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Robot-Assisted Therapy for Upper Limb Rehabilitation After Stroke: Umbrella Review

Background: Stroke is a leading cause of long-term upper limb disability, severely impacting patients’ independence and quality of life. Robot-assisted therapy (RAT) has emerged as a promising, high-intensity rehabilitation alternative. However, conclusions from existing systematic reviews on its efficacy are inconsistent and often lack a holistic framework, limiting their use for guiding personalized clinical decisions. Objective: This study aims to systematically synthesize recent evidence on RAT for upper limb rehabilitation after stroke. Guided by the International Classification of Functioning, Disability and Health framework, it moves beyond singular outcomes to provide a multidimensional evaluation across body function, activity, and participation levels. The review aims to provide stratified guidance for clinical decision-making based on patient- and intervention-specific characteristics, thereby supporting evidence-based practice and informing future research. Methods: This study included systematic reviews and meta-analyses published from January 1, 2019, to December 26, 2025, comparing RAT with conventional therapy for upper limb rehabilitation after stroke. Overall, 6 databases, including PubMed, Web of Science, and Embase, were searched. Two reviewers (XZ and LZ) independently performed study selection, data extraction, and quality assessment using the AMSTAR 2 tool. The synthesis integrated outcome measures and subgroup analyses derived from the included studies. Results: This umbrella review included 21 meta-analyses encompassing 535 randomized controlled trials and 27,598 patients across acute, subacute, and chronic stroke stages. According to AMSTAR 2, 17 reviews were high quality, 3 moderate, and 1 critically low. The synthesis demonstrated that RAT was superior in improving upper limb motor function, but no statistically significant advantages were observed in activities of daily living compared to conventional therapy. Subgroup analyses revealed that treatment effects were influenced by stroke stage, upper limb motor impairment level, and robot type. Conclusions: RAT is an effective intervention for improving upper limb motor function after stroke. However, its benefits are primarily observed at the level of body function, with limited evidence for long-term maintenance. The current evidence is constrained by significant outcome heterogeneity and methodological limitations inherent to umbrella reviews. Future research should validate these findings in broader clinical practice, focus on translating functional gains into sustained improvements in daily activities and participation, and include cost-effectiveness evaluations. Trial Registration: PROSPERO CRD42024497183; https://www.crd.york.ac.uk/PROSPERO/view/CRD42024497183

Bridging neuroscience and AI: adaptive, culturally sensitive technologies transforming aphasia rehabilitation

arXiv:2603.22357v1 Announce Type: new Abstract: Aphasia, a language impairment primarily resulting from stroke or brain injury, profoundly disrupts communication and everyday functioning. Despite advances in speech therapy, barriers such as limited therapist availability and the scarcity of personalized, culturally relevant tools continue to hinder optimal rehabilitation outcomes. This paper reviews recent developments in neurocognitive research and language technologies that contribute to the diagnosis and therapy of aphasia. Drawing on findings from our ethnographic field study, we introduce two digital therapy prototypes designed to reflect local linguistic diversity and enhance patient engagement. We also show how insights from neuroscience and the local context guided the design of these tools to better meet patient and therapist needs. Our work highlights the potential of adaptive, AI-enhanced assistive technologies to complement conventional therapy and broaden access to therapy. We conclude by outlining future research directions for advancing personalized and scalable aphasia rehabilitation.

From Static Templates to Dynamic Runtime Graphs: A Survey of Workflow Optimization for LLM Agents

arXiv:2603.22386v1 Announce Type: new Abstract: Large language model (LLM)-based systems are becoming increasingly popular for solving tasks by constructing executable workflows that interleave LLM calls, information retrieval, tool use, code execution, memory updates, and verification. This survey reviews recent methods for designing and optimizing such workflows, which we treat as agentic computation graphs (ACGs). We organize the literature based on when workflow structure is determined, where structure refers to which components or agents are present, how they depend on each other, and how information flows between them. This lens distinguishes static methods, which fix a reusable workflow scaffold before deployment, from dynamic methods, which select, generate, or revise the workflow for a particular run before or during execution. We further organize prior work along three dimensions: when structure is determined, what part of the workflow is optimized, and which evaluation signals guide optimization (e.g., task metrics, verifier signals, preferences, or trace-derived feedback). We also distinguish reusable workflow templates, run-specific realized graphs, and execution traces, separating reusable design choices from the structures actually deployed in a given run and from realized runtime behavior. Finally, we outline a structure-aware evaluation perspective that complements downstream task metrics with graph-level properties, execution cost, robustness, and structural variation across inputs. Our goal is to provide a clear vocabulary, a unified framework for positioning new methods, a more comparable view of existing body of literature, and a more reproducible evaluation standard for future work in workflow optimizations for LLM agents.

