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Yuan Gao

Publications and source records attributed to Yuan Gao.

At least 199 records · Page 11Linked to original sources
arXiv2025

An Exterior-Embedding Neural Operator Framework for Preserving Conservation Laws

Neural operators have demonstrated considerable effectiveness in accelerating the solution of time-dependent partial differential equations (PDEs) by directly learning governing physical laws from data. However, for PDEs governed by conservation laws(e.g., conservation of mass, energy, or matter), existing neural operators fail to satisfy conservation properties, which leads to degraded model performance and limited generalizability. Moreover, we observe that distinct PDE problems generally require different optimal neural network architectures. This finding underscores the inherent limitations of specialized models in generalizing across diverse problem domains. To address these limitations, we propose Exterior-Embedded Conservation Framework (ECF), a universal conserving framework that can be integrated with various data-driven neural operators to enforce conservation laws strictly in predictions. The framework consists of two key components: a conservation quantity encoder that extracts conserved quantities from input data, and a conservation quantity decoder that adjusts the neural operator's predictions using these quantities to ensure strict conservation compliance in the final output. Since our architecture enforces conservation laws, we theoretically prove that it enhances model performance. To validate the performance of our method, we conduct experiments on multiple conservation-law-constrained PDE scenarios, including adiabatic systems, shallow water equations, and the Allen-Cahn problem. These baselines demonstrate that our method effectively improves model accuracy while strictly enforcing conservation laws in the predictions.

cs.OH↗
arXiv2025

Turb-L1: Achieving Long-term Turbulence Tracing By Tackling Spectral Bias

Accurately predicting the long-term evolution of turbulence is crucial for advancing scientific understanding and optimizing engineering applications. However, existing deep learning methods face significant bottlenecks in long-term autoregressive prediction, which exhibit excessive smoothing and fail to accurately track complex fluid dynamics. Our extensive experimental and spectral analysis of prevailing methods provides an interpretable explanation for this shortcoming, identifying Spectral Bias as the core obstacle. Concretely, spectral bias is the inherent tendency of models to favor low-frequency, smooth features while overlooking critical high-frequency details during training, thus reducing fidelity and causing physical distortions in long-term predictions. Building on this insight, we propose Turb-L1, an innovative turbulence prediction method, which utilizes a Hierarchical Dynamics Synthesis mechanism within a multi-grid architecture to explicitly overcome spectral bias. It accurately captures cross-scale interactions and preserves the fidelity of high-frequency dynamics, enabling reliable long-term tracking of turbulence evolution. Extensive experiments on the 2D turbulence benchmark show that Turb-L1 demonstrates excellent performance: (I) In long-term predictions, it reduces Mean Squared Error (MSE) by $80.3\%$ and increases Structural Similarity (SSIM) by over $9\times$ compared to the SOTA baseline, significantly improving prediction fidelity. (II) It effectively overcomes spectral bias, accurately reproducing the full enstrophy spectrum and maintaining physical realism in high-wavenumber regions, thus avoiding the spectral distortions or spurious energy accumulation seen in other methods.

cs.LG↗
arXiv2025

Trajectory Design for UAV-Assisted Logistics Collection in Low-Altitude Economy

Low-altitude economy (LAE) is rapidly emerging as a key driver of innovation, encompassing economic activities taking place in airspace below 500 meters. Unmanned aerial vehicles (UAVs) provide valuable tools for logistics collection within LAE systems, offering the ability to navigate through complex environments, avoid obstacles, and improve operational efficiency. However, logistics collection tasks involve UAVs flying through complex three-dimensional (3D) environments while avoiding obstacles, where traditional UAV trajectory design methods,typically developed under free-space conditions without explicitly accounting for obstacles, are not applicable. This paper presents, we propose a novel algorithm that combines the Lin-Kernighan-Helsgaun (LKH) and Deep Deterministic Policy Gradient (DDPG) methods to minimize the total collection time. Specifically, the LKH algorithm determines the optimal order of item collection, while the DDPG algorithm designs the flight trajectory between collection points. Simulations demonstrate that the proposed LKH-DDPG algorithm significantly reduces collection time by approximately 49 percent compared to baseline approaches, thereby highlighting its effectiveness in optimizing UAV trajectories and enhancing operational efficiency for logistics collection tasks in the LAE paradigm.

