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The imperative of physics-based modeling and inverse theory in computational science

Nature Computational Science volume 1, pages 166–168 (2021)Cite this article

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To best learn from data about large-scale complex systems, physics-based models representing the laws of nature must be integrated into the learning process. Inverse theory provides a crucial perspective for addressing the challenges of ill-posedness, uncertainty, nonlinearity and under-sampling.

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References

  1. Coveney, P. V., Dougherty, E. R. & Highfield, R. R. Philos. Trans. R. Soc. A 374, 20160153 (2016).

    Article  Google Scholar 

  2. Wigner, E. P. In Mathematics and Science 291–306 (World Scientific, 1990).

  3. Engl, H. W., Hanke, M. & Neubauer, A. Regularization of Inverse Problems Vol. 375 (Springer, 1996).

  4. Biegler, L. et al. Large-scale Inverse Problems and Quantification of Uncertainty (Wiley, 2011).

  5. Isaac, T., Petra, N., Stadler, G. & Ghattas, O. J. Comput. Phys. 296, 348–368 (2015).

    Article  MathSciNet  Google Scholar 

  6. Oden, T., Moser, R. & Ghattas, O. SIAM News 43, 1–3 (2010).

    Google Scholar 

  7. Loose, N. & Heimbach, P. J. Adv. Model. Earth Sys. https://doi.org/10.1029/2020MS002386 (2021).

  8. Bauer, P., Thorpe, A. & Brunet, G. Nature 525, 47–55 (2015).

    Article  Google Scholar 

  9. Wunsch, C. In Encyclopedia of Ocean Sciences (eds Cochran, J. K. et al.) 502–512 (Elsevier, 2019).

  10. Tarantola, A. Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2005).

  11. Kaipio, J. & Somersalo, E. Statistical and Computational Inverse Problems (Springer, 2005).

  12. Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. J. Mach. Learn. Res. 18, 1–43 (2018).

    Google Scholar 

  13. Bauer, P., Stevens, B. & Hazeleger, W. Nat. Clim. Change 11, 80–83 (2021).

    Article  Google Scholar 

  14. Palmer, T. N., Buizza, R., Molteni, F., Chen, Y.-Q. & Corti, S. Philos. Trans. R. Soc. London A 348, 459–475 (1994).

    Article  Google Scholar 

  15. Rüde, U., Willcox, K., McInnes, L. C. & De Sterck, H. SIAM Rev. 60, 707–754 (2018).

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

K.E.W. and O.G. acknowledge US Department of Energy grants DE-SC0019303 and DE-SC0021239. P.H. acknowledges NSF grant #1603903 and funding from NASA/ECCO through a JPL/Caltech subcontract.

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Authors and Affiliations

  1. Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA

    Karen E. Willcox, Omar Ghattas & Patrick Heimbach

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  1. Karen E. Willcox
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  2. Omar Ghattas
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  3. Patrick Heimbach
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Correspondence to Karen E. Willcox.

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The authors declare no competing interests.

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Peer review information Nature Computational Science thanks the anonymous reviewers for their contribution to the peer review of this work. Fernando Chirigati was the primary editor on this Comment and managed its editorial process and peer review in collaboration with the rest of the editorial team.

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Willcox, K.E., Ghattas, O. & Heimbach, P. The imperative of physics-based modeling and inverse theory in computational science. Nat Comput Sci 1, 166–168 (2021). https://doi.org/10.1038/s43588-021-00040-z

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