mlsanityData to 7 Oct 2026

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

arXiv 2303.01055 ↗First posted 2 Mar 2023cs.LG cs.NA math.NAcited by 24

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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.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 13 of its 78 references that are in the map. First posted on arXiv 2 Mar 2023.

Builds on

13 of 78 references.

References · 13

  1. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  2. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  4. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  5. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  6. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
  7. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  8. 2017Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modelingcited by 130
  9. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 115
  10. 2020A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scalecited by 58
  11. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 37
  12. 2020Physics Guided Machine Learning Methods for Hydrologycited by 17
1 more
  1. 2021Physics-Guided Generative Adversarial Networks for Sea Subsurface Temperature Predictioncited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 9; 2025: 7; 2026: 5.

24 papers.

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  1. 2024Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plantscited by 11
  2. 2023Neural oscillators for generalization of physics-informed machine learningcited by 9
  3. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  4. 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
  5. 2023A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Mediacited by 7
  6. 2024Advancing Generalization in PINNs through Latent-Space Representationscited by 5
  7. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  8. 2024Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systemscited by 4
  9. 2024Magnetic Hysteresis Modeling with Neural Operatorscited by 3
  10. 2024Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beamscited by 2
  11. 2024Adaptive Runge-Kutta Dynamics for Spatiotemporal Predictioncited by 1
  12. 2025Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networkscited by 1
12 more
  1. 2025A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beamcited by 1
  2. 2024Quantitative Analysis of Molecular Transport in the Extracellular Space Using Physics-Informed Neural Networkcited by 0
  3. 2024Physics-Informed Neural Network Based Digital Image Correlation Methodcited by 0
  4. 2025MeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generationcited by 0
  5. 2025Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracycited by 0
  6. 2025Toward using explainable data-driven surrogate models for treating performance-based seismic design as an inverse engineering problemcited by 0
  7. 2025Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Weldingcited by 0
  8. 2026Dual-Level Models for Physics-Informed Multi-Step Time Series Forecastingcited by 0
  9. 2026Meta-Inverse Physics-Informed Neural Networks for High-Dimensional Ordinary Differential Equationscited by 0
  10. 2026Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solverscited by 0
  11. 2026Curvature-aware dynamic precision approach for physics-informed neural networkscited by 0
  12. 2026Wrong Operator or Blind Design? A Reference-Free Diagnostic for Physics-Informed Coefficient Learningcited by 0