Understanding LLM Performance Degradation in Multi-Instance Processing: The Roles of Instance Count and Context Length

arXiv:2603.22608v1 Announce Type: new Abstract: Users often rely on Large Language Models (LLMs) for processing multiple documents or performing analysis over a number of instances. For example, analysing the overall sentiment of a number of movie reviews requires an LLM to process the sentiment of each review individually in order to provide a final aggregated answer. While LLM performance on such individual tasks is generally high, there has been little research on how LLMs perform when dealing with multi-instance inputs. In this paper, we perform a comprehensive evaluation of the multi-instance processing (MIP) ability of LLMs for tasks in which they excel individually. The results show that all LLMs follow a pattern of slight performance degradation for small numbers of instances (approximately 20-100), followed by a performance collapse on larger instance counts. Crucially, our analysis shows that while context length is associated with this degradation, the number of instances has a stronger effect on the final results. This finding suggests that when optimising LLM performance for MIP, attention should be paid to both context length and, in particular, instance count.

Improving Safety Alignment via Balanced Direct Preference Optimization

arXiv:2603.22829v1 Announce Type: new Abstract: With the rapid development and widespread application of Large Language Models (LLMs), their potential safety risks have attracted widespread attention. Reinforcement Learning from Human Feedback (RLHF) has been adopted to enhance the safety performance of LLMs. As a simple and effective alternative to RLHF, Direct Preference Optimization (DPO) is widely used for safety alignment. However, safety alignment still suffers from severe overfitting, which limits its actual performance. This paper revisits the overfitting phenomenon from the perspective of the model's comprehension of the training data. We find that the Imbalanced Preference Comprehension phenomenon exists between responses in preference pairs, which compromises the model's safety performance. To address this, we propose Balanced Direct Preference Optimization (B-DPO), which adaptively modulates optimization strength between preferred and dispreferred responses based on mutual information. A series of experimental results show that B-DPO can enhance the safety capability while maintaining the competitive general capabilities of LLMs on various mainstream benchmarks compared to state-of-the-art methods. \color{red}{Warning: This paper contains examples of harmful texts, and reader discretion is recommended.

PhySe-RPO: Physics and Semantics Guided Relative Policy Optimization for Diffusion-Based Surgical Smoke Removal

arXiv:2603.22844v2 Announce Type: new Abstract: Surgical smoke severely degrades intraoperative video quality, obscuring anatomical structures and limiting surgical perception. Existing learning-based desmoking approaches rely on scarce paired supervision and deterministic restoration pipelines, making it difficult to perform exploration or reinforcement-driven refinement under real surgical conditions. We propose PhySe-RPO, a diffusion restoration framework optimized through Physics- and Semantics-Guided Relative Policy Optimization. The core idea is to transform deterministic restoration into a stochastic policy, enabling trajectory-level exploration and critic-free updates via group-relative optimization. A physics-guided reward imposes illumination and color consistency, while a visual-concept semantic reward learned from CLIP-based surgical concepts promotes smoke-free and anatomically coherent restoration. Together with a reference-free perceptual constraint, PhySe-RPO produces results that are physically consistent, semantically faithful, and clinically interpretable across synthetic and real robotic surgical datasets, providing a principled route to robust diffusion-based restoration under limited paired supervision.

