Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures (2002.10253v1)

Abstract: This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific principles) into deep long short-term memory (LSTM) networks, which boosts the learning within a feasible solution space. The physics constraints are embedded in the loss function to enforce the model training which can accurately capture latent system nonlinearity even with very limited available training datasets. Specifically for dynamic structures, physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. In particular, two physics-informed multi-LSTM network architectures are proposed for structural metamodeling. The satisfactory performance of the proposed framework is successfully demonstrated through two illustrative examples (e.g., nonlinear structures subjected to ground motion excitation). It turns out that the embedded physics can alleviate overfitting issues, reduce the need of big training datasets, and improve the robustness of the trained model for more reliable prediction. As a result, the physics-informed deep learning paradigm outperforms classical non-physics-guided data-driven neural networks.

• The paper presents physics-informed multi-LSTM networks (PhyLSTM² and PhyLSTM³) that integrate physical laws into the training process.
• The paper shows improved accuracy in predicting displacement, velocity, and latent hysteretic variables compared to standard neural networks.
• The paper demonstrates reduced data dependency and enhanced generalizability, offering promising applications in complex structural metamodeling.

Analysis of Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures

The paper under discussion introduces a sophisticated physics-informed deep learning framework, centered around multi-long short-term memory (LSTM) networks, aimed at enhancing the metamodeling of nonlinear structural systems, especially under scenarios of limited data availability. The framework innovatively integrates laws of physics and scientific principles into LSTM networks, refining the learning process by embedding physics constraints into the loss function. This incorporation facilitates the accurate modeling of complex nonlinearities even when training datasets are sparse.

Methodological Advances

The primary innovation presented is the development of two architectures: the physics-reinforced double-LSTM (PhyLSTM²) and the physics-reinforced triple-LSTM (PhyLSTM³) networks. These architectures leverage physics inclusion via graph-based tensor differentiators to interconnect LSTM networks in modeling the dynamic behavior of nonlinear structures.

• PhyLSTM² is designed to capture rate-independent hysteresis, effectively predicting displacement and velocity, as well as latent variables such as hysteretic parameters and mass-normalized restoring forces without direct measurements.
• PhyLSTM³ extends this capability to systems with rate-dependent hysteresis, incorporating an additional LSTM network to accurately model the additional complexity introduced by rate dependencies.

Both architectures integrate deep neural networks with physics-guided training, enhancing generalizability and interpretability, crucial for metamodels intended for complex engineering systems.

Numerical Results

The efficacy of these models is demonstrated through numerical experiments involving a 3-story Moment Resisting Frame (MRF) and a single degree-of-freedom (SDOF) Bouc-Wen model representing a nonlinear hysteretic system. The results reveal that:

• Both PhyLSTM² and PhyLSTM³ outperform traditional non-physics-guided data-driven neural networks, with higher accuracy and robustness observed across various predictive tasks.
• PhyLSTM², due to its more parsimonious form, better models systems with rate-independent hysteresis, while PhyLSTM³ excels in capturing the dynamics of systems demonstrating rate-dependent hysteresis.
• The incorporation of physics allows these models to predict latent variables without requiring direct training data, representing a significant improvement over classical approaches.

Implications and Future Directions

The embedding of physics into machine learning frameworks like LSTM networks mitigates overfitting, reduces the necessity for large labeled datasets, and enhances the reliability of predictions in complex systems characterized by nonlinear behavior and limited data. As computational mechanics increasingly intersect with AI and machine learning, this physics-informed paradigm offers a promising direction for efficient structural response modeling, especially in fields where the fidelity and completeness of physical simulations are constrained.

Looking forward, this framework could be adapted and expanded for broader engineering applications beyond seismic metamodeling, including real-time monitoring, control systems, and predictive maintenance of civil infrastructure. The adaptability and robustness it offers may spur its application to model other types of physical systems governed by complex, nonlinear dynamics where incomplete data presents a central challenge. Continued progress in this direction will likely emphasize the symbiosis between evolving computational models and the underlying physical realities they aim to approximate.