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Jingrun Chen

Publications and source records attributed to Jingrun Chen.

At least 19 recordsLinked to original sources
arXiv2026

Fourier Neural Operators for Composition-Driven Crystal Structure Discovery

Crystalline materials discovery is essential for energy, electronics, and catalysis, but the vast chemical and structural space makes exhaustive screening infeasible. Existing voxel-based methods are limited by the local receptive fields of three-dimensional convolutional neural networks and the posterior collapse of high-dimensional variational autoencoders. Here, we develop a Fourier Neural Operator (FNO)-based crystal-field solver that maps a prescribed chemical formula and lattice parameters to periodic number-density and electron-density fields. By operating on global Fourier modes, the solver captures long-range correlations in periodic crystal fields beyond conventional local convolutions. Building on this solver, we construct a coupled generation-solving framework in which a conditional variational autoencoder generates diverse candidate lattice parameters in a low-dimensional basis-coefficient space, followed by density-field prediction and atomic reconstruction through peak detection, position optimization, and weight optimization. The reconstructed structures are further screened using voxel-level filtering, machine-learning interatomic-potential relaxation, and first-principle calculations. The framework generates novel structures across 104 chemical formulas with competitive reconstruction accuracy, demonstrating high generative diversity and structural validity. By extending Fourier neural operators to periodic crystal fields and coupling them with composition-conditioned lattice generation, our approach provides a scalable route to crystal structure discovery from prescribed chemical compositions.

cond-mat.mtrl-sci↗
arXiv2026

Advantage-Guided Gate: Reshaping Open-Ended Reasoning for Vision-Based Spatial Intelligence

Multimodal large language models (MLLMs) have demonstrated significant potential in complex spatial scene understanding and reasoning tasks. However, their open-ended reasoning process is prone to decision errors and error accumulation, leading to instability in answer quality. To address this, we propose an advantage-guided gating framework that dynamically intervenes in and corrects deviations during the reasoning process. Specifically, we model step-by-step reasoning as a finite-horizon decision process and introduce Monte Carlo value evaluation on the reasoning tree to provide intermediate supervision signals. The framework includes Step-Advantage Gate and Trajectory-Advantage Gate, which dynamically select high-value reasoning steps and high-quality complete reasoning trajectories, respectively. During training, we perform supervised learning for the gates using reasoning trees generated via multi-branch sampling, and combine shared-parameter initialization with task-specific heads to achieve cross-task robustness and diversity. During inference, the model greedily selects high-value prefix reasoning steps while choosing the optimal reasoning head based on the problem type, thereby significantly improving the accuracy of the final answer. Furthermore, we constructed the Reasoning-Tree-160k dataset and performed two-stage learning on it. Extensive experiments demonstrate that this advantage-guided gating framework effectively enhances the performance of benchmark MLLMs in visual-based spatial understanding and reasoning tasks. The code is open to the public for research: https://github.com/LingLin-ll/Advantage-Guided-Gate.

cs.CV↗
arXiv2026

MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers

Conventional patchified Transformers operate on uniform spatial partitions, distributing computational effort evenly across the domain irrespective of local features. This inflexible tokenization scheme is inherently limited in its ability to efficiently represent and process solutions to complex PDEs. To address this, we propose MeshTok, an adaptive mesh refinement (AMR)-inspired tokenization and sequence modeling framework. This method selectively refines spatial regions exhibiting sharp gradients, transient features, or multiscale structures, generating a heterogeneous set of multiscale tokens defined on a fixed simulation grid. These tokens are processed within a unified Transformer sequence, enabling the model to simultaneously capture coarse-grained global context and fine-grained local details without requiring specialized architectural components. Although adaptive refinement moderately increases token count, it promotes a more targeted allocation of computational resources to physically informative regions, which we view as a practical inductive bias rather than a formal optimality guarantee. Experimental evaluations across multiple PDE families and benchmark datasets demonstrate that MeshTok consistently improves the efficiency-accuracy trade-off compared to uniform-grid baselines. This suggests adaptive multiscale tokenization as a scalable and generalizable design principle for neural PDE modeling. Code is available at https://github.com/SCAILab-USTC/MeshTok.