Separating Diagnosis from Control: Auditable Policy Adaptation in Agent-Based Simulations with LLM-Based Diagnostics

arXiv:2603.22904v1 Announce Type: new Abstract: Mitigating elderly loneliness requires policy interventions that achieve both adaptability and auditability. Existing methods struggle to reconcile these objectives: traditional agent-based models suffer from static rigidity, while direct large language model (LLM) controllers lack essential traceability. This work proposes a three-layer framework that separates diagnosis from control to achieve both properties simultaneously. LLMs operate strictly as diagnostic instruments that assess population state and generate structured risk evaluations, while deterministic formulas with explicit bounds translate these assessments into traceable parameter updates. This separation ensures that every policy decision can be attributed to inspectable rules while maintaining adaptive response to emergent needs. We validate the framework through systematic ablation across five experimental conditions in elderly care simulation. Results demonstrate that explicit control rules outperform end-to-end black-box LLM approaches by 11.7\% while preserving full auditability, confirming that transparency need not compromise adaptive performance.

ProGRank: Probe-Gradient Reranking to Defend Dense-Retriever RAG from Corpus Poisoning

arXiv:2603.22934v1 Announce Type: new Abstract: Retrieval-Augmented Generation (RAG) improves the reliability of large language model applications by grounding generation in retrieved evidence, but it also introduces a new attack surface: corpus poisoning. In this setting, an adversary injects or edits passages so that they are ranked into the Top-$K$ results for target queries and then affect downstream generation. Existing defences against corpus poisoning often rely on content filtering, auxiliary models, or generator-side reasoning, which can make deployment more difficult. We propose ProGRank, a post hoc, training-free retriever-side defence for dense-retriever RAG. ProGRank stress-tests each query--passage pair under mild randomized perturbations and extracts probe gradients from a small fixed parameter subset of the retriever. From these signals, it derives two instability signals, representational consistency and dispersion risk, and combines them with a score gate in a reranking step. ProGRank preserves the original passage content, requires no retraining, and also supports a surrogate-based variant when the deployed retriever is unavailable. Extensive experiments across three datasets, three dense retriever backbones, representative corpus poisoning attacks, and both retrieval-stage and end-to-end settings show that ProGRank provides stronger defence performance and a favorable robustness--utility trade-off. It also remains competitive under adaptive evasive attacks.

PERMA: Benchmarking Personalized Memory Agents via Event-Driven Preference and Realistic Task Environments

arXiv:2603.23231v1 Announce Type: new Abstract: Empowering large language models with long-term memory is crucial for building agents that adapt to users' evolving needs. However, prior evaluations typically interleave preference-related dialogues with irrelevant conversations, reducing the task to needle-in-a-haystack retrieval while ignoring relationships between events that drive the evolution of user preferences. Such settings overlook a fundamental characteristic of real-world personalization: preferences emerge gradually and accumulate across interactions within noisy contexts. To bridge this gap, we introduce PERMA, a benchmark designed to evaluate persona consistency over time beyond static preference recall. Additionally, we incorporate (1) text variability and (2) linguistic alignment to simulate erratic user inputs and individual idiolects in real-world data. PERMA consists of temporally ordered interaction events spanning multiple sessions and domains, with preference-related queries inserted over time. We design both multiple-choice and interactive tasks to probe the model's understanding of persona along the interaction timeline. Experiments demonstrate that by linking related interactions, advanced memory systems can extract more precise preferences and reduce token consumption, outperforming traditional semantic retrieval of raw dialogues. Nevertheless, they still struggle to maintain a coherent persona across temporal depth and cross-domain interference, highlighting the need for more robust personalized memory management in agents. Our code and data are open-sourced at https://github.com/PolarisLiu1/PERMA.

A Synchronous EEG-fNIRS BCI: A Proof-of-Concept for Multimodal Avalanche Analysis of Motor Cognition in Older Adults

arXiv:2603.23358v1 Announce Type: new Abstract: This proof-of-concept study introduces a novel multimodal framework combining synchronized EEG-fNIRS modalities with neuronal avalanche analysis to identify early network dysfunction in Alzheimer's disease. The approach leverages complementary neural signals to examine motor network dynamics during execution and imagery tasks within an interactive task environment. Preliminary analysis of a small pilot cohort (N=4 subjects, including one with Mild Cognitive Impairment) validated the technical feasibility of the multimodal framework and revealed observable condition-dependent patterns in network organization. Two primary observations emerged: a reduced neural contrast between motor execution and imagery states, and increased trial-to-trial variability in network organization in the MCI participant. These initial results successfully validate the technical pipeline and provide hypothesis-generating observations for future statistically powered studies. The convergence of findings across modalities suggests that multimodal assessment of network flexibility may help detect functional changes in early Alzheimer's continuum, supporting the future development of this BCI-inspired framework into an engaging diagnostic tool.

