https://github.com/Crunch-UQ4MI/neuraluq
https://github.com/Crunch-UQ4MI/neuraluq
Last synced: 15 days ago
JSON representation
- Host: GitHub
- URL: https://github.com/Crunch-UQ4MI/neuraluq
- Owner: Crunch-UQ4MI
- Created: 2022-08-24T07:48:06.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-02-24T01:38:39.000Z (about 1 year ago)
- Last Synced: 2024-08-02T14:06:16.445Z (9 months ago)
- Language: Python
- Size: 58.1 MB
- Stars: 150
- Watchers: 6
- Forks: 34
- Open Issues: 7
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
- awesome-scientific-machine-learning - `code`
README
# NeuralUQ
Scientific machine learning (SciML) has emerged recently as an effective and powerful tool for data fusion, solving ordinary/partial differential equations (ODEs, PDEs), and learning operator mappings in various scientific and engineering disciplines. Physics-informed neural networks ([PINNs](https://www.sciencedirect.com/science/article/pii/S0021999118307125)) and deep operator networks ([DeepONets](https://www.nature.com/articles/s42256-021-00302-5)) are two such models for solving ODEs/PDEs and learning operator mappings, respectively. Quantifying predictive uncertainties is crucial for risk-sensitive applications as well as for efficient and economical design. **NeuralUQ** is a Python library for uncertainty quantification in various SciML algorithms. In NeuralUQ, each UQ method is decomposed into a surrogate and an inference method for posterior estimation. NeuralUQ has included various surrogates and inference methods, i.e.,
- Surrogates
- Bayesian Neural Networks (BNNs)
- Deterministic Neural Networks, e.g., fully-connected neural networks (FNNs)
- Deep Generative Models, e.g., Generative Adversarial Nets (GANs)
- Inference Methods
- Sampling methods
- Hamiltonian Monte Carlo (HMC)
- Langevin Dynamics (LD)
- No-U-Turn (NUTS)
- Metropolis-adjusted Langevin algorithm (MALA)
- Variational Methods
- Mean-field Variational Inference (MFVI)
- Monte Carlo Dropout (MCD)
- Ensemble Methods
- Deep ensembles (DEns)
- Snapshot ensemble (SEns)
- Laplace approximation (LA)
Users can refer to this paper for the design and description, as well as the examples, of the NeuralUQ library:
- [NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators](https://epubs.siam.org/doi/pdf/10.1137/22M1518189)
Users can refer to the following papers for more details on the algorithms:
- [A comprehensive review on uncertainty quantification in scientific machine learning](https://www.sciencedirect.com/science/article/pii/S0021999122009652)
- UQ for physics-informed neural networks
- [B-PINNs: Bayesian physics-informed neural networks](https://www.sciencedirect.com/science/article/pii/S0021999120306872)
- [Learning functional priors and posteriors from data and physics](https://www.sciencedirect.com/science/article/pii/S0021999122001358)
- [Physics-informed generative adversarial networks for stochastic differential equations](https://epubs.siam.org/doi/abs/10.1137/18M1225409)
- ...
- UQ for DeepONets
- [Learning functional priors and posteriors from data and physics](https://www.sciencedirect.com/science/article/pii/S0021999122001358)
- [Bayesian DeepONets](https://arxiv.org/abs/2111.02484)
- [Randomized priors for DeepONets](https://www.sciencedirect.com/science/article/pii/S0045782522004595)
- ...
# Installation
**NeuralUQ** requires the following dependencies to be installed:
- Python 3.7.0
- Tensorflow 2.9.1
- TensorFlow Probability 0.17.0
Then install with `python`:
```
$ python setup.py install
```
For developers, you could clone the folder to your local machine via
```
$ git clone https://github.com/Crunch-UQ4MI/neuraluq.git
```
# Explore more
NeuralUQ for uncertainty quantification in general neural differential equations and operators:
- [NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators](https://epubs.siam.org/doi/abs/10.1137/22M1518189)
- [Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons](https://www.sciencedirect.com/science/article/pii/S0021999122009652)
- [Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators](https://www.sciencedirect.com/science/article/pii/S0045782524007333)
NeuralUQ for physical model misspecification and uncertainty:
- [Correcting model misspecification in physics-informed neural networks (PINNs)](https://www.sciencedirect.com/science/article/pii/S0021999124001670)
NeuralUQ for physics-informed Kolmogorov-Arnold networks (PIKANs):
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://www.sciencedirect.com/science/article/pii/S0045782524005462)
NeuralUQ for Biomechanical constitutive models with experimental data (inferring model parameters from known model and data; inferring functions from pre-trained GAN and data):
- [A generative modeling framework for inferring families of biomechanical constitutive laws in data-sparse regimes](https://www.sciencedirect.com/science/article/pii/S0022509623002284?dgcid=rss_sd_all)
NeuralUQ for learning and discovering multiple solutions:
- [Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble](https://arxiv.org/abs/2503.06320)
Extensions of NeuralUQ:
- [Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification](https://www.sciencedirect.com/science/article/abs/pii/S002199912500230X)
# Cite NeuralUQ
```
@article{zou2024neuraluq,
title={NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators},
author={Zou, Zongren and Meng, Xuhui and Psaros, Apostolos F and Karniadakis, George E},
journal={SIAM Review},
volume={66},
number={1},
pages={161--190},
year={2024},
publisher={SIAM}
}
```
# The Team
NeuralUQ was developed by Zongren Zou and Xuhui Meng under the supervision of [Professor George Em Karniadakis](https://sites.brown.edu/crunch-group/) at [Brown University](https://www.brown.edu/) between 2022 and 2024, with helpful discussion and invaluable support from [Dr. Apostolos F Psaros](https://www.afpsaros.com/) and [Professor Ling Guo](https://scholar.google.com/citations?user=Ys5ZVhEAAAAJ&hl=en). The project is currently maintained by Zongren Zou at California Institute of Technology and Xuhui Meng at Huazhong University of Science and Technology.