arXiv subjects

Zhuojia Fu

Publications and source records attributed to Zhuojia Fu.

14 recordsLinked to original sources

arXiv2026

Multi-Partitioned Computing Quantum-Particle Approach: A Hybrid Quantum Framework for Fluid Flow

This study established a quantum-classical hybrid framework that integrates quantum computing paradigm with meshfree finite particle method. By harnessing quantum superposition and entanglement, it hybridized the critical computational kernels (termed as quantum finite particle method). A resource-efficient quantum computational strategy on multi-partitioned zones was proposed, which leverages a fixed small-scale quantum circuit as a fundamental processing unit to handle inner product for arbitrarily sized arrays. This approach employs iterative nesting of the quantum-core operation to accommodate varying input dimensions while maintaining hardware feasibility throughout. Motivated with developed quantum framework, the novel numerical discretization for hybrid quantum computational particle dynamics can be derived commonly and applied in fluid flows. Through a sequence of numerical experiments purposefully, the proposed numerical model was thoroughly validated and analyzed. Results demonstrate that integrating quantum computing to hybridize conventional linear combinations of particle dynamics serves as a novel computing paradigm. By further extending into the numerical investigation of viscoelastic, highly elastic, and purely elastic fluids under high Weissenberg number conditions, the applicability of simulation framework is broadened. Despite bottlenecks in quantum hardware and computational efficiency on this process, these advances offer critical insights for transitioning quantum-enhanced fluid simulation to practical engineering applications.

physics.flu-dyn↗

arXiv2026

PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function

This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture. Unlike traditional neural operators such as DeepONet, which rely on deep networks to implicitly learn basis functions, PIKFNO constrains the trunk network through physics informed kernel functions, thereby aligning its operator structure with the kernel expansions used in meshless collocation methods. Two construction strategies are introduced: one learns kernel functions directly from data, where the learned kernel can be regarded as a nonsingular fundamental solution, while the other builds them through transformations of analytical fundamental solutions. Numerical experiments demonstrate that PIKFNO achieves high predictive accuracy with substantially improved interpretability and superior generalization under limited training data. The proposed framework offers a new pathway for developing efficient, physically consistent, and interpretable neural operators.

cs.LG↗

arXiv2026

An improved PINN framework integrating localized collocation scheme and PIKF

We propose a localized physics-informed kernel function neural network (LPIKFNN), which is an improved physics-informed neural network (PINN) based on physics-informed kernel function (PIKF). In the LPIKFNN framework, the localized collocation scheme discretizes the physical quantities within the local domain, where the physical field is represented as a linear combination of PIKFs. Based on this representation, the multilayer perceptron is trained to iteratively learn the physical quantities. To overcome the computational challenges of conventional PINN in higher-order derivative and high wavenumber problems, the LPIKFNN constructs the loss function using the PIKF and a localized collocation scheme rather than relying on automatic differentiation. As a result, the costly derivative evaluations required to enforce governing equations during iterative training are eliminated, leading to significantly improved computational efficiency and training performance. Moreover, incorporating PIKFs into the loss function enables the proposed LPIKFNN to significantly improve computational accuracy in high-wavenumber problems characterized by highly oscillatory physical fields. To overcome the computational bottleneck of the physics-informed kernel function neural network (PIKFNN) in heterogeneous problems, the LPIKFNN introduces a localized collocation scheme that removes reliance on global PIKFs, enabling accurate predictions where global PIKFs are unavailable. The feasibility and accuracy of the proposed LPIKFNN are demonstrated through a series of benchmark studies, including high wavenumber problems, higher-order derivative problems, nonlinear problems, heterogeneous problems, and potential-based inverse electromyography. The numerical predictions obtained by LPIKFNN show excellent agreement with available analytical solutions and experimental measurements.

cs.CE↗

arXiv2026

Mapping-based Hard-constrained Physics-Informed Neural Networks for unbounded wave problems