eess.SP↗
arXiv2025

Advancing Ocean State Estimation with efficient and scalable AI

Accurate and efficient global ocean state estimation remains a grand challenge for Earth system science, hindered by the dual bottlenecks of computational scalability and degraded data fidelity in traditional data assimilation (DA) and deep learning (DL) approaches. Here we present an AI-driven Data Assimilation Framework for Ocean (ADAF-Ocean) that directly assimilates multi-source and multi-scale observations, ranging from sparse in-situ measurements to 4 km satellite swaths, without any interpolation or data thinning. Inspired by Neural Processes, ADAF-Ocean learns a continuous mapping from heterogeneous inputs to ocean states, preserving native data fidelity. Through AI-driven super-resolution, it reconstructs 0.25$^\circ$ mesoscale dynamics from coarse 1$^\circ$ fields, which ensures both efficiency and scalability, with just 3.7\% more parameters than the 1$^\circ$ configuration. When coupled with a DL forecasting system, ADAF-Ocean extends global forecast skill by up to 20 days compared to baselines without assimilation. This framework establishes a computationally viable and scientifically rigorous pathway toward real-time, high-resolution Earth system monitoring.

cs.LG↗
arXiv2025

Rethinking Facial Expression Recognition in the Era of Multimodal Large Language Models: Benchmark, Datasets, and Beyond

Multimodal Large Language Models (MLLMs) have revolutionized numerous research fields, including computer vision and affective computing. As a pivotal challenge in this interdisciplinary domain, facial expression recognition (FER) has evolved from separate, domain-specific models to more unified approaches. One promising avenue to unify FER tasks is converting conventional FER datasets into visual question-answering (VQA) formats, enabling the direct application of powerful generalist MLLMs for inference. However, despite the success of cutting-edge MLLMs in various tasks, their performance on FER tasks remains largely unexplored. To address this gap, we provide FERBench, a systematic benchmark that incorporates 20 state-of-the-art MLLMs across four widely used FER datasets. Our results reveal that, while MLLMs exhibit good classification performance, they still face significant limitations in reasoning and interpretability. To this end, we introduce post-training strategies aimed at enhancing the facial expression reasoning capabilities of MLLMs. Specifically, we curate two high-quality and large-scale datasets: UniFER-CoT-230K for cold-start initialization and UniFER-RLVR-360K for reinforcement learning with verifiable rewards (RLVR), respectively. Building upon them, we develop a unified and interpretable FER foundation model termed UniFER-7B, which outperforms many open-sourced and closed-source generalist MLLMs (e.g., Gemini-2.5-Pro and Qwen2.5-VL-72B).

cs.CV↗
arXiv2025

Learning from History: A Retrieval-Augmented Framework for Spatiotemporal Prediction

Accurate and long-term spatiotemporal prediction for complex physical systems remains a fundamental challenge in scientific computing. While deep learning models, as powerful parametric approximators, have shown remarkable success, they suffer from a critical limitation: the accumulation of errors during long-term autoregressive rollouts often leads to physically implausible artifacts. This deficiency arises from their purely parametric nature, which struggles to capture the full constraints of a system's intrinsic dynamics. To address this, we introduce a novel \textbf{Retrieval-Augmented Prediction (RAP)} framework, a hybrid paradigm that synergizes the predictive power of deep networks with the grounded truth of historical data. The core philosophy of RAP is to leverage historical evolutionary exemplars as a non-parametric estimate of the system's local dynamics. For any given state, RAP efficiently retrieves the most similar historical analog from a large-scale database. The true future evolution of this analog then serves as a \textbf{reference target}. Critically, this target is not a hard constraint in the loss function but rather a powerful conditional input to a specialized dual-stream architecture. It provides strong \textbf{dynamic guidance}, steering the model's predictions towards physically viable trajectories. In extensive benchmarks across meteorology, turbulence, and fire simulation, RAP not only surpasses state-of-the-art methods but also significantly outperforms a strong \textbf{analog-only forecasting baseline}. More importantly, RAP generates predictions that are more physically realistic by effectively suppressing error divergence in long-term rollouts.

