arXiv subjects

Liming Wu

Publications and source records attributed to Liming Wu.

At least 19 recordsLinked to original sources

arXiv2026

Non-asymptotic estimates of the minimal risk in statistical learning

In this paper we prove some concentration inequalities for two types of error probabilities in the Empirical Risk Principle (ERP) in statistical learning, which provide a lower bound and an upper bound for the minimal risk (in terms of the minimal empirical risk) with non-asymptotic high confidence. The usual boundedness condition of the empirical risk function is relaxed to the Gaussian or exponential integrability condition. The confidence of the lower bound of the minimal risk is shown to be independent of the number of training parameters and the dimension of the input vectors, allowing one to detect the deficiency of a learning machine efficiently; and the confidence of the upper bound of the minimal risk is proved to be high provided that the sample size $n$ is much greater than the box dimension of the parameter set $\Theta$ in the Orlicz metric $d_{\psi_1}$ associated with the risk functions. Our work is based on Talagrand's concentration inequalities (the sharp versions by Bousquet and Klein-Rio), transport-entropy inequalities and the recent progress in the theory of empirical processes and statistical learning.

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↗

arXiv2026

DMFlow: Disordered Materials Generation by Flow Matching

The design of materials with tailored properties is crucial for technological progress. However, most deep generative models focus exclusively on perfectly ordered crystals, neglecting the important class of disordered materials. To address this gap, we introduce DMFlow, a generative framework specifically designed for disordered crystals. Our approach introduces a unified representation for ordered, Substitutionally Disordered (SD), and Positionally Disordered (PD) crystals, and employs a flow matching model to jointly generate all structural components. A key innovation is a Riemannian flow matching framework with spherical reparameterization, which ensures physically valid disorder weights on the probability simplex. The vector field is learned by a novel Graph Neural Network (GNN) that incorporates physical symmetries and a specialized message-passing scheme. Finally, a two-stage discretization procedure converts the continuous weights into multi-hot atomic assignments. To support research in this area, we release a benchmark containing SD, PD, and mixed structures curated from the Crystallography Open Database. Experiments on Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks demonstrate that DMFlow significantly outperforms state-of-the-art baselines adapted from ordered crystal generation. We hope our work provides a foundation for the AI-driven discovery of disordered materials.

cs.LG↗

arXiv2025

Quasi-stationarity of the Dyson Brownian motion with collisions

In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. C{\'e}pa and D. L{\'e}pingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].

math.PR↗

arXiv2025

Siamese Foundation Models for Crystal Structure Prediction

Predicting crystal structures from chemical compositions is a fundamental challenge in materials discovery, complicated by complex 3D geometries that distinguish it from fields like protein folding. Here, we present Diffusion-based Crystal Omni (DAO), a pretrain-finetune framework for crystal structure prediction integrating two Siamese foundation models: a structure generator and an energy predictor. The generator is pretrained via a two-stage pipeline on a vast dataset of stable and unstable structures, leveraging the predictor to relax unstable configurations and guide the generative sampling. Across two well-known benchmarks, pretraining significantly enhances performance across multiple backbone architectures. Ablation studies confirm that the synergy between the generator and predictor mutually benefits both components. We further validate DAO on three real-world superconductors ($\text{Cr}_6\text{Os}_2$, $\text{Zr}_{16}\text{Rh}_8\text{O}_4$, and $\text{Zr}_{16}\text{Pd}_8\text{O}_4$) typically inaccessible to conventional computation. For $\text{Cr}_6\text{Os}_2$, DAO achieves a 100\% match rate with experimental references and an atomic-position error of 0.0012 under 20-shot generation, performing over 2000$\times$ faster per iteration than DFT-based structure predictors. These compelling results collectively highlight the potential of our approach for advancing materials science research.

cond-mat.mtrl-sci↗

arXiv2024

Large deviations of the empirical measures of a strong-Feller Markov process inside a subset and quasi-ergodic distribution

In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanishes only at a unique measure, which is the so-called quasi-ergodic distribution of the process in this subregion. In addition, we show that the rate function is the Dirichlet form in the particular case when the process is reversible. We apply our results to several stochastic processes such as the solutions of elliptic stochastic differential equations driven by a rotationally invariant $\alpha$-stable process, the kinetic Langevin process, and the overdamped Langevin process driven by a Brownian motion.