cs.LG↗
arXiv2026

Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs). Existing architectures typically obtain expressivity by parameterizing integral kernels in prescribed transform domains or by applying attention-like interactions over discretized spatial points. While these approaches have achieved substantial progress, they often face a persistent trade-off among physical interpretability, nonlocal spatial communication, mesh scalability, and computational cost. We propose a Light-inspired neural operator(LiNO), an operator-learning architecture whose latent evolution is decomposed into three mechanisms motivated by elementary light transport: reflection, refraction, and scattering. Reflection and refraction act as adaptive pointwise transformations in latent feature space, enabling local feature reorientation and anisotropic modulation, whereas scattering performs input-dependent nonlocal propagation over the physical domain. We first formulate scattering as a normalized pairwise kernel with relative positional bias, and then develop an efficient scattering variant that replaces explicit pairwise interactions with positive-feature global propagation and a local diffusion branch, reducing the dominant spatial complexity from quadratic to linear. This yields a structured neural operator that separates local feature modulation from global spatial communication while retaining a modular and interpretable latent evolution.

cs.LG↗
arXiv2026

Composition-Weighted Symbolic Regression for General-Purpose Property Prediction

We introduce a composition-weighted symbolic regression framework for interpretable prediction of materials properties directly from chemical composition. The method jointly learns analytical functional forms and task-dependent elemental weightings without predefined descriptors. By incorporating max/min operators, it naturally enforces constraints such as non-negative band gaps and bounded classification probabilities, unifying regression and classification tasks. Efficient search is achieved through a hybrid Monte Carlo tree search--genetic programming algorithm with gradient-based refinement and parallel computation. Benchmarks on MatBench tasks show competitive accuracy relative to state-of-the-art black-box models while yielding explicit analytical expressions. Applied to III--V semiconductor alloys, the model produces smooth composition-dependent trends and learned elemental weights with chemically meaningful periodic behavior. This framework provides a scalable and interpretable route for materials discovery and property screening.

cond-mat.mtrl-sci↗
arXiv2026

A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws

Hyperbolic conservation laws govern a wide range of transport-driven dynamics featuring shocks, contact discontinuities, and complex wave interactions, posing distinct challenges for deep-learning-based surrogate modeling. While classical numerical methods provide robust and physically admissible solutions, their computational cost restricts applicability in many-query tasks such as parametric studies and design optimization. Conversely, existing neural surrogates offer rapid inference but often fail to respect intrinsic PDE structures, leading to non-physical artifacts, rollout instability, and poor generalization. We present an interpretable, structure-preserving graph neural solver that bridges classical numerical principles with graph neural networks (GNNs). The network is designed as a learned reconstruction-and-flux operator rather than a black-box state updater, thereby inherently preserving key properties such as local conservation and upwinding. Inspired by Arbitrary high-order DERivatives schemes, we further recast message-passing GNNs as high-order space-time predictors, enabling conservative and stable neural updates with large time steps. Evaluation is performed on challenging supersonic flow benchmarks spanning broad parametric variations in geometry, initial/boundary conditions, and flow regimes. The neural solver achieves superior long-horizon rollout stability and accuracy compared with strong surrogate baselines, outperforms low-order discretizations, and delivers orders-of-magnitude runtime speedups over high-resolution simulations.

