Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs

• URL: http://arxiv.org/abs/2606.20326v2
• Date: Sun, 21 Jun 2026 02:30:32 GMT
• Title: Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
• Abstract summary: We develop QCPIKAN, the first quantum-classical physics-informed network designed to solve partial differential equations (PDEs)<n>Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency.<n>Compared with existing quantum-classical physics-informed neural networks, QCPIKAN achieves superior performance in global prediction accuracy, local error control, dynamic evolution tracking and displacement front localization.
• Score: 1.5469452301122175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios in porous media, including single-phase flow, component transport and two-phase flow. Compared with existing quantum-classical physics-informed neural networks, QCPIKAN achieves superior performance in global prediction accuracy, local error control, dynamic evolution tracking and displacement front localization. This work provides a robust and efficient alternative for solving complex PDEs.

Related papers

• The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics [46.539149169728624]
  We introduce the Kuramoto Neural Operator (KNO), which represents the solution through the evolution of a latent field of interacting oscillators.<n>KNO achieves strong predictive performance, with improvements over competing approaches.
  arXiv  Detail & Related papers  (2026-08-10T21:11:58Z)
• Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations [1.5469452301122175]
  We propose a quantum-classical hybrid physics-informed computational framework for fuzzy partial differential equations.<n>QCPIKAN captures the overall contraction of the solution interval as increases.<n>However, both models still exhibit local fuzzy-structure violations near boundaries, in high-gradient regions, and around the wavefront.
  arXiv  Detail & Related papers  (2026-08-09T16:01:03Z)
• Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics [0.0]
  Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs)<n>We present a hybrid quantum-classical framework that enhances Quantum PINNs through adaptive collocation point sampling and loss-aware attention mechanisms.
  arXiv  Detail & Related papers  (2026-08-01T20:11:21Z)
• Hybrid quantum-classical physics-informed neural networks for solving nonlinear PDEs: when and where hybridization is effective? [0.0]
  We develop a hybrid quantum-classical physics-informed neural network (HQPINN)<n>HQPINN integrates a classical neural-network backbone with a parameterized quantum circuit (PQC) to enrich the solution representation.<n>Results show that HQPINNs exhibit smoother training dynamics, reduced loss oscillations, and improved final accuracy.
  arXiv  Detail & Related papers  (2026-06-03T10:02:20Z)
• A Trainable-Embedding Quantum Physics-Informed Framework for Multi-Species Reaction-Diffusion Systems [1.7887197093662073]
  We study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion systems.<n>We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings.
  arXiv  Detail & Related papers  (2026-02-10T00:19:12Z)
• Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations [1.376408511310322]
  Solving partial differential equations (PDEs) for reservoir seepage is critical for optimizing oil and gas field development and predicting production performance.<n>Traditional numerical methods suffer from mesh-dependent errors and high computational costs, while classical Physics-Informed Neural Networks (PINNs) face bottlenecks in parameter efficiency, high-dimensional expression, and strong nonlinear fitting.<n>We propose a Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it to three typical reservoir seepage models for the first time.
  arXiv  Detail & Related papers  (2025-12-03T16:14:16Z)
• Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation [46.40087254928057]
  We present SPARK, a physics-guided quantitative augmentation plugin.<n>Experiments on diverse benchmarks demonstrate that SPARK significantly outperforms state-of-the-art baselines.
  arXiv  Detail & Related papers  (2025-10-28T09:30:35Z)
• Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators [37.65214107289304]
  We introduce a physics-informed neural operator framework for the lattice Boltzmann equation (LBE)<n>Our framework is discretization-invariant, enabling models trained on coarse lattices to generalise to finer ones.<n>Results demonstrate robustness across complex flow scenarios, including von Karman vortex shedding, ligament breakup, and bubble adhesion.
  arXiv  Detail & Related papers  (2025-09-26T14:36:23Z)
• PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations [4.7903561901859355]
  We present PhysicsCorrect, a training-free correction framework that enforces PDE consistency at each prediction step.<n>Our key innovation is an efficient caching strategy that precomputes the Jacobian and its pseudoinverse during an offline warm-up phase.<n>Across three representative PDE systems, PhysicsCorrect reduces prediction errors by up to 100x while adding negligible inference time.
  arXiv  Detail & Related papers  (2025-07-03T01:22:57Z)
• KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches [43.872190335490515]
  This paper introduces KITINet, a novel architecture that reinterprets feature propagation through the lens of non-equilibrium particle dynamics.<n>At its core, we propose a residual module that models update as the evolution of a particle system.<n>This formulation mimics particle collisions and energy exchange, enabling adaptive feature refinement via physics-informed interactions.
  arXiv  Detail & Related papers  (2025-05-23T13:58:29Z)
• KO: Kinetics-inspired Neural Optimizer with PDE Simulation Approaches [45.173398806932376]
  This paper introduces KO, a novel neural gradient inspired by kinetic theory and partial differential equation (PDE) simulations.<n>We reimagine the dynamics of network parameters as the evolution of a particle system governed by kinetic principles.<n>This physics-driven approach inherently promotes parameter diversity during optimization, mitigating the phenomenon of parameter condensation.
  arXiv  Detail & Related papers  (2025-05-20T18:00:01Z)
• Multi-stream Physics Hybrid Networks for solving Navier-Stokes equations [36.136619420474766]
  Multi-stream Physics Hybrid Network is a novel neural architecture that integrates quantum and classical layers in parallel.<n>This approach decomposes the solution into separate frequency components, each predicted by independent Parallel Hybrid Networks.<n>Our results show that the Multi-stream Physics Hybrid Network achieves a reduction in root mean square error by 36% for velocity components and 41% for pressure prediction compared to the classical model.
  arXiv  Detail & Related papers  (2025-04-02T16:50:54Z)
• QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs [0.45880283710344066]
  Physics-informed neural networks (PINNs) have emerged as promising methods for solving partial differential equations (PDEs) by embedding physical laws within neural architectures.<n>We present a quantum-classical physics-informed neural network (QCPINN) that combines quantum and classical components, allowing us to solve PDEs with significantly fewer parameters while maintaining comparable accuracy and convergence to classical PINNs.
  arXiv  Detail & Related papers  (2025-03-20T19:52:26Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs)<n>We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations.<n>We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations [64.78260098263489]
  In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs) We show that PINNs eventually fail to produce correct solutions to these benchmarks as their complexity increases. We identify several reasons why this may be the case, including insufficient network capacity, poor conditioning of the ODEs, and high local curvature, as measured by the Laplacian of the PINN loss.
  arXiv  Detail & Related papers  (2022-10-14T15:01:32Z)

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.