math.PR↗

arXiv2024

Long time behavior of killed Feynman-Kac semigroups with singular Schr{\"o}dinger potentials

In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general singular Schr{\"o}dinger potentials. The processes we consider cover a large class of processes used in statistical physics, with strong links with quantum mechanics and (local or not) Schr{\"o}dinger operators (including e.g. fractional Laplacians). For instance we consider solutions to elliptic differential equations, L{\'e}vy processes, the kinetic Langevin process with locally Lipschitz gradient fields, and systems of interacting L{\'e}vy particles. Our analysis relies on a Perron-Frobenius type theorem derived in a previous work [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.] for Feller kernels and on the tools introduced in [L. Wu, 2004, Probab. Theory Relat. Fields] to compute bounds on the essential spectral radius of a bounded nonnegative kernel.

math.PR↗

arXiv2024

Powder Diffraction Crystal Structure Determination Using Generative Models

Accurate crystal structure determination is critical across all scientific disciplines involving crystalline materials. However, solving and refining inorganic crystal structures from powder X-ray diffraction (PXRD) data is traditionally a labor-intensive and time-consuming process that demands substantial expertise. In this work, we introduce PXRDGen, an end-to-end neural network that determines crystal structures by learning joint structural distributions from experimentally stable crystals and their PXRD, producing atomically accurate structures refined through PXRD data. PXRDGen integrates a pretrained XRD encoder, a diffusion/flow-based structure generator, and a Rietveld refinement module, enabling the solution of structures with unparalleled accuracy in a matter of seconds. Evaluation on MP-20 inorganic dataset reveals a remarkable matching rate of 82% (1 sample) and 96% (20 samples) for valid compounds, with Root Mean Square Error (RMSE) approaching the precision limits of Rietveld refinement. PXRDGen effectively tackles key challenges in XRD, such as the precise localization of light atoms, differentiation of neighboring elements, and resolution of overlapping peaks. Overall, PXRDGen marks a significant advancement in the automated determination of crystal structures from powder diffraction data.

cond-mat.mtrl-sci↗

arXiv2024

Equivariant Spatio-Temporal Attentive Graph Networks to Simulate Physical Dynamics

Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations, rotations, etc, leading to better generalization ability. Nevertheless, their frame-to-frame formulation of the task overlooks the non-Markov property mainly incurred by unobserved dynamics in the environment. In this paper, we reformulate dynamics simulation as a spatio-temporal prediction task, by employing the trajectory in the past period to recover the Non-Markovian interactions. We propose Equivariant Spatio-Temporal Attentive Graph Networks (ESTAG), an equivariant version of spatio-temporal GNNs, to fulfill our purpose. At its core, we design a novel Equivariant Discrete Fourier Transform (EDFT) to extract periodic patterns from the history frames, and then construct an Equivariant Spatial Module (ESM) to accomplish spatial message passing, and an Equivariant Temporal Module (ETM) with the forward attention and equivariant pooling mechanisms to aggregate temporal message. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level. Experimental results verify the effectiveness of ESTAG compared to typical spatio-temporal GNNs and equivariant GNNs.

cs.LG↗

arXiv2024

Generalized Langevin And Nos{\'e}-hoover Processes Absorbed At The Boundary Of A Metastable Domain

In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential conver- gence towards the quasi-stationary distribution for the generalized Langevin and the Nos{\'e}-Hoover processes, two processes which are widely used in molecular dynamics. The case of singular potentials is considered. With the techniques used in this work, we are also able to greatly improve existing results on quasi-stationary distributions for the kinetic Langevin process to a weak regularity setting.

math.PR↗

arXiv2024

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↗

arXiv2023

Maximum Entropy Estimator for Hidden Markov Models: Reduction to Dimension 2

In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator is too consuming in time by the classical Baum-Welch EM algorithm. We prove the consistency and the asymptotic normality of the maximum entropy estimator in a quite general framework, where the asymptotic covariance matrix is explicitly estimated in terms of the 2-dimensional Fisher information. To complement it, the 2-dimensional relative entropy is skillfully used to study the hypotheses testing problem. Furthermore, we propose 2-dimensional maximum entropy algorithm for finding the maximum entropy estimator, which works for very large observation dataset and large hidden states set. Some numerical examples are furnished and commented for illustrating our theoretical results.