The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that compactifies the infinite physical domain into a finite computational space. This effectively resolves the sampling difficulties inherent to standard PINNs in unbounded regions. Additionally, it avoids the artificial truncation errors introduced by traditional methods such as perfectly matched layers. Second, we design a physics-based hard-constrained network structure that automatically satisfies both the inner boundary conditions and the far-field radiation conditions. This structure eliminates boundary loss terms, yielding high computational efficiency and fast convergence, which effectively addresses the challenges of high-frequency problems. Third, we introduce an inverse factor correction for boundary coefficients to address the influence of asymptotic factors,which makes the method highly geometrically adaptable. Finally, we present numerical examples covering various acoustic radiation and scattering scenarios as well as elastic dynamics scenarios to demonstrate the efficiency and accuracy of our algorithm.It highlights its potential for broader applications in the field of computational wave dynamics.

math.NA↗

arXiv2026

Virtual boundary integral neural network for three-dimensional exterior acoustic problems

This paper presents a virtual boundary integral neural network (VBINN) for exterior acoustic problems in three dimensions. The method introduces a virtual boundary inside the scatterer or vibrating body and represents the associated source density with a neural network. Coupled with the acoustic fundamental solution, this representation satisfies the Sommerfeld radiation condition by construction and enables direct evaluation of the acoustic pressure and its normal derivative at arbitrary field points. Because the integration surface is separated from the physical boundary, the formulation avoids the singular and near singular kernel evaluations associated with coincident source and collocation points in conventional boundary integral learning methods. To reduce sensitivity to boundary placement, the geometric parameters of the virtual boundary are optimized jointly with the source density during training. Numerical examples for acoustic scattering, multiple body interaction, and underwater acoustic propagation show close agreement with analytical solutions and COMSOL results, and the Burton Miller extension further improves stability near characteristic frequencies. These results demonstrate the potential of VBINN for exterior acoustic analysis in three dimensions.

cs.SD↗

arXiv2026

Quantum AS-DeepOnet: Quantum Attentive Stacked DeepONet for Solving 2D Evolution Equations

DeepONet enables retraining-free inference across varying initial conditions or source terms at the cost of high computational requirements. This paper proposes a hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D evolution equations. By combining Parameterized Quantum Circuits and cross-subnet attention methods, we can solve 2D evolution equations using only 60% of the trainable parameters while maintaining accuracy and convergence comparable to the classical DeepONet method.

quant-ph↗

arXiv2025

Fatigue reliability analysis of offshore wind turbines under combined wind-wave excitation via DPIM

As offshore wind turbines develop into deepwater operations, accurately quantifying the impact of stochastic excitations in complex sea environments on offshore wind turbines and conducting structural fatigue reliability analysis has become challenging. In this paper, based on long-term wind-wave reanalysis data from a site in the South China Sea, a novel direct probability integral method (DPIM) is developed for the stochastic response and fatigue reliability analyses of the key components for the floating offshore wind turbine structures under combined wind-wave excitation. A 5MW floating offshore wind turbine is considered as the research object, and a fully coupled dynamic response analysis of the wind turbine system is conducted to calculate the short-term fatigue damage value of tower base and blade root. The DPIM is applied to calculate the fatigue reliability of the wind turbine structure. The accuracy and efficiency of the proposed method are validated by comparing the obtained results with those of Monte Carlo simulations. Furthermore, the results indicate that the fatigue life of floating offshore wind turbine structures under combined wind-wave excitation meets the design requirements. Notably, the fatigue reliability of the wind turbine under aligned wind-wave condition is lower compared to misaligned wind-wave condition.

math.NA↗

arXiv2025

Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks

This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.

cs.LG↗

arXiv2024

A physics-driven sensor placement optimization methodology for temperature field reconstruction

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.

cs.LG↗

arXiv2023

FEM-PIKFNNs for underwater acoustic propagation induced by structural vibrations in different ocean environments

