# Physics-informed neural networks for solving forward and inverse problems in complex beam systems

arXiv: https://arxiv.org/abs/2303.01055 · HTML: https://mlsanity.com/paper/2303.01055/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 78 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 13 of 13)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs](https://mlsanity.com/paper/2006.16144/) (2020)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks](https://mlsanity.com/paper/2012.03133/) (2020)
- [Physics Guided Machine Learning Methods for Hydrology](https://mlsanity.com/paper/2012.02854/) (2020)
- [Physics-Guided Generative Adversarial Networks for Sea Subsurface Temperature Prediction](https://mlsanity.com/paper/2111.03064/) (2021)

## Built on by (most cited first, 24 of 24)

- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [Neural oscillators for generalization of physics-informed machine learning](https://mlsanity.com/paper/2308.08989/) (2023)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [BiLO: Bilevel Local Operator Learning for PDE Inverse Problems](https://mlsanity.com/paper/2404.17789/) (2024)
- [A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media](https://mlsanity.com/paper/2308.06436/) (2023)
- [Advancing Generalization in PINNs through Latent-Space Representations](https://mlsanity.com/paper/2411.19125/) (2024)
- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems](https://mlsanity.com/paper/2408.14951/) (2024)
- [Magnetic Hysteresis Modeling with Neural Operators](https://mlsanity.com/paper/2407.03261/) (2024)
- [Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beams](https://mlsanity.com/paper/2408.02698/) (2024)
- [Adaptive Runge-Kutta Dynamics for Spatiotemporal Prediction](https://mlsanity.com/paper/2405.14504/) (2024)
- [MeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generation](https://mlsanity.com/paper/2501.11937/) (2025)
- [Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks](https://mlsanity.com/paper/2503.20222/) (2025)
- [A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam](https://mlsanity.com/paper/2601.00866/) (2025)
- [Quantitative Analysis of Molecular Transport in the Extracellular Space Using Physics-Informed Neural Network](https://mlsanity.com/paper/2401.12435/) (2024)
- [Physics-Informed Neural Network Based Digital Image Correlation Method](https://mlsanity.com/paper/2409.00956/) (2024)
- [Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy](https://mlsanity.com/paper/2507.20929/) (2025)
- [Toward using explainable data-driven surrogate models for treating performance-based seismic design as an inverse engineering problem](https://mlsanity.com/paper/2508.00286/) (2025)
- [Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding](https://mlsanity.com/paper/2508.04595/) (2025)
- [Dual-Level Models for Physics-Informed Multi-Step Time Series Forecasting](https://mlsanity.com/paper/2601.07640/) (2026)
- [Meta-Inverse Physics-Informed Neural Networks for High-Dimensional Ordinary Differential Equations](https://mlsanity.com/paper/2605.03511/) (2026)
- [Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers](https://mlsanity.com/paper/2606.02623/) (2026)
- [Curvature-aware dynamic precision approach for physics-informed neural networks](https://mlsanity.com/paper/2606.04736/) (2026)
- [Wrong Operator or Blind Design? A Post-Training Diagnostic for Physics-Informed Coefficient Learning](https://mlsanity.com/paper/2608.16925/) (2026)

## Abstract (arXiv)

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler-Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher-order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e-3 percent error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space-time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.