math.ST↗

arXiv2022

Global Gravity Field Model from Taiji-1 Observations

Taiji-1 is the first technology demonstration satellite of the Taiji program of China's space-borne gravitational wave antenna. After the demonstration of the key individual technologies, Taiji-1 continues collecting the data of the precision orbit determinations, satellite attitudes, and non-conservative forces exerted on the S/C. Therefore, during its free-fall, Taiji-1 can be viewed as operating in the high-low satellite-to-satellite tracking mode of a gravity recovery mission. In this work, we have selected and analyzed the one month data from Taiji-1's observations, and developed the techniques to resolve the long term interruptions and disturbances in the data due to the scheduled technology demonstration experiments. The first global gravity model \texttt{TJGM-r1911}, that independently derived from China's own satellite mission, is successfully built from Taiji-1's observations. Compared with gravity models from CHAMP and other satellite gravity missions, the accuracy discrepancies exist, which is mainly caused by the data discontinuity problem. As the extended free-falling phase been approved, Taiji-1 could serve as a gravity recovery mission for China since 2022 and it will provide us the independent measurement of both the static and the monthly time-variable global gravity field.

gr-qc↗

arXiv2021

RCNN-SliceNet: A Slice and Cluster Approach for Nuclei Centroid Detection in Three-Dimensional Fluorescence Microscopy Images

Robust and accurate nuclei centroid detection is important for the understanding of biological structures in fluorescence microscopy images. Existing automated nuclei localization methods face three main challenges: (1) Most of object detection methods work only on 2D images and are difficult to extend to 3D volumes; (2) Segmentation-based models can be used on 3D volumes but it is computational expensive for large microscopy volumes and they have difficulty distinguishing different instances of objects; (3) Hand annotated ground truth is limited for 3D microscopy volumes. To address these issues, we present a scalable approach for nuclei centroid detection of 3D microscopy volumes. We describe the RCNN-SliceNet to detect 2D nuclei centroids for each slice of the volume from different directions and 3D agglomerative hierarchical clustering (AHC) is used to estimate the 3D centroids of nuclei in a volume. The model was trained with the synthetic microscopy data generated using Spatially Constrained Cycle-Consistent Adversarial Networks (SpCycleGAN) and tested on different types of real 3D microscopy data. Extensive experimental results demonstrate that our proposed method can accurately count and detect the nuclei centroids in a 3D microscopy volume.

eess.IV↗

arXiv2021

An Odor Labeling Convolutional Encoder-Decoder for Odor Sensing in Machine Olfaction

Deep learning methods have been widely applied to visual and acoustic technology. In this paper, we proposed an odor labeling convolutional encoder-decoder (OLCE) for odor identification in machine olfaction. OLCE composes a convolutional neural network encoder and decoder where the encoder output is constrained to odor labels. An electronic nose was used for the data collection of gas responses followed by a normative experimental procedure. Several evaluation indexes were calculated to evaluate the algorithm effectiveness: accuracy 92.57%, precision 92.29%, recall rate 92.06%, F1-Score 91.96%, and Kappa coefficient 90.76%. We also compared the model with some algorithms used in machine olfaction. The comparison result demonstrated that OLCE had the best performance among these algorithms. In the paper, some perspectives of machine olfactions have been also discussed.

cs.LG↗

arXiv2020

Long-time behaviors of mean-field interacting particle systems related to McKean-Vlasov equations

In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the mean-field weakly interacting particle system related to McKean-Vlasov equation. By means of the known approximate componentwise reflection coupling and with the help of some new cost function, we obtain explicit estimates for those three problems, avoiding the technical conditions in the known results. Our results apply when the confinement potential $V$ has many wells, the interaction potential $W$ has bounded second mixed derivative $\nabla^2_{xy}W$ which should be not too big so that there is no phase transition. As an application, we obtain the concentration inequality of the mean-field interacting particle system with explicit and sharp constants, uniform in time. Several examples are provided to illustrate the results.

math.PR↗

arXiv2019

Poincar{é} and logarithmic sobolev inequalities for nearly radial measures

If Poincar{é} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincar{é} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.

math.FA↗

arXiv2019

The Kinetic Fokker-planck Equation With Mean Field Interaction

We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in the number of particles) exponential convergence to equilibrium for the solutions in the weighted Sobolev space H 1 ($μ$) with a rate of convergence which is explicitly computable and independent of the number of particles. The originality of the proof relies on functional inequalities and hypocoercivity with Lyapunov type conditions, usually not suitable to provide adimensional results.

math.AP↗