Machine learning for science: mathematics at the interface of data-driven and mechanistic modelling. Abstracts from the workshop held June 11–16, 2023. (English) Zbl 1528.68032
Summary: Rapid progress in machine learning is enabling scientific advances across a range of disciplines. However, the utility of machine learning for science remains constrained by its current inability to translate insights from data about the dynamics of a system to new scientific knowledge about why those dynamics emerge, as traditionally represented by physical modelling. Mathematics is the interface that bridges data-driven and physical models of the world and can provide a foundation for delivering such knowledge. This workshop convened researchers working across domains with a shared interest in mathematics, machine learning, and their application in the sciences, to explore how tools of mathematics can help build machine learning tools for scientific discovery.
MSC:
| 00B05 | Collections of abstracts of lectures |
| 00B25 | Proceedings of conferences of miscellaneous specific interest |
| 68-06 | Proceedings, conferences, collections, etc. pertaining to computer science |
| 62-06 | Proceedings, conferences, collections, etc. pertaining to statistics |
| 00A71 | General theory of mathematical modeling |
| 62Hxx | Multivariate analysis |
| 62Rxx | Statistics on algebraic and topological structures |
| 68Txx | Artificial intelligence |
References:
| [1] | Lance et al, Multimodal single cell data integration challenge: Results and lessons learned, Proceedings of Machine Learning Research 176:162-176, 2022 NeurIPS 2021 Competition and Demonstration Track. |
| [2] | Chan et al, Lineage plasticity in prostate cancer depends on JAK/STAT inflammatory signaling, Science, 2022. |
| [3] | Lynch et al, MIRA: joint regulatory modeling of multimodal expression and chromatin accessibility in single cells, Nature Methods 19 (2022), 1097-1108. |
| [4] | Hiernaux, P. et al, Allometric equations to estimate the dry mass of Sahel woody plants from very-high resolution satellite imagery, Forest Ecology, Management 529, 2023 . |
| [5] | Igel, C. and Oehmcke, S., Remember to correct the bias when using deep learning for re-gression!, Kunstliche Intelligenz, 2023. |
| [6] | Li, S. et al, Deep learning enables image-based tree counting, crown segmentation and height prediction at national scale, PNAS Nexus 2(4) (2023). |
| [7] | Mugabowindekwe, M., et al Nation-wide mapping of tree-level aboveground carbon stocks in Rwanda, Nature Climate Change, 13 (2022), 91-97. |
| [8] | Oehmcke, S., et al Deep Learning Based 3D Point Cloud Regression for Estimating Forest Biomass, International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL), ACM (2022). |
| [9] | Tucker, C., et al Sub-continental scale carbon stocks of individual trees in African drylands, Nature, 615 (2023), 80-86. |
| [10] | Machuve, D., Nwankwo, E., Mduma, N. and Mbelwa, J. , Poultry diseases diagnostics models using deep learning, Front. Artif. Intell 5:733345, 2022 . |
| [11] | Machuve, D., Nwankwo, E., Mduma, N., Mbelwa, H., Maguo, E., and Munisi, C., Machine Learning Dataset for Poultry Diseases Diagnostics, https://zenodo.org/record/5801834, 2021. References |
| [12] | Beckenback, E. and Bellman, R. Inequalities, Springer-Verlag, 1965. · Zbl 0128.27401 |
| [13] | Babai, L. and Seress, A. On the diameter of permutation groups, European Jounral of Combinatorics, 13, 4: 231-243, 1992. · Zbl 0783.20001 |
| [14] | Birch, B. and Swinnerton-Dyer, H. Notes on elliptic curves i, Journal fur die reine und angewandte Mathematik, 212: 7-25, 1963. · Zbl 0118.27601 |
| [15] | Birch, B. and Swinnerton-Dyer, H. Notes on elliptic curves ii, Journal fur die reine und angewandte Mathematik, 212: 79-108, 1963 . · Zbl 0147.02506 |
| [16] | Dijkgraaf, R. The subtle art of the mathematical conjecture, Quanta Magazine 5, 2019 . |
| [17] | Davies, A. et al, Advancing mathematics by guiding human intuition with AI, Nature 600, 787:70-74, 2021 . · Zbl 1505.57001 |
| [18] | Fawzi, A. et al, Discovering faster matrix multiplication algorithms with reinforcement learning, Nature 610, 7930:43-45, 2022 . |
| [19] | Guy, R. Unsolved Problems in Number Theory. Problem Books in Mathematics, Springer, NY, 3rd Edition, 2004 . · Zbl 1058.11001 |
| [20] | He, Y.H. et al. Machine learning finite simple groups. work in progress, 2023 . |
| [21] | Hui, Y.H. and Kim, M., Learning algebraic structures: preliminary investigations, Interna-tional Journal of Data Science in the Mathematical Sciences, 1-20, 2022 . |
