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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils
van Genuchten, M. T. (1980) · Soil Science Society of America Journal · doi:10.2136/sssaj1980.03615995004400050002x · Cited by 27,578
Unpaired image-to-image translation using cycle-consistent adversarial networks
Zhu, J.-Y., Park, T., Isola, P., & Efros, A. A. (2017) · 2017 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.244 · Cited by 23,602
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384
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
Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., & Chen, X. (2016) · arXiv · doi:10.48550/arxiv.1606.03498 · Cited by 6,965
Human-level concept learning through probabilistic program induction
Lake, B. M., Salakhutdinov, R., & Tenenbaum, J. B. (2015) · Science · doi:10.1126/science.aab3050 · Cited by 2,817
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Adversarial uncertainty quantification in physics-informed neural networks. https://app.cochat.ai/papers/10.1016/j.jcp.2019.05.027
- The paper
- Yang, Y., & Perdikaris, P. (2019). Adversarial uncertainty quantification in physics-informed neural networks. Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2019.05.027
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
