both O(3) and crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https: //github. com/divelab/AIRS).

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ICLR Conference 2024 Conference Paper

Complete and Efficient Graph Transformers for Crystal Material Property Prediction

Keqiang Yan
Cong Fu 0003
Xiaofeng Qian
Xiaoning Qian
Shuiwang Ji

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

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NeurIPS Conference 2024 Conference Paper

Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation

Keqiang Yan
Xiner Li
Hongyi Ling
Kenna Ashen
Carl Edwards
Raymundo Arróyave
Marinka Zitnik
Heng Ji

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods.

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ICML Conference 2023 Conference Paper

Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

Haiyang Yu 0005
Zhao Xu 0005
Xiaofeng Qian
Xiaoning Qian
Shuiwang Ji

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https: //github. com/divelab/AIRS).

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NeurIPS Conference 2023 Conference Paper

QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules

Haiyang Yu
Meng Liu
Youzhi Luo
Alex Strasser
Xiaofeng Qian
Xiaoning Qian
Shuiwang Ji

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 2, 399 molecular dynamics trajectories and 130, 831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at \url{https: //github. com/divelab/AIRS/tree/main/OpenDFT/QHBench}.

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AAAI Conference 2021 Conference Paper

Physics-constrained Automatic Feature Engineering for Predictive Modeling in Materials Science

Ziyu Xiang
Mingzhou Fan
Guillermo Vázquez Tovar
William Trehern
Byung-Jun Yoon
Xiaofeng Qian
Raymundo Arroyave
Xiaoning Qian

Automatic Feature Engineering (AFE) aims to extract useful knowledge for interpretable predictions given data for the machine learning tasks. Here, we develop AFE to extract dependency relationships that can be interpreted with functional formulas to discover physics meaning or new hypotheses for the problems of interest. We focus on materials science applications, where interpretable predictive modeling may provide principled understanding of materials systems and guide new materials discovery. It is often computationally prohibitive to exhaust all the potential relationships to construct and search the whole feature space to identify interpretable and predictive features. We develop and evaluate new AFE strategies by exploring a feature generation tree (FGT) with deep Qnetwork (DQN) for scalable and efficient exploration policies. The developed DQN-based AFE strategies are benchmarked with the existing AFE methods on several materials science datasets.

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