Evolving Error States: Failure-Aware Progressive Repair for Ultrasound Lesion Segmentation
为解决医学图像分割中稀疏和异质错误的问题，提出了一种基于动态错误状态演变的Failure-Aware Progressive Repair方法，通过迭代修正提高复杂情况下的准确性。
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Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations
This work addresses the challenges of insufficient accuracy and difficulty in satisfying structural constraints when solving α-cut-based fuzzy partial differential equations. The authors propose QCPIKAN, a quantum-classical hybrid physics-informed network that takes spatiotemporal coordinates and membership degrees as inputs to jointly approximate the upper and lower bounds of α-cuts, while embedding governing equations, initial/boundary conditions, and fuzzy structural constraints for end-to-end training. By innovatively integrating parameterized quantum circuits with ChebyKAN modules, they establish a unified error analysis framework and prove that, under sufficient quantum entanglement gain, QCPIKAN achieves a tighter prior error bound than its classical counterpart. Numerical experiments demonstrate that QCPIKAN reduces the average relative L² error by 1.1–2.7 times and decreases wavefront location error by approximately 1.77 times across elliptic, parabolic, and hyperbolic fuzzy PDEs, significantly enhancing solution accuracy.
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GeoRouteNet: Geometry-Enhanced Non-Autoregressive Neural Solver for the Traveling Salesman Problem
This work addresses the limited cross-scale and cross-distribution generalization of non-autoregressive neural solvers for the Traveling Salesman Problem (TSP), which stems from insufficient geometric inductive bias and unstable training signals. To overcome these limitations, the authors propose GeoRouteNet, a novel architecture that enhances geometric representation through centralized node features, learnable radial distance basis functions, and a distance-aware graph attention mechanism. Training stability is further improved via Multi-Candidate Self-comparative Reinforcement Learning (MCS-RL). The model achieves state-of-the-art optimality gaps of 0.32% and 1.26% on TSP50 and TSP100, respectively, and reduces the average optimality gap on TSPLIB EUC_2D instances from 17.12% to 3.60%. Moreover, GeoRouteNet demonstrates significantly higher batch inference throughput compared to Concorde and LKH3.
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Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
This work addresses persistent challenges in solving partial differential equations (PDEs)—notably slow convergence of high-frequency errors, severe numerical dispersion, and insufficient physical consistency—by introducing QCPIKAN, a hybrid quantum-classical architecture that integrates Chebyshev polynomial-based Kolmogorov–Arnold Network (KAN) layers with parameterized quantum circuits. To the best of our knowledge, this is the first framework to combine KANs with quantum computing for PDE solving, embedding physical constraints directly into the loss function. Theoretical analysis demonstrates exponential convergence of high-frequency errors, substantially mitigating numerical dispersion. Evaluated on three representative scenarios of flow through porous media, QCPIKAN consistently outperforms existing methods in global accuracy, local error control, dynamic evolution tracking, and front localization.
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Full waveform inversion method based on diffusion model
Full-waveform inversion (FWI) is highly nonlinear and sensitive to the initial model, often converging to local minima while neglecting the physical coupling between parameters such as velocity and density. To address these limitations, this work proposes a FWI method regularized by a conditional diffusion model, which— for the first time—incorporates two-dimensional density information as a conditional input into an enhanced U-Net backbone network to explicitly model the physical coupling between velocity and density. This approach significantly improves the resolution, structural fidelity, and robustness of inversion results, demonstrating superior stability and practical applicability in complex geological scenarios.
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Evolving Error States: Failure-Aware Progressive Repair for Ultrasound Lesion Segmentation
为解决医学图像分割中稀疏和异质错误的问题，提出了一种基于动态错误状态演变的Failure-Aware Progressive Repair方法，通过迭代修正提高复杂情况下的准确性。
0 citationsRead paper
Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations
This work addresses the challenges of insufficient accuracy and difficulty in satisfying structural constraints when solving α-cut-based fuzzy partial differential equations. The authors propose QCPIKAN, a quantum-classical hybrid physics-informed network that takes spatiotemporal coordinates and membership degrees as inputs to jointly approximate the upper and lower bounds of α-cuts, while embedding governing equations, initial/boundary conditions, and fuzzy structural constraints for end-to-end training. By innovatively integrating parameterized quantum circuits with ChebyKAN modules, they establish a unified error analysis framework and prove that, under sufficient quantum entanglement gain, QCPIKAN achieves a tighter prior error bound than its classical counterpart. Numerical experiments demonstrate that QCPIKAN reduces the average relative L² error by 1.1–2.7 times and decreases wavefront location error by approximately 1.77 times across elliptic, parabolic, and hyperbolic fuzzy PDEs, significantly enhancing solution accuracy.
0 citationsRead paper
GeoRouteNet: Geometry-Enhanced Non-Autoregressive Neural Solver for the Traveling Salesman Problem
This work addresses the limited cross-scale and cross-distribution generalization of non-autoregressive neural solvers for the Traveling Salesman Problem (TSP), which stems from insufficient geometric inductive bias and unstable training signals. To overcome these limitations, the authors propose GeoRouteNet, a novel architecture that enhances geometric representation through centralized node features, learnable radial distance basis functions, and a distance-aware graph attention mechanism. Training stability is further improved via Multi-Candidate Self-comparative Reinforcement Learning (MCS-RL). The model achieves state-of-the-art optimality gaps of 0.32% and 1.26% on TSP50 and TSP100, respectively, and reduces the average optimality gap on TSPLIB EUC_2D instances from 17.12% to 3.60%. Moreover, GeoRouteNet demonstrates significantly higher batch inference throughput compared to Concorde and LKH3.
0 citationsRead paper
Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
This work addresses persistent challenges in solving partial differential equations (PDEs)—notably slow convergence of high-frequency errors, severe numerical dispersion, and insufficient physical consistency—by introducing QCPIKAN, a hybrid quantum-classical architecture that integrates Chebyshev polynomial-based Kolmogorov–Arnold Network (KAN) layers with parameterized quantum circuits. To the best of our knowledge, this is the first framework to combine KANs with quantum computing for PDE solving, embedding physical constraints directly into the loss function. Theoretical analysis demonstrates exponential convergence of high-frequency errors, substantially mitigating numerical dispersion. Evaluated on three representative scenarios of flow through porous media, QCPIKAN consistently outperforms existing methods in global accuracy, local error control, dynamic evolution tracking, and front localization.
0 citationsRead paper
Full waveform inversion method based on diffusion model
Full-waveform inversion (FWI) is highly nonlinear and sensitive to the initial model, often converging to local minima while neglecting the physical coupling between parameters such as velocity and density. To address these limitations, this work proposes a FWI method regularized by a conditional diffusion model, which— for the first time—incorporates two-dimensional density information as a conditional input into an enhanced U-Net backbone network to explicitly model the physical coupling between velocity and density. This approach significantly improves the resolution, structural fidelity, and robustness of inversion results, demonstrating superior stability and practical applicability in complex geological scenarios.
0 citationsRead paper