# Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios

arXiv: https://arxiv.org/abs/2205.07731 · HTML: https://mlsanity.com/paper/2205.07731/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2022.

## Built on by (most cited first, 30 of 46)

- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws](https://mlsanity.com/paper/2401.07364/) (2024)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks](https://mlsanity.com/paper/2308.12716/) (2023)
- [A practical PINN framework for multi-scale problems with multi-magnitude loss terms](https://mlsanity.com/paper/2308.06672/) (2023)
- [A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains](https://mlsanity.com/paper/2405.12465/) (2024)
- [Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation](https://mlsanity.com/paper/2502.00782/) (2025)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations](https://mlsanity.com/paper/2404.00074/) (2024)
- [Sub-Sequential Physics-Informed Learning with State Space Model](https://mlsanity.com/paper/2502.00318/) (2025)
- [Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning](https://mlsanity.com/paper/2401.02810/) (2024)
- [Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)](https://mlsanity.com/paper/2406.03172/) (2024)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [Physics Informed Neural Network for Dynamic Stress Prediction](https://mlsanity.com/paper/2211.16190/) (2022)
- [Challenges and opportunities for machine learning in multiscale computational modeling](https://mlsanity.com/paper/2303.12261/) (2023)
- [Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations](https://mlsanity.com/paper/2407.10836/) (2024)
- [Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data](https://mlsanity.com/paper/2212.07723/) (2022)
- [Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations](https://mlsanity.com/paper/2401.02363/) (2024)
- [iPINNs: Incremental learning for Physics-informed neural networks](https://mlsanity.com/paper/2304.04854/) (2023)
- [Solving Differential Equations with Constrained Learning](https://mlsanity.com/paper/2410.22796/) (2024)
- [Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs](https://mlsanity.com/paper/2412.05719/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filter](https://mlsanity.com/paper/2506.00731/) (2025)
- [ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance](https://mlsanity.com/paper/2509.09611/) (2025)
- [A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials](https://mlsanity.com/paper/2605.31231/) (2026)
- [Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics](https://mlsanity.com/paper/2412.09453/) (2024)
- [Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulence](https://mlsanity.com/paper/2504.15487/) (2025)

## Abstract (arXiv)

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial differential equations (PDEs) via embedding physical laws into the loss function. Many inverse problems can be tackled by simply combining the data from real life scenarios with existing PINN algorithms. In this paper, we present a multi-task learning method using uncertainty weighting to improve the training efficiency and accuracy of PINNs for inverse problems in linear elasticity and hyperelasticity. Furthermore, we demonstrate an application of PINNs to a practical inverse problem in structural analysis: prediction of external loads of diverse engineering structures based on limited displacement monitoring points. To this end, we first determine a simplified loading scenario at the offline stage. By setting unknown boundary conditions as learnable parameters, PINNs can predict the external loads with the support of measured data. When it comes to the online stage in real engineering projects, transfer learning is employed to fine-tune the pre-trained model from offline stage. Our results show that, even with noisy gappy data, satisfactory results can still be obtained from the PINN model due to the dual regularization of physics laws and prior knowledge, which exhibits better robustness compared to traditional analysis methods. Our approach is capable of bridging the gap between various structures with geometric scaling and under different loading scenarios, and the convergence of training is also greatly accelerated through not only the layer freezing but also the multi-task weight inheritance from pre-trained models, thus making it possible to be applied as surrogate models in actual engineering projects.