# Physics-informed deep generative models

arXiv: https://arxiv.org/abs/1812.03511 · HTML: https://mlsanity.com/paper/1812.03511/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2018.

## Built on by (most cited first, 16 of 16)

- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors](https://mlsanity.com/paper/2203.03048/) (2022)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Artificial Intelligence and Generative Models for Materials Discovery -- A Review](https://mlsanity.com/paper/2508.03278/) (2025)
- [HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions](https://mlsanity.com/paper/2509.05117/) (2025)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions](https://mlsanity.com/paper/2206.05183/) (2022)
- [Dream to Adapt: Meta Reinforcement Learning by Latent Context Imagination and MDP Imagination](https://mlsanity.com/paper/2311.06673/) (2023)
- [AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning](https://mlsanity.com/paper/2401.15948/) (2024)
- [LatentPINNs: Generative physics-informed neural networks via a latent representation learning](https://mlsanity.com/paper/2305.07671/) (2023)
- [CausalWrap: Model-Agnostic Causal Constraint Wrappers for Tabular Synthetic Data](https://mlsanity.com/paper/2603.02015/) (2026)
- [Semantically Adversarial Scenario Generation with Explicit Knowledge Guidance](https://mlsanity.com/paper/2106.04066/) (2021)
- [Knowledge-Integrated Informed AI for National Security](https://mlsanity.com/paper/2202.03188/) (2022)
- [Output-Constrained Decision Trees](https://mlsanity.com/paper/2405.15314/) (2024)

## Abstract (arXiv)

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep probabilistic models for modeling physical systems in which the cost of data acquisition is high and training data-sets are typically small. This provides a scalable framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations. We demonstrate the effectiveness of our approach through a canonical example in transport dynamics.