Physics-informed deep generative models

By Yibo Yang, Paris Perdikaris. 2018

70 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yibo Yang
2. Stefania Fresca
3. Andrea Manzoni
4. Michael S. Steinbach
5. Vipin Kumar
6. Xiaowei Jia
7. Jared D. Willard
8. Shaoming Xu

In Computer Vision and Pattern Recognition

1. Sifan Wang
2. Stefania Fresca
3. Andrea Manzoni
4. Paris Perdikaris
5. Vipin Kumar
6. Michael S. Steinbach
7. Xiaowei Jia
8. Shaoming Xu

In Statistical and Nonlinear Physics

1. Sifan Wang
2. Stefania Fresca
3. Andrea Manzoni
4. Yibo Yang
5. Paris Perdikaris
6. Michael S. Steinbach
7. Xiaowei Jia
8. Jared D. Willard

Citations in the corpus

• When and why PINNs fail to train: A neural tangent kernel perspective (2020, background): “…5], bio-engineering [6, 7], meta-material design [8, 9, 10], free boundary problems [11], Bayesian networks and uncertainty quantification [12, 13, 14, 15, 16], high-dimensional PDEs [17, 18], stochastic differential equations [19], fractional differential equations [20, 21], and beyond [22, 23,…”
• Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “In Yang et al. [303] and Yang et al. [304], physics-based loss is implemented in a deep probabilistic generative model for uncertainty quantification based on adherence to the structure imposed by PDEs.”
• Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, background): “An extension to generative models is possible, too [43].”
• Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “In Yang et al. [281] and Yang et al. [282], physics-based loss is implemented in a deep probabilistic generative model for uncertainty quantification based on adherence to the structure imposed by PDEs.”
• Machine learning in cardiovascular flows modeling: Predicting pulse wave propagation from non-invasive clinical measurements using physics-informed deep learning (2019, methodology): “Alternatively, Bayesian approaches based on Markov Chain Monte Carlo sampling [18] or generative models can be employed [64].”
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition (2021, methodology): “Regarding this latter, we mention, for instance, physics-informed neural networks (PINNs) [19, 20, 21, 22] or physics-informed deep generative models [23, 24].”