Artificial intelligence, chaos, prediction and understanding in science. (English) Zbl 1479.37088
Summary: Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main thesis here is that prediction and understanding are two very different and important ideas that should guide us to follow the progress of science. Furthermore, the important role played by nonlinear dynamical systems is emphasized for the process of understanding. The path of the future of science will be marked by a constructive dialogue between big data and big theory, without which we cannot understand.
MSC:
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
Software:
AlphaZeroReferences:
| [1] | Aguirre, J., Viana, R. & Sanjuan, M. A. F. [2009] “ Fractal structures in nonlinear dynamics,” Rev. Mod. Phys.81, 333-386. |
| [2] | Anderson, C. [2008] “The end of theory: The data deluge makes the scientific method obsolete,” Wired Magazine. Retrieved from https://www.wired.com/2008/06/pb-theory/. |
| [3] | Baldovin, M., Cecconi, F., Cencini, M., Puglisi, A. & Vulpiani, A. [2018] “ The tole of data in model building and prediction: A survey through examples,” Entropy20, 807. |
| [4] | Berry, T., Giannakis, D. & Harlim, J. [2020] “ Bridging data science and dynamical systems theory,” Not. Am. Math. Soc.67, 1336-1349. · Zbl 1460.37074 |
| [5] | Bieger, J. & Thórisson, K. R. [2017] “Evaluating understanding,” A copy can be downloaded from http://dmip.webs.upv.es/EGPAI2017/Papers/EGPAI_2017_paper_6_JBieger.pdf. |
| [6] | Breen, P. G., Foley, C. N., Boekholt, T. & Zwart, S. P. [2020] “ Newton vs the machine: Solving the chaotic three-body problem using deep neural networks,” Month. Not. Roy. Astron. Soc.494, 2465-2470. |
| [7] | Broadbent, A. [2018] “ Prediction, understanding, and medicine,” J. Med. Phil.43, 289-305. |
| [8] | Buchanan, M. [2019] “ The limits of machine prediction,” Nat. Phys.15, 304. |
| [9] | Bunimovich, L., Passey, D. J., Smith, D. & Webb, B. [2020] “ Spectral and dynamic consequences of network specialization,” Int. J. Bifurcation and Chaos30, 2050091-1-32. · Zbl 1442.90025 |
| [10] | Cecconi, F., Cencini, M., Falcioni, M. & Vulpiani, A. [2012] “ The prediction of future from the past: An old problem from a modern perspective,” Am. J. Phys.80, 1001-1008. |
| [11] | Coveney, P. V., Dougherty, E. R. & Highfield, R. R. [2016] “ Big data need big theory too,” Philos. Trans. Roy. Soc. A374, 20160153. |
| [12] | Crutchfield, J. P. [2014] “ The dreams of theory,” WIREs Comput. Stat.6, 75-79. · Zbl 07912710 |
| [13] | Dawson, S. P., Grebogi, C., Sauer, T. & Yorke, J. A. [1994] “ Obstructions to shadowing when a Lyapunov exponent fluctuates about zero,” Phys. Rev. Lett.73, 1927. |
| [14] | Daza, A., Wagemakers, A., Georgeot, B., Guéry-Odelin, D. & Sanjuán, M. A. F. [2016] “ Basin entropy: A new tool to analyze uncertainty in dynamical systems,” Sci. Rep.6, 31416. · Zbl 1386.37080 |
| [15] | Dougherty, E. R. & Bittner, M. L. [2011] Epistemology of the Cell: A Systems Perspective on Biological Knowledge, (John Wiley, NY). |
| [16] | Edge [2015] “2015: What do you think about mach-ines that think,” https://www.edge.org/annual-ques-tion/what-do-you-think-about-machines-that-think], (accessed May 19, 2016). |
| [17] | Franklin, R. L. [1983] “ On understanding,” Philos. Phenomenol. Res.43, 307-328. |
| [18] | Hartnett, K. [2018] “To build truly intelligent machines, teach them cause and effect,” https://www.quantamagazine.org/to-build-truly-intelligent-machines-teach-them-cause-and-effect-20180515/. |
| [19] | Himmelfarb, J., Stenvinkel, P., Ikizler, T. A. & Hakim, R. M. [2002] “ The elephant in uremia: Oxidant stress as a unifying concept of cardiovascular disease in uremia,” Kidney Int.62, 1524-1538. |
| [20] | Hirata, Y. & Aihara, K. [2020] “ Deep learning for nonlinear time series: Examples for inferring slow driving forces,” Int. J. Bifurcation and Chaos30, 2050226-1-13. · Zbl 1459.37070 |
| [21] | Hosni, H. & Vulpiani, A. [2018a] “ Forecasting in light of Big Data,” Philos. Technol.31, 557-569. |
| [22] | Hosni, H. & Vulpiani, A. [2018b] “ Data science and the art of modelling,” Lett. Mat. Int.6, 121-129. · Zbl 1432.00039 |
| [23] | Ichinose, N. [2021] “ Quasiperiodic-chaotic neural networks and short-term analog memory,” Int. J. Bifurcation and Chaos31, 2130003-1-18. · Zbl 1462.37101 |
| [24] | Kitano, H. [2016] “Artificial intelligence to win the nobel prize and beyond: Creating the engine for scientific discovery,” AI Mag.37, 39-49. |
| [25] | Kostelich, E. J., Kan, I., Grebogi, C., Ott, E. & Yorke, J. A. [1997] “ Unstable dimension variability: A source of nonhyperbolicity in chaotic systems,” Physica D109, 81. · Zbl 0925.58048 |
