Physics-Aware Latent-Space Surrogates Improve Parameter Calibration

Forward and inverse modeling of complex parametric dynamical systems, such as those in computational fluid dynamics, heavily relies on accurate surrogate models for both state prediction and parameter calibration. A significant gap exists in systematically integrating deep-learning-based reduced-order surrogates with end-to-end differentiable variational parameter estimation. This research addresses this by proposing a novel physics-aware neural-network-based latent-space framework. The core of the approach is an autoencoder-based surrogate that maps physical parameters to predicted flow fields via a latent representation. Crucially, observable supervision is incorporated during offline training. This ensures that the latent variables are explicitly encouraged to retain information highly correlated with the system parameters, rather than just focusing on reconstruction accuracy. The online inverse problem is then solved efficiently within the parameter space using the surrogate-induced observation operator. Evaluations on two computational fluid dynamics benchmarks demonstrate that mere reconstruction accuracy in surrogates is insufficient for effective inverse modeling, particularly due to a lack of end-to-end differentiability or physics awareness for parameter calibration. Quantitative analysis of the latent space further confirms that observable supervision significantly enhances case-level separability and temporal organization of latent representations. The framework also proves robust under realistic measurement conditions, including noisy, low-resolution, randomly masked, and block-wise partial observations, consistently reducing calibration error and variability compared to standard surrogate models.