# Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

arXiv: https://arxiv.org/abs/2608.11435 · HTML: https://mlsanity.com/paper/2608.11435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations](https://mlsanity.com/paper/2103.06183/) (2021)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Grasping Extreme Aerodynamics on a Low-Dimensional Manifold](https://mlsanity.com/paper/2305.08024/) (2023)
- [Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations](https://mlsanity.com/paper/2408.00157/) (2024)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2503.16678/) (2025)
- [State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics](https://mlsanity.com/paper/2407.21314/) (2024)
- [Mechanics-Informed Autoencoder Enables Automated Detection and Localization of Unforeseen Structural Damage](https://mlsanity.com/paper/2402.15492/) (2024)
- [Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids](https://mlsanity.com/paper/2407.10732/) (2024)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)
- [A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2504.02459/) (2025)
- [Adversarial autoencoders and adversarial LSTM for improved forecasts of urban air pollution simulations](https://mlsanity.com/paper/2104.06297/) (2021)
- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)
- [Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models](https://mlsanity.com/paper/2409.05709/) (2024)
- [Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs](https://mlsanity.com/paper/2411.05486/) (2024)
- [Estimating Varying Parameters in Dynamical Systems: A Modular Framework Using Switch Detection, Optimization, and Sparse Regression](https://mlsanity.com/paper/2412.16198/) (2024)

## Abstract (arXiv)

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.