Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

Forward and inverse modeling of parametric dynamical systems require surrogate models that are both accurate for state prediction and informative for parameter calibration. Traditional deep-learning reduced-order models rely purely on data reconstruction, meaning their latent spaces are not structured for parameter identification. Furthermore, standard approaches lack end-to-end differentiability or physics awareness, making them poorly suited for gradient-based variational data assimilation. This work addresses these gaps by developing a physics-aware neural-network latent-space framework that couples a reduced-order surrogate directly with variational parameter estimation.

The proposed framework introduces an observable-augmented convolutional autoencoder (OACAE) that maps physical parameters to predicted flow fields through a structured latent representation. During the offline training phase, an auxiliary multilayer perceptron branch supervises the latent space using known physical parameters and temporal indices, forcing the latent variables to retain information correlated with system dynamics. An additional parameter-to-latent regressor maps new physical parameters directly to the latent space. In the online phase, this differentiable surrogate acts as the observation operator within three-dimensional (3D-Var) and four-dimensional (4D-Var) variational data assimilation formulations, allowing direct gradient-based optimization of the control parameters.

Evaluated on two computational fluid dynamics benchmarks, the framework demonstrates that reconstruction accuracy alone is insufficient for inverse modeling. Quantitative latent-space analysis reveals that observable supervision significantly improves case-level separability and the temporal organization of latent representations. When tested under realistic, degraded measurement settings—such as noisy, low-resolution, randomly masked, and block-wise partial observations—the OACAE-based surrogate consistently outperforms standard autoencoder and POD-GPR baselines by reducing both calibration error and estimation variability.