Efficient Global-Local Fusion Sampling for Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2510.24026v1
• Date: Tue, 28 Oct 2025 03:10:54 GMT
• Title: Efficient Global-Local Fusion Sampling for Physics-Informed Neural Networks
• Abstract summary: We propose a Global-Local Fusion (GLF) Sampling Strategy that combines the strengths of both approaches.<n>New collocation points are generated by perturbing training points with Gaussian noise scaled inversely to the residual.<n>To further reduce computational overhead, a lightweight linear surrogate is introduced to approximate the global residual-based distribution.
• Score: 5.257115841810259
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The accuracy of Physics-Informed Neural Networks (PINNs) critically depends on the placement of collocation points, as the PDE loss is approximated through sampling over the solution domain. Global sampling ensures stability by covering the entire domain but requires many samples and is computationally expensive, whereas local sampling improves efficiency by focusing on high-residual regions but may neglect well-learned areas, reducing robustness. We propose a Global-Local Fusion (GLF) Sampling Strategy that combines the strengths of both approaches. Specifically, new collocation points are generated by perturbing training points with Gaussian noise scaled inversely to the residual, thereby concentrating samples in difficult regions while preserving exploration. To further reduce computational overhead, a lightweight linear surrogate is introduced to approximate the global residual-based distribution, achieving similar effectiveness at a fraction of the cost. Together, these components, residual-adaptive sampling and residual-based approximation, preserve the stability of global methods while retaining the efficiency of local refinement. Extensive experiments on benchmark PDEs demonstrate that GLF consistently improves both accuracy and efficiency compared with global and local sampling strategies. This study provides a practical and scalable framework for enhancing the reliability and efficiency of PINNs in solving complex and high-dimensional PDEs.

Related papers

• ViCrop-Det: Spatial Attention Entropy Guided Cropping for Training-Free Small-Object Detection [6.1221124436192875]
  ViCrop-Det is a training-free inference framework that introduces adaptive spatial trust region shrinkage.<n>We show that ViCrop-Det consistently adds +1-3 mAP@50 to RT-DETR-R50 and Deformable DETR with a marginal 20-23% latency overhead.<n>Under compute-matched settings, our adaptive routing strategy comprehensively surpasses uniform slicing baselines, achieving a highly optimized accuracy-speed trade-off.
  arXiv  Detail & Related papers  (2026-04-29T15:35:03Z)
• SCOPE: Semantic Coreset with Orthogonal Projection Embeddings for Federated learning [0.7799711162530713]
  Current ML approaches either require impractical data aggregation or fail due to class imbalance.<n>We introduce SCOPE, a coreset framework for federated data that filters anomalies and adaptively prunes redundant data to long-tail skew.<n>SCOPE yields competitive global accuracy and robust convergence, all while achieving exceptional efficiency with a 128x to 512x reduction in uplink bandwidth.
  arXiv  Detail & Related papers  (2026-03-13T13:24:12Z)
• Adaptive Dual-Weighting Framework for Federated Learning via Out-of-Distribution Detection [53.45696787935487]
  Federated Learning (FL) enables collaborative model training across large-scale distributed service nodes.<n>In real-world service-oriented deployments, data generated by heterogeneous users, devices, and application scenarios are inherently non-IID.<n>We propose FLood, a novel FL framework inspired by out-of-distribution (OOD) detection.
  arXiv  Detail & Related papers  (2026-02-01T05:54:59Z)
• Federated Reinforcement Learning in Heterogeneous Environments [9.944647907864255]
  We investigate a Federated Reinforcement Learning with Environment Heterogeneity (FRL-EH) framework, where local environments exhibit statistical heterogeneity.<n>Within this framework, agents collaboratively learn a global policy by aggregating their collective experiences while preserving the privacy of their local trajectories.<n>We present a novel global objective function that ensures robust performance across heterogeneous local environments and their plausible perturbations.<n>We extend FedRQ to environments with continuous state space through the use of expectile loss, addressing the key challenge of minimizing a value function over a continuous subset of the state space.
  arXiv  Detail & Related papers  (2025-07-19T05:06:38Z)
• Distributionally Robust Federated Learning with Client Drift Minimization [35.08453461129848]
  textitDRDM is a distributionally robust optimization framework with dynamic regularization to mitigate client drift.<n>textitDRDM frames the training as a min-max optimization problem aimed at maximizing performance for the worst-case client.<n>Experiments show that textitDRDM significantly improves worst-case test accuracy while requiring fewer communication rounds.
