The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
When and why PINNs fail to train: A neural tangent kernel perspective
Open accessOverview
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
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-citationFourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., & Ng, R. (2020) · arXiv · doi:10.48550/arxiv.2006.10739 · Cited by 1,459
fPINNs: Fractional Physics-Informed Neural Networks
Pang, G., Lu, L., & Karniadakis, G. E. (2019) · SIAM Journal on Scientific Computing · doi:10.1137/18m1229845 · Cited by 1,105
Research works printed but not linked: 18
- Raissi, 2020, Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations, Science, 367, 1026, 10.1126/science.aaw4741 · DOI · Paper page
- Sun, 2020, Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Comput. Methods Appl. Mech. Eng., 361, 10.1016/j.cma.2019.112732 · DOI · Paper page
- Raissi, 2019, Deep learning of turbulent scalar mixing, Phys. Rev. Fluids, 4, 10.1103/PhysRevFluids.4.124501 · DOI
- Raissi, 2019, Deep learning of vortex-induced vibrations, J. Fluid Mech., 861, 119, 10.1017/jfm.2018.872 · DOI · Paper page
- Sahli Costabal, 2020, Physics-informed neural networks for cardiac activation mapping, Front. Phys., 8, 42, 10.3389/fphy.2020.00042 · DOI · Paper page
- Kissas, 2020, Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks, Comput. Methods Appl. Mech. Eng., 358, 10.1016/j.cma.2019.112623 · DOI · Paper page
- Fang, 2019, Deep physical informed neural networks for metamaterial design, IEEE Access, 8, 24506, 10.1109/ACCESS.2019.2963375 · DOI · Paper page
- Liu, 2019, Multi-fidelity physics-constrained neural network and its application in materials modeling, J. Mech. Des., 141, 10.1115/1.4044400 · DOI · Paper page
- Chen, 2020, Physics-informed neural networks for inverse problems in nano-optics and metamaterials, Opt. Express, 28, 11618, 10.1364/OE.384875 · DOI · Paper page
- Yang, 2019, Adversarial uncertainty quantification in physics-informed neural networks, J. Comput. Phys., 394, 136, 10.1016/j.jcp.2019.05.027 · DOI · Paper page
- Zhu, 2019, Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data, J. Comput. Phys., 394, 56, 10.1016/j.jcp.2019.05.024 · DOI · Paper page
- Sirignano, 2018, DGM: a deep learning algorithm for solving partial differential equations, J. Comput. Phys., 375, 1339, 10.1016/j.jcp.2018.08.029 · DOI · Paper page
- Han, 2018, Solving high-dimensional partial differential equations using deep learning, Proc. Natl. Acad. Sci. USA, 115, 8505, 10.1073/pnas.1718942115 · DOI · Paper page
- Zhang, 2020, Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks, SIAM J. Sci. Comput., 42, A639, 10.1137/19M1260141 · DOI · Paper page
- Tartakovsky, 2020, Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems, Water Resour. Res., 56, 10.1029/2019WR026731 · DOI · Paper page
- Tchelepi, 2020, Limitations of physics informed machine learning for nonlinear two-phase transport in porous media, J. Mach. Learn. Model. Comput., 1
- Raissi, 2018, Deep hidden physics models: deep learning of nonlinear partial differential equations, J. Mach. Learn. Res., 19, 932
- MacKay, 1998, Introduction to Gaussian Processes, vol. 168, 133
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-citationPhysics-Informed Neural Networks for Heat Transfer Problems
Cai, S., Wang, Z., Wang, S., Perdikaris, P., & Karniadakis, G. E. (2021) · Journal of Heat Transfer · doi:10.1115/1.4050542 · Cited by 1,312
Self-citationGradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Yu, J., Lu, L., Meng, X., & Karniadakis, G. E. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2022.114823 · Cited by 722
Perspectives on the integration between first-principles and data-driven modeling
Bradley, W., Kim, J., Kilwein, Z., Blakely, L., Eydenberg, M., Jalvin, J., Laird, C., & Boukouvala, F. (2022) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2022.107898 · Cited by 231
Bandai, T., & Ghezzehei, T. A. (2022) · Hydrology and Earth System Sciences · doi:10.5194/hess-26-4469-2022 · Cited by 111
Metadata
- Authors
- Wang, S., Yu, X., & Perdikaris, P.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2022-01
- Volume
- 449
- Pages
- 110768
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W3205073660
- Cited by
- 1,496
- References
- 3
- FWCI
- 59.37
- 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: When and why PINNs fail to train: A neural tangent kernel perspective. https://app.cochat.ai/papers/10.1016/j.jcp.2021.110768
- The paper
- Wang, S., Yu, X., & Perdikaris, P. (2022). When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2021.110768
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.