physics.comp-ph↗
arXiv2026

OODBench: Out-of-Distribution Benchmark for Large Vision-Language Models

Existing Visual-Language Models (VLMs) have achieved significant progress by being trained on massive-scale datasets, typically under the assumption that data are independent and identically distributed (IID). However, in real-world scenarios, it is often impractical to expect that all data processed by an AI system satisfy this assumption. Furthermore, failure to appropriately handle out-of-distribution (OOD) objects may introduce safety risks in real-world applications (e.g., autonomous driving or medical assistance). Unfortunately, current research has not yet provided valid benchmarks that can comprehensively assess the performance of VLMs in response to OOD data. Therefore, we propose OODBench, a predominantly automated method with minimal human verification, for constructing new benchmarks and evaluating the ability of VLMs to process OOD data. OODBench contains 40K instance-level OOD instance-category pairs, and we show that current VLMs still exhibit notable performance degradation on OODBench, even when the underlying image categories are common. In addition, we propose a reliable automated assessment metric that employs a Basic-to-Advanced Progression of prompted questions to assess the impact of OOD data on questions of varying difficulty more fully. Lastly, we summarize substantial findings and insights to facilitate future research in the acquisition and evaluation of OOD data.

cs.CV↗
arXiv2025

Physics-Informed Deformable Gaussian Splatting: Towards Unified Constitutive Laws for Time-Evolving Material Field

Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the diverse physics-driven motion patterns in dynamic scenes. To fill this gap, we propose Physics-Informed Deformable Gaussian Splatting (PIDG), which treats each Gaussian particle as a Lagrangian material point with time-varying constitutive parameters and is supervised by 2D optical flow via motion projection. Specifically, we adopt static-dynamic decoupled 4D decomposed hash encoding to reconstruct geometry and motion efficiently. Subsequently, we impose the Cauchy momentum residual as a physics constraint, enabling independent prediction of each particle's velocity and constitutive stress via a time-evolving material field. Finally, we further supervise data fitting by matching Lagrangian particle flow to camera-compensated optical flow, which accelerates convergence and improves generalization. Experiments on a custom physics-driven dataset as well as on standard synthetic and real-world datasets demonstrate significant gains in physical consistency and monocular dynamic reconstruction quality.

cs.CV↗
arXiv2025

Uniformly accurate structure-preserving neural surrogates for radiative transfer

In this work, we propose a uniformly accurate, structure-preserving neural surrogate for the radiative transfer equation with periodic boundary conditions based on a multiscale parity decomposition framework. The formulation introduces a refined decomposition of the particle distribution into macroscopic, odd, and higher-order even components, leading to an asymptotic-preserving neural network system that remains stable and accurate across all parameter regimes. By constructing key higher-order correction functions, we establish rigorous uniform error estimates with respect to the scale parameter $\varepsilon$, which ensures $\varepsilon$-independent accuracy. Furthermore, the neural architecture is designed to preserve intrinsic physical structures such as parity symmetry, conservation, and positivity through dedicated architectural constraints. The framework extends naturally from one to two dimensions and provides a theoretical foundation for uniformly accurate neural solvers of multiscale kinetic equations. Numerical experiments confirm the effectiveness of our approach.

math.NA↗
arXiv2025

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while machine learning-based approaches such as Physics-Informed Neural Networks (PINNs) and the Random Feature Method (RFM) -- though computationally efficient for inverse problems -- lack the intrinsic machinery to handle the sharp morphological features in such singular problems, leading to inaccurate solutions. To address this issue, we propose the Morphology-Adaptive Random Feature Method (MA-RFM), a novel two-phase framework that adaptively locates critical regions and adds morphology activation functions for tackling the multi-frequency inverse source problem with complex geometry. Our framework recasts the ill-posed inverse problem into a well-posed, strictly convex optimization problem by reformulating the governing Helmholtz equation as a Tikhonov-regularized integral equation via its fundamental solution. In the first stage, the Integral Adaptive RFM (IA-RFM), employs an adaptive algorithm to rapidly localize the source support, thereby reducing computational overhead and accelerating convergence. In the second stage, posterior geometric information is progressively integrated into the solver via hybrid basis functions, enabling a precise reconstruction of complex morphologies. The MA-RFM extends the capabilities of RFM to handle PDEs with singular solutions while preserving its mesh-free efficiency. We demonstrate the superior performance of our approach through ample challenging 2D and 3D benchmark problems, even under limited and noisy measurement conditions, highlighting its robustness and accuracy in reconstructing complex and disjoint sources.