cs.LG↗
arXiv2025

LiDAR Remote Sensing Meets Weak Supervision: Concepts, Methods, and Perspectives

Light detection and ranging (LiDAR) remote sensing encompasses two major directions: data interpretation and parameter inversion. However, both directions rely heavily on costly and labor-intensive labeled data and field measurements, which constrains their scalability and spatiotemporal adaptability. Weakly Supervised Learning (WSL) provides a unified framework to address these limitations. This paper departs from the traditional view that treats interpretation and inversion as separate tasks and offers a systematic review of recent advances in LiDAR remote sensing from a unified WSL perspective. We cover typical WSL settings including incomplete supervision(e.g., sparse point labels), inexact supervision (e.g., scene-level tags), inaccurate supervision (e.g., noisy labels), and cross-domain supervision (e.g., domain adaptation/generalization) and corresponding techniques such as pseudo-labeling, consistency regularization, self-training, and label refinement, which collectively enable robust learning from limited and weak annotations.We further analyze LiDAR-specific challenges (e.g., irregular geometry, data sparsity, domain heterogeneity) that require tailored weak supervision, and examine how sparse LiDAR observations can guide joint learning with other remote-sensing data for continuous surface-parameter retrieval. Finally, we highlight future directions where WSL acts as a bridge between LiDAR and foundation models to leverage large-scale multimodal datasets and reduce labeling costs, while also enabling broader WSL-driven advances in generalization, open-world adaptation, and scalable LiDAR remote sensing.

cs.CV↗
arXiv2025

BLiSS 1.0: Evaluating Bilingual Learner Competence in Second Language Small Language Models

To bridge the gap between performance-oriented benchmarks and the evaluation of cognitively inspired models, we introduce BLiSS 1.0, a Benchmark of Learner Interlingual Syntactic Structure. Our benchmark operationalizes a new paradigm of selective tolerance, testing whether a model finds a naturalistic learner error more plausible than a matched, artificial error within the same sentence. Constructed from over 2.8 million naturalistic learner sentences, BLiSS provides 136,867 controlled triplets (corrected, learner, artificial) for this purpose. Experiments on a diverse suite of models demonstrate that selective tolerance is a distinct capability from standard grammaticality, with performance clustering strongly by training paradigm. This validates BLiSS as a robust tool for measuring how different training objectives impact a model's alignment with the systematic patterns of human language acquisition.

cs.CL↗
arXiv2025

Spatiotemporal Forecasting as Planning: A Model-Based Reinforcement Learning Approach with Generative World Models

To address the dual challenges of inherent stochasticity and non-differentiable metrics in physical spatiotemporal forecasting, we propose Spatiotemporal Forecasting as Planning (SFP), a new paradigm grounded in Model-Based Reinforcement Learning. SFP constructs a novel Generative World Model to simulate diverse, high-fidelity future states, enabling an "imagination-based" environmental simulation. Within this framework, a base forecasting model acts as an agent, guided by a beam search-based planning algorithm that leverages non-differentiable domain metrics as reward signals to explore high-return future sequences. These identified high-reward candidates then serve as pseudo-labels to continuously optimize the agent's policy through iterative self-training, significantly reducing prediction error and demonstrating exceptional performance on critical domain metrics like capturing extreme events.

cs.LG↗
arXiv2025

OneForecast: A Universal Framework for Global and Regional Weather Forecasting

Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link https://github.com/YuanGao-YG/OneForecast.

