# InVAErt networks: a data-driven framework for model synthesis and identifiability analysis

arXiv: https://arxiv.org/abs/2307.12586 · HTML: https://mlsanity.com/paper/2307.12586/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 68 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [Solving Bayesian Inverse Problems via Variational Autoencoders](https://mlsanity.com/paper/1912.04212/) (2019)
- [PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations](https://mlsanity.com/paper/2203.11363/) (2022)
- [Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2210.03008/) (2022)

## Built on by (most cited first, 6 of 6)

- [FUSE: Fast Unified Simulation and Estimation for PDEs](https://mlsanity.com/paper/2405.14558/) (2024)
- [Disentangled Representation Learning for Parametric Partial Differential Equations](https://mlsanity.com/paper/2410.02136/) (2024)
- [InVAErt networks for amortized inference and identifiability analysis of lumped parameter hemodynamic models](https://mlsanity.com/paper/2408.08264/) (2024)
- [Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics](https://mlsanity.com/paper/2512.13919/) (2025)
- [Synthetic Flight Data Generation Using Generative Models](https://mlsanity.com/paper/2604.20293/) (2026)
- [Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks](https://mlsanity.com/paper/2605.04134/) (2026)

## Abstract (arXiv)

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system synthesis including model inversion and identifiability. We introduce inVAErt (pronounced "invert") networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally investigate the selection of penalty coefficients in the loss function and strategies for latent space sampling, since we find that these significantly affect both training and testing performance. We validate our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.