The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Adversarial uncertainty quantification in physics-informed neural networks
Open accessAbstract
Abstract We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial inference procedure for training them on data, while constraining their predictions to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep generative models as surrogates of physical systems in which the cost of data acquisition is high, and training data-sets are typically small. This provides a flexible framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations that entirely bypasses the need for repeatedly sampling expensive experiments or numerical simulators. We demonstrate the effectiveness of our approach through a series of examples involving uncertainty propagation in non-linear conservation laws, and the discovery of constitutive laws for flow through porous media directly from noisy data.
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Cites
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A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils
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Unpaired image-to-image translation using cycle-consistent adversarial networks
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Self-citationConditional Generative Adversarial Nets
Mirza, M., & Osindero, S. (2014) · arXiv · doi:10.48550/arxiv.1411.1784 · Cited by 8,863
Improved Techniques for Training GANs
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Cited by
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Self-citationA review of uncertainty quantification in deep learning: Techniques, applications and challenges
Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., Fieguth, P., Cao, X., Khosravi, A., Acharya, U. R., et al. (2021) · Information Fusion · doi:10.1016/j.inffus.2021.05.008 · Cited by 3,111
“[234] proposed a deep learning approach for propagating and quantifying uncertainty in models inspired by non-linear differential equations utilized by physicsinformed neural networks.”
Weak adversarial networks for high-dimensional partial differential equations
Zang, Y., Bao, G., Ye, X., & Zhou, H. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109409 · Cited by 444
Metadata
- Authors
- Yang, Y., & Perdikaris, P.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2019-10
- Volume
- 394
- Pages
- 136-152
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W2900369848
- Cited by
- 414
- References
- 9
- FWCI
- 20.87
- Type
- journal article
- Language
- en
- Open access
- bronze
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