math-ph↗
arXiv2025

A Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we introduce a hybrid computational framework by coupling discontinuous Galerkin (DG) discretizations with a temporally progressive neural network architecture. Our method incorporates a structure-preserving weak-form loss -- combining DG residuals and Rankine-Hugoniot jump conditions -- with a causality-respecting progressive training strategy. The proposed framework trains neural networks sequentially across temporally decomposed subintervals, leveraging pseudo-label supervision to ensure temporal coherence and solution continuity. This approach mitigates error accumulation and enhances the model's capacity to resolve shock waves and steep gradients without explicit limiters. Besides, a theoretical analysis establishes error bounds for the proposed framework, demonstrating convergence toward the physical solution under mesh refinement and regularized training. Numerical experiments on Burgers and Euler equations show that our method consistently outperforms standard PINNs, PINNs-WE, and first-order DG schemes in both accuracy and robustness, particularly in capturing shocks and steep gradients. These results highlight the promise of combining classical discretization techniques with machine learning to develop robust and accurate solvers for nonlinear hyperbolic systems.

math.NA↗
arXiv2025

Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients

In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale problems on fine meshes incurs prohibitive computational costs. To address this challenge, we propose an efficient coarse scale approximation through localized basis functions derived from energy minimization within the Generalized Rough Polyharmonic Splines (GRPS) framework. These basis functions preserve critical multiscale features while operating on a computationally tractable coarse mesh. The nonlinear, vectorial, and non-symmetric nature of the Landau-Lifshitz equation necessitates careful design of variational formulations for basis construction. We introduce several such formulations, each tailored to specific structural aspects of the problem. Through systematic numerical experiments, we demonstrate that our approach achieves significant computational savings without compromising accuracy, offering a robust framework for simulating multiscale magnetic systems with complex microstructures.

math.NA↗
arXiv2025

Xinyu AI Search: Enhanced Relevance and Comprehensive Results with Rich Answer Presentations

Traditional search engines struggle to synthesize fragmented information for complex queries, while generative AI search engines face challenges in relevance, comprehensiveness, and presentation. To address these limitations, we introduce Xinyu AI Search, a novel system that incorporates a query-decomposition graph to dynamically break down complex queries into sub-queries, enabling stepwise retrieval and generation. Our retrieval pipeline enhances diversity through multi-source aggregation and query expansion, while filtering and re-ranking strategies optimize passage relevance. Additionally, Xinyu AI Search introduces a novel approach for fine-grained, precise built-in citation and innovates in result presentation by integrating timeline visualization and textual-visual choreography. Evaluated on recent real-world queries, Xinyu AI Search outperforms eight existing technologies in human assessments, excelling in relevance, comprehensiveness, and insightfulness. Ablation studies validate the necessity of its key sub-modules. Our work presents the first comprehensive framework for generative AI search engines, bridging retrieval, generation, and user-centric presentation.

cs.IR↗
arXiv2025

Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models

Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing error accumulation. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to the out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at https://github.com/SCAILab-USTC/PITA.

cs.LG↗
arXiv2025

Weak Random Feature Method for Solving Partial Differential Equations

The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches while achieving spectral accuracy for smooth solutions, without the need for iterative procedures. However, the implementation of RFM in the identification of weak solutions remains a subject of limited comprehension, despite crucial role of weak solutions in addressing numerous applied problems. While the direct application of RFM to problems without strong solutions is fraught with potential challenges, we propose an enhancement to the original random feature method that is specifically suited for finding weak solutions and is termed as Weak RFM. Essentially, Weak RFM reformulates the original RFM by adopting the weak form of the governing equations and constructing a new linear system through the use of carefully designed test functions, ensuring that the resulting solution satisfies the weak form by default. To rigorously evaluate the performance of the proposed method, we conduct extensive experiments on a variety of benchmark problems, including challenging three-dimensional cases, and compare its performance with state of the art machine learning-based approaches. The results demonstrate that Weak RFM achieves comparable or superior accuracy while significantly reducing computational time and memory consumption, highlighting its potential as a highly efficient and robust tool for finding weak solutions to various PDE problems.