MERIT: Memory-Enhanced Retrieval for Interpretable Knowledge Tracing

arXiv:2603.22289v1 Announce Type: cross Abstract: Knowledge Tracing (KT) models students' evolving knowledge states to predict future performance, serving as a foundation for personalized education. While traditional deep learning models achieve high accuracy, they often lack interpretability. Large Language Models (LLMs) offer strong reasoning capabilities but struggle with limited context windows and hallucinations. Furthermore, existing LLM-based methods typically require expensive fine-tuning, limiting scalability and adaptability to new data. We propose MERIT (Memory-Enhanced Retrieval for Interpretable Knowledge Tracing), a training-free framework combining frozen LLM reasoning with structured pedagogical memory. Rather than updating parameters, MERIT transforms raw interaction logs into an interpretable memory bank. The framework uses semantic denoising to categorize students into latent cognitive schemas and constructs a paradigm bank where representative error patterns are analyzed offline to generate explicit Chain-of-Thought (CoT) rationales. During inference, a hierarchical routing mechanism retrieves relevant contexts, while a logic-augmented module applies semantic constraints to calibrate predictions. By grounding the LLM in interpretable memory, MERIT achieves state-of-the-art performance on real-world datasets without gradient updates. This approach reduces computational costs and supports dynamic knowledge updates, improving the accessibility and transparency of educational diagnosis.

Scaling Attention via Feature Sparsity

arXiv:2603.22300v1 Announce Type: cross Abstract: Scaling Transformers to ultra-long contexts is bottlenecked by the $O(n^2 d)$ cost of self-attention. Existing methods reduce this cost along the sequence axis through local windows, kernel approximations, or token-level sparsity, but these approaches consistently degrade accuracy. In this paper, we instead explore an orthogonal axis: feature sparsity. We propose Sparse Feature Attention (SFA), where queries and keys are represented as $k$-sparse codes that preserve high-dimensional expressivity while reducing the cost of attention from $\Theta(n^2 d)$ to $\Theta(n^2 k^2/d)$. To make this efficient at scale, we introduce FlashSFA, an IO-aware kernel that extends FlashAttention to operate directly on sparse overlaps without materializing dense score matrices. Across GPT-2 and Qwen3 pretraining, SFA matches dense baselines while improving speed by up to $2.5\times$ and reducing FLOPs and KV-cache by nearly 50\%. On synthetic and downstream benchmarks, SFA preserves retrieval accuracy and robustness at long contexts, outperforming short-embedding baselines that collapse feature diversity. These results establish feature-level sparsity as a complementary and underexplored axis for efficient attention, enabling Transformers to scale to orders-of-magnitude longer contexts with minimal quality loss. Code is available at https://github.com/YannX1e/Sparse-Feature-Attention.

CN-Buzz2Portfolio: A Chinese-Market Dataset and Benchmark for LLM-Based Macro and Sector Asset Allocation from Daily Trending Financial News

arXiv:2603.22305v1 Announce Type: cross Abstract: Large Language Models (LLMs) are rapidly transitioning from static Natural Language Processing (NLP) tasks including sentiment analysis and event extraction to acting as dynamic decision-making agents in complex financial environments. However, the evolution of LLMs into autonomous financial agents faces a significant dilemma in evaluation paradigms. Direct live trading is irreproducible and prone to outcome bias by confounding luck with skill, whereas existing static benchmarks are often confined to entity-level stock picking and ignore broader market attention. To facilitate the rigorous analysis of these challenges, we introduce CN-Buzz2Portfolio, a reproducible benchmark grounded in the Chinese market that maps daily trending news to macro and sector asset allocation. Spanning a rolling horizon from 2024 to mid-2025, our dataset simulates a realistic public attention stream, requiring agents to distill investment logic from high-exposure narratives instead of pre-filtered entity news. We propose a Tri-Stage CPA Agent Workflow involving Compression, Perception, and Allocation to evaluate LLMs on broad asset classes such as Exchange Traded Funds (ETFs) rather than individual stocks, thereby reducing idiosyncratic volatility. Extensive experiments on nine LLMs reveal significant disparities in how models translate macro-level narratives into portfolio weights. This work provides new insights into the alignment between general reasoning and financial decision-making, and all data, codes, and experiments are released to promote sustainable financial agent research.

