Physics-Constrained Data-Driven Variational Method for Discrepancy Modeling.

Area of Science:

• Computational Mechanics
• Data-Driven Modeling
• Scientific Computing

Background:

• Physics-based models often struggle to incorporate real-world sensor data effectively.
• Discrepancies between theoretical models and experimental measurements are common in dynamical systems.
• Integrating measured data can improve model accuracy and predictive power.

Purpose of the Study:

• To present a novel data-driven discrepancy modeling (DDV) method.
• To demonstrate the variational embedding of measured data into a physics-based framework.
• To investigate the impact of data assimilation on the accuracy of dynamical system simulations.

Main Methods:

• Developed a data-driven discrepancy modeling method that variationally embeds measured data.
• Augmented physics-based models with a loss function derived from the residual between theory and measurements.
• Applied the method to linear elastodynamics, incorporating high-fidelity data from a subset of the domain.

Main Results:

• The DDV method successfully incorporated high-fidelity data into forward simulations.
• Analysis showed the method recovers the energy and fundamental frequency band of the target system.
• Strain and kinetic energy time histories were accurately recovered for a cantilever beam, even with an undamped model.

Conclusions:

• The data-driven discrepancy modeling method effectively integrates sparse measurement data.
• The approach enhances the accuracy of physics-based models by accounting for model discrepancies.
• This method offers a robust framework for analyzing dynamical systems with embedded sensor data.