cs.LG↗
arXiv2025

Composite Optimization with Error Feedback: the Dual Averaging Approach

Communication efficiency is a central challenge in distributed machine learning training, and message compression is a widely used solution. However, standard Error Feedback (EF) methods (Seide et al., 2014), though effective for smooth unconstrained optimization with compression (Karimireddy et al., 2019), fail in the broader and practically important setting of composite optimization, which captures, e.g., objectives consisting of a smooth loss combined with a non-smooth regularizer or constraints. The theoretical foundation and behavior of EF in the context of the general composite setting remain largely unexplored. In this work, we consider composite optimization with EF. We point out that the basic EF mechanism and its analysis no longer stand when a composite part is involved. We argue that this is because of a fundamental limitation in the method and its analysis technique. We propose a novel method that combines Dual Averaging with EControl (Gao et al., 2024), a state-of-the-art variant of the EF mechanism, and achieves for the first time a strong convergence analysis for composite optimization with error feedback. Along with our new algorithm, we also provide a new and novel analysis template for inexact dual averaging method, which might be of independent interest. We also provide experimental results to complement our theoretical findings.

math.OC↗
arXiv2025

Spin Seebeck Effect of Triangular-lattice Spin Supersolid

Using thermal tensor-network approach, we investigate the spin Seebeck effect (SSE) of the triangular-lattice quantum antiferromagnet hosting spin supersolid phase. We focus on the low-temperature scaling behaviors of the normalized spin current across the interface. For the 1D Heisenberg chain, we find a negative spinon spin in the bulk current with algebraic temperature scaling; at low fields, boundary effects induce a second sign reversal at lower temperatures. These benchmark results are consistent with field-theoretical analysis. On the triangular lattice, spin frustration dramatically enhances the low-temperature SSE, with distinct spin-current signatures -- particularly the sign reversal and characteristic temperature dependence -- distinguishing different spin states. Remarkably, we discover a persistent, negative spin current in the spin supersolid phase, which saturates to a non-zero value in the low-temperature limit and can be ascribed to the Goldstone-mode-mediated spin supercurrents. Moreover, a universal scaling $T^{d/z}$ is found at the U(1)-symmetric polarization quantum critical points. These distinct quantum spin transport traits provide sensitive spin current probes for spin supersolid states in quantum magnets such as Na$_2$BaCo(PO$_4$)$_2$. Furthermore, our results also establish spin supersolids as a tunable quantum platform for spin caloritronics in the ultralow-temperature regime.

cond-mat.str-el↗
arXiv2025

ProbMed: A Probabilistic Framework for Medical Multimodal Binding

Medical decision-making requires integrating diverse medical information, from imaging to clinical narratives. These medical modalities are often acquired in a many-to-many manner. However, current medical vision-language pretraining models (Med-VLPMs) fail to directly account for this many-to-many mapping in their model training and embeddings. To address this, we present Probabilistic Modality-Enhanced Diagnosis (ProbMED), a multimodal Med-VLPM that employs probabilistic contrastive learning to model distributions over embeddings rather than deterministic estimates. ProbMED aligns four distinct modalities -- chest X-rays, electrocardiograms, echocardiograms, and clinical text -- into a unified probabilistic embedding space. We use InfoNCE loss with Hellinger distance to integrate inter-modality distributions. We introduce a probabilistic synthetic sampling loss that captures modality-specific mean and variance to improve intra-modality binding. Extensive experiments across 13 medical datasets demonstrate that our model outperforms current Med-VLPMs in cross-modality retrieval, zero-shot, and few-shot classification. We also demonstrate the robust integration of multiple modalities for prognostication, showing improved intra- and inter-medical modality binding.

cs.CV↗
arXiv2025

EchoingECG: An Electrocardiogram Cross-Modal Model for Echocardiogram Tasks

Electrocardiogram (ECG) is a widely used tool for assessing cardiac function due to its low cost and accessibility. Emergent research shows that ECGs can help make predictions on key outcomes traditionally derived from more complex modalities such as echocardiograms (ECHO), enabling the use of ECGs as a more accessible method to predict broader measurements of cardiac function. ECHO, in particular, are of great importance because they require considerable hospital resources while playing a key role in clinical cardiac assessment. To aid this use case, we introduce EchoingECG, a probabilistic student-teacher model that leverages uncertainty-aware ECG embeddings and ECHO supervision to improve ECG-based cardiac function prediction. Our approach integrates Probabilistic Cross-Modal Embeddings (PCME++), a probabilistic contrastive framework, with ECHO-CLIP, a vision-language pre-trained model trained on ECHO-text pairs, to distill ECHO knowledge into ECG representations. Through experiments and external validation, we showed that EchoingECG outperforms state-of-the-art foundation ECG models in zero-shot, few-shot, and fine-tune settings for ECHO predictions based on ECG. We also highlighted that variance estimation (enabled through our method) enhanced our understanding of model performance by identifying underlying regions of uncertainty within ECGs. The code is available: https://github.com/mcintoshML/EchoingECG.