math.NA↗
arXiv2025

An Unsupervised Network Architecture Search Method for Solving Partial Differential Equations

Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed neural network (PINN). Typically, a deep learning method has three main components: a neural network, a loss function, and an optimizer. While the construction of the loss function is rooted in the definition of solution space, how to choose a optimal neural network is somewhat ad hoc, leaving much room for improvement. In the framework of PINN, we propose an unsupervised network architecture search method for solving PDEs, termed PINN-DARTS, which applies the differentiable architecture search (DARTS) to find the optimal network architecture structure in a given set of neural networks. In this set, the number of layers and the number of neurons in each layer can change. In the searching phase, both network and architecture parameters are updated simultaneously, so the running time is close to that of PINN with a pre-determined network structure. Unlike available works, our approach is unsupervised and purely based on the PDE residual without any prior usage of solutions. PINN-DARTS outputs the optimal network structure as well as the associated numerical solution. The performance of PINN-DARTS is verified on several benchmark PDEs, including elliptic, parabolic, wave, and Burgers' equations. Compared to traditional architecture search methods, PINN-DARTS achieves significantly higher architectural accuracy. Another interesting observation is that both the solution complexity and the PDE type have a prominent impact on the optimal network architecture. Our study suggests that architectures with uneven widths from layer to layer may have superior performance across different solution complexities and different PDE types.

math.NA↗
arXiv2025

STSA: Spatial-Temporal Semantic Alignment for Visual Dubbing

Existing audio-driven visual dubbing methods have achieved great success. Despite this, we observe that the semantic ambiguity between spatial and temporal domains significantly degrades the synthesis stability for the dynamic faces. We argue that aligning the semantic features from spatial and temporal domains is a promising approach to stabilizing facial motion. To achieve this, we propose a Spatial-Temporal Semantic Alignment (STSA) method, which introduces a dual-path alignment mechanism and a differentiable semantic representation. The former leverages a Consistent Information Learning (CIL) module to maximize the mutual information at multiple scales, thereby reducing the manifold differences between spatial and temporal domains. The latter utilizes probabilistic heatmap as ambiguity-tolerant guidance to avoid the abnormal dynamics of the synthesized faces caused by slight semantic jittering. Extensive experimental results demonstrate the superiority of the proposed STSA, especially in terms of image quality and synthesis stability. Pre-trained weights and inference code are available at https://github.com/SCAILab-USTC/STSA.

cs.CV↗
arXiv2025

A PINN-enriched finite element method for linear elliptic problems

In this paper, we propose a hybrid method that combines finite element method (FEM) and physics-informed neural network (PINN) for solving linear elliptic problems. This method contains three steps: (1) train a PINN and obtain an approximate solution $u_{\theta}$; (2) enrich the finite element space with $u_{\theta}$; (3) obtain the final solution by FEM in the enriched space. In the second step, the enriched space is constructed by addition $v + u_{\theta}$ or multiplication $v \cdot u_{\theta}$, where $v$ belongs to the standard finite element space. We conduct the convergence analysis for the proposed method. Compared to the standard FEM, the same convergence order is obtained and higher accuracy can be achieved when solution derivatives are well approximated in PINN. Numerical examples from one dimension to three dimensions verify these theoretical results. For some examples, the accuracy of the proposed method can be reduced by a couple of orders of magnitude compared to the standard FEM.

math.NA↗