# Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2410.01340 · HTML: https://mlsanity.com/paper/2410.01340/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 76 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [Correcting model misspecification in physics-informed neural networks (PINNs)](https://mlsanity.com/paper/2310.10776/) (2023)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification](https://mlsanity.com/paper/2402.15115/) (2024)
- [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [A Latent Restoring Force Approach to Nonlinear System Identification](https://mlsanity.com/paper/2109.10681/) (2021)
- [BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo](https://mlsanity.com/paper/2408.08062/) (2024)
- [Bayesian Hidden Physics Models: Uncertainty Quantification for Discovery of Nonlinear Partial Differential Operators from Data](https://mlsanity.com/paper/2006.04228/) (2020)
- [Sequential Bayesian Inference for Uncertain Nonlinear Dynamic Systems: A Tutorial](https://mlsanity.com/paper/2201.08180/) (2022)
- [Physics Enhanced Artificial Intelligence](https://mlsanity.com/paper/1903.04442/) (2019)
- [Deep learning for solution and inversion of structural mechanics and vibrations](https://mlsanity.com/paper/2105.09477/) (2021)

## Built on by (most cited first, 4 of 4)

- [Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimation](https://mlsanity.com/paper/2502.20772/) (2025)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [LLM-Based Test Oracles: Source-of-Authority Taxonomy -- A Systematic Literature Review](https://mlsanity.com/paper/2607.05031/) (2026)
- [PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems](https://mlsanity.com/paper/2606.04290/) (2026)

## Abstract (arXiv)

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.