cs.CV↗
arXiv2025

Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes

In user-generated-content (UGC) applications, non-expert users often rely on image-to-3D generative models to create 3D assets. In this context, primitive-based shape abstraction offers a promising solution for UGC scenarios by compressing high-resolution meshes into compact, editable representations. Towards this end, effective shape abstraction must therefore be structure-aware, characterized by low overlap between primitives, part-aware alignment, and primitive compactness. We present Light-SQ, a novel superquadric-based optimization framework that explicitly emphasizes structure-awareness from three aspects. (a) We introduce SDF carving to iteratively udpate the target signed distance field, discouraging overlap between primitives. (b) We propose a block-regrow-fill strategy guided by structure-aware volumetric decomposition, enabling structural partitioning to drive primitive placement. (c) We implement adaptive residual pruning based on SDF update history to surpress over-segmentation and ensure compact results. In addition, Light-SQ supports multiscale fitting, enabling localized refinement to preserve fine geometric details. To evaluate our method, we introduce 3DGen-Prim, a benchmark extending 3DGen-Bench with new metrics for both reconstruction quality and primitive-level editability. Extensive experiments demonstrate that Light-SQ enables efficient, high-fidelity, and editable shape abstraction with superquadrics for complex generated geometry, advancing the feasibility of 3D UGC creation.

cs.GR↗
arXiv2025

State-Constrained Chemical Reactions: Discrete-to-Continuous Hamilton--Jacobi Equations and Large Deviations

We study the macroscopic behavior of chemical reactions modeled as random time-changed Poisson processes on discrete state spaces. Using the WKB reformulation, the backward equation of the rescaled process leads to a discrete Hamilton--Jacobi equation with state constraints. As the grid size tends to zero, the limiting solution and its associated variational representation are closely connected to the good rate function of the large deviation principle for state-constrained chemical reactions in the thermodynamic limit. In this work, we focus on the limiting behavior of discrete Hamilton--Jacobi equations defined on bounded domains with state-constraint boundary conditions. For a single chemical reaction, we show that, under a suitable reparametrization, the solution of the discrete Hamilton--Jacobi equation converges to the solution of a continuous Hamilton--Jacobi equation with a Neumann boundary condition. Building on this convergence result and the associated variational representation, we establish the large deviation principle for the rescaled chemical reaction process in bounded domains.

math.AP↗
arXiv2025

VISION: Prompting Ocean Vertical Velocity Reconstruction from Incomplete Observations

Reconstructing subsurface ocean dynamics, such as vertical velocity fields, from incomplete surface observations poses a critical challenge in Earth science, a field long hampered by the lack of standardized, analysis-ready benchmarks. To systematically address this issue and catalyze research, we first build and release KD48, a high-resolution ocean dynamics benchmark derived from petascale simulations and curated with expert-driven denoising. Building on this benchmark, we introduce VISION, a novel reconstruction paradigm based on Dynamic Prompting designed to tackle the core problem of missing data in real-world observations. The essence of VISION lies in its ability to generate a visual prompt on-the-fly from any available subset of observations, which encodes both data availability and the ocean's physical state. More importantly, we design a State-conditioned Prompting module that efficiently injects this prompt into a universal backbone, endowed with geometry- and scale-aware operators, to guide its adaptive adjustment of computational strategies. This mechanism enables VISION to precisely handle the challenges posed by varying input combinations. Extensive experiments on the KD48 benchmark demonstrate that VISION not only substantially outperforms state-of-the-art models but also exhibits strong generalization under extreme data missing scenarios. By providing a high-quality benchmark and a robust model, our work establishes a solid infrastructure for ocean science research under data uncertainty. Our codes are available at: https://github.com/YuanGao-YG/VISION.

cs.LG↗