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) and deep operator networks (DeepONets) 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

Users can refer to the following papers for more details on the algorithms:

• A comprehensive review on uncertainty quantification in scientific machine learning
• UQ for physics-informed neural networks
  • B-PINNs: Bayesian physics-informed neural networks
  • Learning functional priors and posteriors from data and physics
  • Physics-informed generative adversarial networks for stochastic differential equations
  • ...
• UQ for DeepONets
  • Learning functional priors and posteriors from data and physics
  • Bayesian DeepONets
  • Randomized priors for DeepONets
  • ...

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
• Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
• Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators

NeuralUQ for physical model misspecification and uncertainty:

• Correcting model misspecification in physics-informed neural networks (PINNs)

NeuralUQ for physics-informed Kolmogorov-Arnold networks (PIKANs):

• A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

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

NeuralUQ for learning and discovering multiple solutions:

• Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

Extensions of NeuralUQ:

• Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

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 at Brown University between 2022 and 2024, with helpful discussion and invaluable support from Dr. Apostolos F Psaros and Professor Ling Guo. The project is currently maintained by Zongren Zou at California Institute of Technology and Xuhui Meng at Huazhong University of Science and Technology.