In this paper, a novel hybrid method based on the finite element method (FEM) and physics-informed kernel function neural networks (PIKFNNs) is proposed and applied to the prediction of underwater acoustic propagation induced by structural vibrations in the unbounded ocean, deep ocean and shallow ocean. In the hybrid method, PIKFNNs are a class of improved shallow physics-informed neural networks (PINNs) that replace the activation functions in PINNs with the physics-informed kernel functions (PIKFs), thereby integrating prior physical information into the neural network model. Moreover, this neural network circumvents the step of embedding the governing equations into the loss function in PINNs, and requires only training on boundary data. By using the Green's functions as the PIKFs and the structural-acoustic coupling response information obtained from the FEM as boundary training data, the PIKFNNs can inherently capture the Sommerfeld radiation condition at infinity, which is naturally suitable for predicting ocean acoustic propagation. Numerical experiments demonstrate the accuracy and feasibility of the FEM-PIKFNNs in comparison with the true solutions and finite element results.

math.NA↗

arXiv2023

Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces

This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or inclusions.

math.NA↗

arXiv2023

Physics-Informed Kernel Function Neural Networks for Solving Partial Differential Equations

This paper proposed a novel radial basis function neural network (RBFNN) to solve various partial differential equations (PDEs). In the proposed RBF neural networks, the physics-informed kernel functions (PIKFs), which are derived according to the governing equations of the considered PDEs, are used to be the activation functions instead of the traditional RBFs. Similar to the well-known physics-informed neural networks (PINNs), the proposed physics-informed kernel function neural networks (PIKFNNs) also include the physical information of the considered PDEs in the neural network. The difference is that the PINNs put this physical information in the loss function, and the proposed PIKFNNs put the physical information of the considered governing equations in the activation functions. By using the derived physics-informed kernel functions satisfying the considered governing equations of homogeneous, nonhomogeneous, transient PDEs as the activation functions, only the boundary/initial data are required to train the neural network. Finally, the feasibility and accuracy of the proposed PIKFNNs are validated by several benchmark examples referred to high-wavenumber wave propagation problem, infinite domain problem, nonhomogeneous problem, long-time evolution problem, inverse problem, spatial structural derivative diffusion model, and so on.

math.NA↗

arXiv2021

Physics-informed Neural Networks for Elliptic Partial Differential Equations on 3D Manifolds

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the deep learning-based techniques. Based on the data and physical models, PINNs introduce the standard feedforward neural networks (NNs) to approximate the solutions to the PDE systems. By using automatic differentiation, the PDEs system could be explicitly encoded into NNs and consequently, the sum of mean squared residuals from PDEs could be minimized with respect to the NN parameters. In this study, the residual in the loss function could be constructed validly by using the automatic differentiation because of the relationship between the surface differential operators $\nabla_S/Δ_S$ and the standard Euclidean differential operators $\nabla/Δ$. We first consider the unit sphere as surface to investigate the numerical accuracy and convergence of the PINNs with different training example sizes and the depth of the NNs. Another examples are provided with different complex manifolds to verify the robustness of the PINNs.

math.NA↗

arXiv2017

A scale-dependent finite difference method for time fractional derivative relaxation type equations

Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of fractional dynamic systems, this paper proposes a scale-dependent finite difference method (S-FDM) in which the non-uniform mesh depends on the time fractional derivative order of FRE. The purpose is to establish a stable numerical method with low computation cost for FREs by making a bridge between the fractional derivative order and space-time discretization steps. The proposed method is proved to be unconditional stable with (2-α)-th convergence rate. Moreover, three examples are carried out to make a comparison among the uniform difference method, common non-uniform method and S-FDM in term of accuracy, convergence rate and computational costs. It has been confirmed that the S-FDM method owns obvious advantages in computational efficiency compared with uniform mesh method, especially for long-time range computation (e.g. the CPU time of S-FDM is ~1/400 of uniform mesh method with better relative error for time T=500 and fractional derivative order alpha=0.4).

math.NA↗