ST-GDance++: A Scalable Spatial-Temporal Diffusion for Long-Duration Group Choreography

arXiv:2603.22316v1 Announce Type: cross Abstract: Group dance generation from music requires synchronizing multiple dancers while maintaining spatial coordination, making it highly relevant to applications such as film production, gaming, and animation. Recent group dance generation models have achieved promising generation quality, but they remain difficult to deploy in interactive scenarios due to bidirectional attention dependencies. As the number of dancers and the sequence length increase, the attention computation required for aligning music conditions with motion sequences grows quadratically, leading to reduced efficiency and increased risk of motion collisions. Effectively modeling dense spatial-temporal interactions is therefore essential, yet existing methods often struggle to capture such complexity, resulting in limited scalability and unstable multi-dancer coordination. To address these challenges, we propose ST-GDance++, a scalable framework that decouples spatial and temporal dependencies to enable efficient and collision-aware group choreography generation. For spatial modeling, we introduce lightweight distance-aware graph convolutions to capture inter-dancer relationships while reducing computational overhead. For temporal modeling, we design a diffusion noise scheduling strategy together with an efficient temporal-aligned attention mask, enabling stream-based generation for long motion sequences and improving scalability in long-duration scenarios. Experiments on the AIOZ-GDance dataset show that ST-GDance++ achieves competitive generation quality with significantly reduced latency compared to existing methods.

A Multi-Task Targeted Learning Framework for Lithium-Ion Battery State-of-Health and Remaining Useful Life

arXiv:2603.22323v1 Announce Type: cross Abstract: Accurately predicting the state-of-health (SOH) and remaining useful life (RUL) of lithium-ion batteries is crucial for ensuring the safe and efficient operation of electric vehicles while minimizing associated risks. However, current deep learning methods are limited in their ability to selectively extract features and model time dependencies for these two parameters. Moreover, most existing methods rely on traditional recurrent neural networks, which have inherent shortcomings in long-term time-series modeling. To address these issues, this paper proposes a multi-task targeted learning framework for SOH and RUL prediction, which integrates multiple neural networks, including a multi-scale feature extraction module, an improved extended LSTM, and a dual-stream attention module. First, a feature extraction module with multi-scale CNNs is designed to capture detailed local battery decline patterns. Secondly, an improved extended LSTM network is employed to enhance the model's ability to retain long-term temporal information, thus improving temporal relationship modeling. Building on this, the dual-stream attention module-comprising polarized attention and sparse attention to selectively focus on key information relevant to SOH and RUL, respectively, by assigning higher weights to important features. Finally, a many-to-two mapping is achieved through the dual-task layer. To optimize the model's performance and reduce the need for manual hyperparameter tuning, the Hyperopt optimization algorithm is used. Extensive comparative experiments on battery aging datasets demonstrate that the proposed method reduces the average RMSE for SOH and RUL predictions by 111.3\% and 33.0\%, respectively, compared to traditional and state-of-the-art methods.

DAQ: Delta-Aware Quantization for Post-Training LLM Weight Compression

arXiv:2603.22324v1 Announce Type: cross Abstract: We introduce Delta-Aware Quantization (DAQ), a data-free post-training quantization framework that preserves the knowledge acquired during post-training. Standard quantization objectives minimize reconstruction error but are agnostic to the base model, allowing quantization noise to disproportionately corrupt the small-magnitude parameter deltas ($\Delta W$) that encode post-training behavior -- an effect we analyze through the lens of quantization as implicit regularization. DAQ replaces reconstruction-based objectives with two delta-aware metrics -- Sign Preservation Rate and Cosine Similarity -- that directly optimize for directional fidelity of $\Delta W$, requiring only the base and post-trained weight matrices. In a pilot FP8 study, DAQ recovers style-specific capabilities lost under standard quantization while maintaining general performance.

Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Framework

arXiv:2603.22362v1 Announce Type: cross Abstract: Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

SynLeaF: A Dual-Stage Multimodal Fusion Framework for Synthetic Lethality Prediction Across Pan- and Single-Cancer Contexts

arXiv:2603.22369v1 Announce Type: cross Abstract: Accurate prediction of synthetic lethality (SL) is important for guiding the development of cancer drugs and therapies. SL prediction faces significant challenges in the effective fusion of heterogeneous multi-source data. Existing multimodal methods often suffer from "modality laziness" due to disparate convergence speeds, which hinders the exploitation of complementary information. This is also one reason why most existing SL prediction models cannot perform well on both pan-cancer and single-cancer SL pair prediction. In this study, we propose SynLeaF, a dual-stage multimodal fusion framework for SL prediction across pan- and single-cancer contexts. The framework employs a VAE-based cross-encoder with a product of experts mechanism to fuse four omics data types (gene expression, mutation, methylation, and CNV), while simultaneously utilizing a relational graph convolutional network to capture structured gene representations from biomedical knowledge graphs. To mitigate modality laziness, SynLeaF introduces a dual-stage training mechanism employing featurelevel knowledge distillation with adaptive uni-modal teacher and ensemble strategies. In extensive experiments across eight specific cancer types and a pancancer dataset, SynLeaF achieves superior performance in 17 out of 19 scenarios. Ablation studies and gradient analyses further validate the critical contributions of the proposed fusion and distillation mechanisms to model robustness and generalization. To facilitate community use, a web server is available at https://synleaf.bioinformatics-lilab.cn.

FAAR: Format-Aware Adaptive Rounding for NVFP4

arXiv:2603.22370v1 Announce Type: cross Abstract: Deploying large language models (LLMs) on edge devices requires extremely low-bit quantization. Ultra-low precision formats such as NVFP4 offer a promising solution for reducing memory footprint and accelerating computation. However, existing quantization methods typically rely on conventional rounding strategies and fail to account for the non-uniformity of the NVFP4 numerical grid, resulting in suboptimal rounding decisions and amplified quantization errors. To address this, we propose Format-Aware Adaptive Rounding (FAAR), a learnable rounding strategy tailored for the NVFP4 format. Unlike conventional quantization paradigms, FAAR explicitly incorporates the non-uniform NVFP4 grid into the optimization process. By adaptively adjusting rounding decisions guided by loss gradients, our method effectively approximates the theoretically optimal quantization. To complement FAAR, we introduce a 2-stages Format Alignment (2FA) fine-tuning scheme that aligns LLM parameters layer-by-layer to the NVFP4 numerical space, further narrowing the performance gap. Remarkably, this learnable optimization incurs a minimal training overhead of only 4 GPU hours on Llama3-1B. Extensive experiments demonstrate the effectiveness of our approach. Compared with Round-to-Nearest (RTN), our method reduces perplexity on WikiText-2 from 14.28 to 12.60 on Llama3-1B and from 23.06 to 21.27 on Qwen3-1.7B. Additionally, our method consistently outperforms state-of-the-art approaches across various zero-shot downstream tasks.

Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data

arXiv:2603.22380v1 Announce Type: cross Abstract: Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and limited by sparse sampling, which poses significant challenges to existing approaches based on numerical differentiation or integral formulations. In this work, we propose a Symbolic Graph Network (SGN) framework for PDE discovery under noisy and sparse conditions. Instead of relying on local differential approximations, SGN leverages graph message passing to model spatial interactions, providing a non-local representation that is less sensitive to high frequency noise. Based on this representation, the learned latent features are further processed by a symbolic regression module to extract interpretable mathematical expressions. We evaluate the proposed method on several benchmark systems, including the wave equation, convection-diffusion equation, and incompressible Navier-Stokes equations. Experimental results show that SGN can recover meaningful governing relations or solution forms under varying noise levels, and demonstrates improved robustness compared to baseline methods in sparse and noisy settings. These results suggest that combining graph-based representations with symbolic regression provides a viable direction for robust data-driven discovery of physical laws from imperfect observations. The code is available at https://github.com/CXY0112/SGN
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