  arXiv  Detail & Related papers  (2025-05-21T11:05:56Z)
• Stochastic Layer-wise Learning: Scalable and Efficient Alternative to Backpropagation [1.0285749562751982]
  Backpropagation underpins modern deep learning, yet its reliance on global synchronization limits scalability and incurs high memory costs.<n>In contrast, fully local learning rules are more efficient but often struggle to maintain the cross-layer coordination needed for coherent global learning.<n>We introduce Layer-wise Learning (SLL), a layer-wise training algorithm that decomposes the global objective into coordinated layer-local updates.
  arXiv  Detail & Related papers  (2025-05-08T12:32:29Z)
• Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization [81.32266996009575]
  In federated learning (FL), the multi-step update and data heterogeneity among clients often lead to a loss landscape with sharper minima. We propose FedLESAM, a novel algorithm that locally estimates the direction of global perturbation on client side.
  arXiv  Detail & Related papers  (2024-05-29T08:46:21Z)
• Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Region [0.18139022013189662]
  Estimating distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem. This paper introduces a Hybrid Assimilation and Regionalization (HDA-PR) approach incorporating learnable regionalization mappings. Results highlight a strong regionalization of HDA-PR especially in the most challenging upstream-to-downstream extrapolation scenario.
  arXiv  Detail & Related papers  (2023-08-02T07:23:50Z)
• Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape [59.841889495864386]
  In federated learning (FL), a cluster of local clients are chaired under the coordination of a global server. Clients are prone to overfit into their own optima, which extremely deviates from the global objective. ttfamily FedSMOO adopts a dynamic regularizer to guarantee the local optima towards the global objective. Our theoretical analysis indicates that ttfamily FedSMOO achieves fast $mathcalO (1/T)$ convergence rate with low bound generalization.
  arXiv  Detail & Related papers  (2023-05-19T10:47:44Z)
• FedLAP-DP: Federated Learning by Sharing Differentially Private Loss Approximations [53.268801169075836]
  We propose FedLAP-DP, a novel privacy-preserving approach for federated learning. A formal privacy analysis demonstrates that FedLAP-DP incurs the same privacy costs as typical gradient-sharing schemes. Our approach presents a faster convergence speed compared to typical gradient-sharing methods.
  arXiv  Detail & Related papers  (2023-02-02T12:56:46Z)
• Disentangled Federated Learning for Tackling Attributes Skew via Invariant Aggregation and Diversity Transferring [104.19414150171472]
  Attributes skews the current federated learning (FL) frameworks from consistent optimization directions among the clients. We propose disentangled federated learning (DFL) to disentangle the domain-specific and cross-invariant attributes into two complementary branches. Experiments verify that DFL facilitates FL with higher performance, better interpretability, and faster convergence rate, compared with SOTA FL methods.
  arXiv  Detail & Related papers  (2022-06-14T13:12:12Z)
• DRFLM: Distributionally Robust Federated Learning with Inter-client Noise via Local Mixup [58.894901088797376]
  federated learning has emerged as a promising approach for training a global model using data from multiple organizations without leaking their raw data. We propose a general framework to solve the above two challenges simultaneously. We provide comprehensive theoretical analysis including robustness analysis, convergence analysis, and generalization ability.
  arXiv  Detail & Related papers  (2022-04-16T08:08:29Z)
• Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learning [58.79085525115987]
  Local methods are one of the promising approaches to reduce communication time. We show that the communication complexity is better than non-local methods when the local datasets is smaller than the smoothness local loss.
  arXiv  Detail & Related papers  (2022-02-12T15:12:17Z)
• DAS: A deep adaptive sampling method for solving partial differential equations [2.934397685379054]
  We propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs) Deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to generate new collocation points that refine the training set. We present a theoretical analysis to show that the proposed DAS method can reduce the error bound and demonstrate its effectiveness with numerical experiments.
  arXiv  Detail & Related papers  (2021-12-28T08:37:47Z)
• Distributionally Robust Federated Averaging [19.875176871167966]
  We present communication efficient distributed algorithms for robust learning periodic averaging with adaptive sampling. We give corroborating experimental evidence for our theoretical results in federated learning settings.
  arXiv  Detail & Related papers  (2021-02-25T03:32:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.