| [26] | Laplane, L., Mantovani, P., Adolphs, R., Chang, H., Mantovani, A., McFall-Ngai, M., Rovelli, C., Sober, E. & Pradeu, T. [2019] “ Why science needs philosophy,” Proc. Natl. Acad. Sci. USA116, 3948-3952. |
| [27] | Laurent, G. [2000] “ What does ‘understanding’ mean?” Nat. Neurosci.3, 1211. |
| [28] | Levenson, T. [2015] The Hunt for Vulcan: …\(\) And How Albert Einstein Destroyed a Planet, Discovered Relativity, and Deciphered the Universe (Random House, NY, USA). |
| [29] | Lovejoy, S.et al. [2009] “ Nonlinear geophysics: Why we need it,” Eos Trans. AGU90, 455-456. |
| [30] | Lovejoy, S. [2019] Weather, Macroweather, and the Climate. Our Random Yet Predictable Atmosphere (Oxford University Press, Oxford, UK). |
| [31] | Ma, H., Zhou, T., Aihara, K. & Chen, L. [2014] “ Predicting time series from short-term high-dimensional data,” Int. J. Bifurcation and Chaos24, 1430033-1-19. · Zbl 1305.37043 |
| [32] | Mitchell, M. [2019] Artificial Intelligence: A Guide for Thinking Humans (Farrar, Straus and Giroux, NY, USA). |
| [33] | Newton, I. S. [1687] Philosophiae Naturalis Principia Mathematica (Royal Society, London, UK). · Zbl 0050.00201 |
| [34] | Pathak, J., Lu, Z., Hunt, B. R., Girvan, M. & Ott, E. [2017] “ Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data,” Chaos27, 121102. · Zbl 1390.37138 |
| [35] | Pathak, J., Hunt, B. R., Girvan, M., Lu, Z. & Ott, E. [2018a] “ Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach,” Phys. Rev. Lett.120, 024102. |
| [36] | Pathak, J., Wikner, A., Fussell, R., Chandra, S., Hunt, B. R., Girvan, M. & Ott, E. [2018b] “ Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model,” Chaos28, 041101. |
| [37] | Pearl, J. & Mackenzie, D. [2018] The Book of Why. The New Science of Cause and Effect (Basic Books, NY, USA). · Zbl 1416.62026 |
| [38] | Poincaré, H. [1890] “ Sur le problème des trois corps et les Équations de la dynamique,” Acta Math.13, 1-270. · JFM 22.0907.01 |
| [39] | Poincaré, H. [1892] Les Méthodes Nouvelles de la Mécanique Céleste, I-III (Gauthier-Villars, Paris, France, 1892-1899). (Also in English translation: New Methods of Celestial Mechanics, with an introduction by D. L. Goroff. American Institute of Physics, NY, 1993). |
| [40] | Reichstein, M., Camps-Valls, G., Stevens, B.et al. [2019] “ Deep learning and process understanding for data-driven Earth system science,” Nature566, 195-204. |
| [41] | Rovelli, C. [2018] “ Physics needs philosophy. Philosophy needs physics,” Found. Phys.48, 481-491. · Zbl 1394.81016 |
| [42] | Saiki, Y., Sanjuán, M. A. F. & Yorke, J. A. [2018] “ Low-dimensional paradigms for high-dimensional hetero-chaos,” Chaos28, 103110. · Zbl 1400.37102 |
| [43] | Sauer, T., Grebogi, C. & Yorke, J. A. [1997] “ How long do numerical chaotic solutions remain valid?,” Phys. Rev. Lett.79, 59. |
| [44] | Schmidt, M. & Lipson, H. [2009] “ Distilling free-form natural laws from experimental data,” Science324, 81-85. |
| [45] | Silver, D., Huang, A., Maddison, C. J.et al. [2016] “ Mastering the game of Go with deep neural networks and tree search,” Nature529, 484-489. |
| [46] | Silver, D., Hubert, T., Schrittwieser, J.et al. [2018] “ A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,” Science362, 1140-1144. · Zbl 1433.68320 |
| [47] | Smith, G. [2018] The AI Delusion (Oxford University Press, Oxford, UK). |
| [48] | Stanley, M. [2016] “ Why should physicists study history?” Phys. Today69, 38-44. |
| [49] | Stinis, P. [2019] “Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning,” arXiv:1905.07501. |
| [50] | Succi, S. & Coveney, P. V. [2019] “ Big data: The end of the scientific method?”, Philos. Trans. Roy. Soc. A377, 20180145. |
| [51] | Tegmark, M. [2017] Life 3.0: Being Human in the Age of Artificial Intelligence (Penguin, UK). |
| [52] | Thórisson, K. R. & Kremelberg, D. [2017] “ Do machines understand?,” Understanding Workshop, 10th Int. Conf. Artificial General Intelligence (AGI-17), August 18, Melbourne, Australia, . |
| [53] | Tian, Z. [2020] “ Preliminary research of chaotic characteristics and prediction of short-term wind speed time series,” Int. J. Bifurcation and Chaos30, 2050176-1-24. · Zbl 1451.86015 |
| [54] | Vallejo, J. C. & Sanjuan, M. A. F. [2019] Predictability of Chaotic Dynamics: A Finite-Time Lyapunov Exponents Approach, 2nd edition (Springer-Nature, Cham, Switzerland). · Zbl 1440.37002 |
| [55] | Vulpiani, A. & Baldovin, M. [2020] “ Effective equations in complex systems: From Langevin to machine learning,” J. Stat. Mech.2020, 014003. · Zbl 1459.82246 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
