Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach

Jul 16, 2026

Upload by Aria

Target-guided selective reweighting is developed for physics-informed neural networks (PINNs) applied to PDE inverse problems via transfer learning. The work addresses instability and ill-posedness in PINN training, where multi-component loss terms (PDE residuals, boundary/initial conditions, and observation errors) scale and converge unevenly, and where multiparameter inversion can yield visually accurate fields but inaccurate parameters. It further evaluates transfer learning by target parameter recovery quality, not only field error or training speed, and introduces a selective soft-decay reweighting strategy for improved parameter inversion robustness.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

Introduction

Physics-informed neural networks for PDE forward and inverse problems

Training instability and ill-posedness in inverse PINNs

Existing stabilization methods

Need for transfer learning evaluation via parameter recovery

Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach Qian Hua , Bin Fana,∗, Yao Xiaoa , Zhicheng Lina , Meixin Xionga a School of Computing and Data Science, Fujian University of Technology, 350118 Fuzhou, Fujian, China arXiv :2607 .05271v1 Keywords: Physics-informed neural networks, Partial differential equation inverse problems, Transfer learning, Negative transfer, Selective soft decay, Parameter inversion 1. Introduction Partial differential equations (PDEs) are fundamental mathematical tools for describing continuous physical systems, widely used in fluid mechanics, heat and mass transfer, elasticity, electromagnetic fields, reaction–diffusion systems, and biomedical engineering. Classical numerical methods, such as finite difference, finite element, and finite volume methods, have established mature theoretical and engineering frameworks for solving PDE forward problems. These methods typically require known governing equations, boundary conditions, and physical parameters, and solve for the target physical field through mesh discretization. However, in many practical engineering scenarios, researchers face not only forward problems but also inverse problems that require inferring unknown material properties, diffusion coefficients, velocity parameters, source terms, or boundary conditions from limited, sparse, or noisy observation data. Inverse problems are typically ill-posed and exhibit parameter correlations, where small errors in observational data may lead to significant fluctuations in inversion results, and different parameter combinations may produce similar physical field responses. Consequently, PDE inverse problems are not merely numerical solution tasks but also parameter ∗ Corresponding author Email address: [bfan@fjut.edu.cn](bfan@fjut.edu.cn) (Bin Fan) estimation problems influenced by observation noise, physical priors, and optimization procedures. Physics-informed neural networks provide a unified differentiable modeling framework for both forward and inverse PDE problems [1, 2] . PINNs approximate the unknown physical field using a neural network uθ (x, t) and compute PDE residuals through automatic differentiation, incorporating governing equations, initial conditions, boundary conditions, and observational data into the loss function. For inverse problems, unknown physical parameters can serve as trainable variables, optimized simultaneously with network weights and biases, thereby completing field reconstruction and parameter inversion within the same framework. Compared with purely data-driven models, PINNs leverage physical constraints to reduce reliance on large-scale labeled data and are applicable to scenarios with sparse or incomplete observations; meanwhile, the comparative advantages of PINNs over traditional methods such as finite elements in terms of accuracy, computational cost, and problem settings differ [3] . Subsequent research has further integrated PINNs into physics-informed machine learning and scientific machine learning frameworks, advancing their application to complex engineering problems [2, 4, 5] . Recent surveys have also summarized the development and challenges of PINNs from perspectives including loss function design, geometric modeling, and structural engineering applications [6, 7] . Despite their concise formulation and unified modeling advantages, PINN training is not inherently stable. The PINN loss function typically comprises multiple components—PDEresiduals, boundary conditions, initial conditions, and observational data errors—which may differ significantly in numerical scale, gradient direction, and convergence speed. Existing studies have analyzed PINN training difficulties and applicability conditions from perspectives of gradient pathology, neural tangent kernel, and theoretical convergence [8, 9, 10], and further identified that training failure modes and complex loss

FAQs

How should transfer learning for inverse problems be evaluated?

Transfer value should be judged by whether the transferred representation improves target physical parameter recovery quality, not merely by training speed or field error reduction. Negative transfer can degrade parameter inversion even if field accuracy improves.

Jul 16, 2026

Upload by Aria