# LatentPINNs: Generative physics-informed neural networks via a latent representation learning

arXiv: https://arxiv.org/abs/2305.07671 · HTML: https://mlsanity.com/paper/2305.07671/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 57 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems](https://mlsanity.com/paper/2205.08304/) (2022)
- [Seismic wave propagation and inversion with Neural Operators](https://mlsanity.com/paper/2108.05421/) (2021)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Meta-Auto-Decoder for Solving Parametric Partial Differential Equations](https://mlsanity.com/paper/2111.08823/) (2021)
- [A novel meta-learning initialization method for physics-informed neural networks](https://mlsanity.com/paper/2107.10991/) (2021)
- [L-HYDRA: Multi-Head Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.02152/) (2023)
- [Variational Autoencoding Neural Operators](https://mlsanity.com/paper/2302.10351/) (2023)
- [Efficient physics-informed neural networks using hash encoding](https://mlsanity.com/paper/2302.13397/) (2023)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs](https://mlsanity.com/paper/2303.14878/) (2023)
- [Learning in latent spaces improves the predictive accuracy of deep neural operators](https://mlsanity.com/paper/2304.07599/) (2023)

## Built on by (most cited first, 5 of 5)

- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields](https://mlsanity.com/paper/2502.17134/) (2025)
- [Variational Rank Reduction Autoencoders for Generative Thermal Design](https://mlsanity.com/paper/2509.08515/) (2025)
- [Latent PDE mapping for efficient physics-informed learning across geometries with limited data](https://mlsanity.com/paper/2607.22215/) (2026)
- [Staged Depth Training: A Representation Curriculum for PINNs](https://mlsanity.com/paper/2609.30299/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence and the need to perform additional, potentially expensive, training for different PDE parameters. To solve this limitation, we introduce latentPINN, a framework that utilizes latent representations of the PDE parameters as additional (to the coordinates) inputs into PINNs and allows for training over the distribution of these parameters. Motivated by the recent progress on generative models, we promote the use of latent diffusion models to learn compressed latent representations of the PDE parameters distribution and act as input parameters to NN functional solutions. We use a two-stage training scheme in which the first stage, we learn the latent representations for the distribution of PDE parameters. In the second stage, we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters. We test the approach on a class of level set equations given by the nonlinear Eikonal equation. We specifically share results corresponding to three different sets of Eikonal parameters (velocity models). The proposed method performs well on new phase velocity models without the need for any additional training.