Physics-informed Neural Networks for Structural Dynamics

**Physics-Informed Neural Networks for Structural Dynamics**:

- Réf **ABG-132123**
- Sujet de Thèse
- 21/05/2025
- Contrat doctoral
- FEMTO-ST institute
- Lieu de travail- Besançon - Bourgogne-Franche-Comté - France
- Intitulé du sujet- Physics-Informed Neural Networks for Structural Dynamics
- Champs scientifiques- Sciences de l’ingénieur
- Mots clés- Structural Dynamics, vibration, Neural Networks

**Description du sujet**:
Physics-Informed Neural Networks (PINNs) have emerged as a paradigm for solving forward and inverse problems in computational mechanics by integrating physical laws directly into the learning process. Recently reintroduced by Raissi et al. (2019), PINNs enforce governing equations, typically partial differential equations (PDEs), as constraints in the neural network loss function, enabling the use of sparse or indirect data to infer system behavior.

In structural dynamics and vibroacoustics, which deal with the response of mechanical systems to dynamic loading, the accurate prediction and identification of structural behavior are often computationally intensive. These problems involve solving complex-valued formulations of elastodynamic and acoustic PDEs. Conventional solvers like the finite element method (FEM) face limitations due to meshing costs, high-dimensional parameter spaces, and sensitivity to input uncertainty, especially in inverse problems such as material identification, force reconstruction, or damage localization.

Recent studies have demonstrated the applicability of PINNs to dynamic problems in solid and structural mechanics. Chen and Ghaboussi (2022) proposed a PINN-based approach for inverse problems in structural dynamics, showing that PINNs can infer boundary conditions and system parameters from vibrational responses. Haghighat et al. (2022) tackled frequency-domain wave propagation using PINNs and identified critical challenges such as accuracy degradation at high frequencies. Extensions of the framework, such as complex-valued PINNs or frequency-domain formulations (Zhang et al., 2023), have shown promise in addressing these challenges by adapting the architecture and loss formulation to better capture oscillatory solutions. More recently, a significant step forward has been taken with the possibility of identifying non-homogeneous properties and even damping properties of heterogeneous beams (Teloli et al., 2025).

In the context of inverse problems, PINNs have shown strong performance in recovering unknown fields (e.g., material parameters or input forces) using only partial observations. Rao et al. (2021), Xu et al. (2021), Teloli et al. (2025) developed PINN models for dynamic elastodynamic inverse problems, material characterization, and damping identification, respectively. These works highlight the capacity of PINNs to generalize across different loading conditions and frequencies, making them particularly suited for structural health monitoring and system identification in complex systems.
- The proposed PhD research aims to extend the capabilities of PINNs in structural dynamics and vibroacoustic problems. This includes:

- Developing complex-valued PINN architectures tailored for frequency-domain PDEs,
- Addressing high-frequency limitations through domain decomposition, adaptive sampling, or hybrid methods combining PINNs with traditional solvers,
- References

**Prise de fonction**:

- 01/10/2025

**Nature du financement**:

- Contrat doctoral

**Précisions sur le financement**:
**Présentation établissement et labo d'accueil**:

- FEMTO-ST institute

See website

**Site web**:
**Intitulé du doctorat**:

- Doctorat de mécanique

**Pays d'obtention du doctorat**:

- France

**Etablissement délivrant le doctorat**:

- SUPMICROTECH

**Ecole doctorale**:

- Sciences physiques pour l'ingénieur et microtechniques - SPIM- 15/06/2025