Physics-Augmented Neural Networks for Constitutive Modeling: Toward an Application for Structural Health Monitoring

Structural health monitoring is now using both detailed physical simulations and live sensor data. Purely data‑driven models often have high variance and need a lot of data, while traditional physics‑based models can be biased because they rely on simplifying assumptions. To overcome these problems, this research looks at a hybrid approach that mixes physics‑augmented neural networks with a bias‑aware modified Constitutive Relation Error (mCRE) formulation. The method enforces solid physical rules—like mechanical equilibrium and thermodynamic limits—while allowing flexibility in parts that are less certain, such as experimental measurements and complex material laws. The hybrid framework combines the mCRE formulation with a Modified Dual Kalman Filter (MDKF) algorithm. This lets the

system estimate states and parameters in real time from dynamic strain measurements. As a result, the approach offers a reliable way to monitor structures and accurately reconstruct internal stress‑strain fields even when operating conditions are uncertain. The implementation guide walks students through: – building the hybrid loss functions, – integrating the MDKF algorithm, and – validating the physics‑augmented neural network using simulated scenarios of structural degradation.

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