| [22] | Hardy, G. and Littlewood, J. Some problems of ’partitio numerorum’; iii: On the expression of a number as a sum of primes, Acta Mathematica 44, 1:1-70, 1923 . · JFM 48.0143.04 |
| [23] | Hardy, G. et al, Inequalities, Cambridge University Press, 1952 . · Zbl 0047.05302 |
| [24] | Hecht-Nielsen, R. A. Kolmogorov’s mapping neural network existence theorem, Proceedings of the international conference on Neural Networks 3, 11-14, 1987 . |
| [25] | Lang, S. Differential and Riemannian manifolds, Springer Science and Business Media, 2012. |
| [26] | Lee, J.M. Smooth manifolds, Springer, 2012 . |
| [27] | Mankowitz, D. et al, Faster sorting algorithms discovered using deep reinforcement learning, Nature 618, 7964:257-263, 2023. |
| [28] | Mincu, G. et al, Properties of some functions connected to prime numbers, Journal of Inequalities in Pure and Applied Mathematics [electronic only] 9, 1, 2008. · Zbl 1196.11124 |
| [29] | Dragoslav, S. et al, Analytic inequalities, Springer, 1970. · Zbl 0199.38101 |
| [30] | Raayoni, G. et al, Generating conjectures on fundamental constants with the Ramanujan Machine, Nature 590, 7844:67-73, 2021. |
| [31] | Rosser, J.B. and Shoenfeld, L. Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics, 6, 1:64-94, 1962. References · Zbl 0122.05001 |
| [32] | Rupp, M., Tkatchenko, A., Müller, K. R., and Von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Physical review letters, 108(5), 058301, 2012.. |
| [33] | Snyder, J. C., Rupp, M., Hansen, K., Müller, K. R., and Burke, K. Finding density func-tionals with machine learning. Physical review letters, 108(25), 253002, 2012. |
| [34] | Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R., and Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nature communications, 8(1), 13890, 2017.. |
| [35] | Schütt, K. T., Sauceda, H. E., Kindermans, P. J., Tkatchenko, A., and Müller, K. R.. |
| [36] | Schnet-a deep learning architecture for molecules and materials. The Journal of Chemical Physics, 148(24), 2018. |
| [37] | Chmiela, S., Tkatchenko, A., Sauceda, H. E., Poltavsky, I., Schütt, K. T., and Müller, K. R. Machine learning of accurate energy-conserving molecular force fields. Science advances, 3(5), e1603015, 2017. |
| [38] | Chmiela, S., Vassilev-Galindo, V., Unke, O. T., Kabylda, A., Sauceda, H. E., Tkatchenko, A., and Müller, K. R. Accurate global machine learning force fields for molecules with hundreds of atoms. Science Advances, 9(2), eadf0873, 2023. |
| [39] | Keith, J. A., Vassilev-Galindo, V., Cheng, B., Chmiela, S., Gastegger, M., Müller, K. R., and Tkatchenko, A. Combining machine learning and computational chemistry for predictive insights into chemical systems. Chemical reviews, 121(16), 9816-9872, 2021. |
| [40] | Unke, O. T., Chmiela, S., Sauceda, H. E., Gastegger, M., Poltavsky, I., Schütt, K. T., ... |
| [41] | and Müller, K. R. Machine learning force fields. Chemical Reviews, 121(16), 10142-10186, 2021. |
| [42] | Unke, O. T., Chmiela, S., Gastegger, M., Schütt, K. T., Sauceda, H. E., and Müller, K. R. SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects. Nature communications, 12(1), 7273, 2021. |
| [43] | MacKay, D.J.C. The Evidence Framework applied to Classification Networks, Neural Com-putation, 1992. |
| [44] | Kristiadi, A., Hein, M., Hennig, P. Being Bayesian, even just a bit, fixes overconfidence in ReLU Networks, ICML 2020. |
| [45] | Daxberger, E. et al. Laplace Redux -Effortless Bayesian Deep Learning, Neural Infiormation Processing Systems (NeurIPS) 2021. |
| [46] | Kristiadi, A., Hein, M., Hennig, P. Learnable Uncertainty under Laplace Approximationsi, UAI 2021. |
| [47] | Kristiadi, A., Hein, M., Hennig, P. An infinite-feature extension for Bayesian ReLU Nets that fixes their asymptotic overconfidnce, NeurIPS 2021. |
| [48] | Tosi, A., Hauberg, Sören, Vellido, A., and Lawrence, N. D. Metrics for probabilistic geome-tries. In , Uncertainty in Artificial Intelligence, 2014. |
| [49] | Hauberg, S. Only bayes should learn a manifold (on the estimation of differential geometric structure from data), https://doi.org/10.48550/arXiv.1806.04994, 2018. · doi:10.48550/arXiv.1806.04994 |
| [50] | Pouplin, A., Eklund, D., Ek, C. H., and Hauberg, S. Identifying Latent Distances With Finslerian Geometry. https://doi.org/10.48550/arXiv.2212.10010, 2022. References · doi:10.48550/arXiv.2212.10010,2022.References |
| [51] | Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Physical review letters 79, 325. 1997. |
| [52] | Roland, J. and Cerf, N. J. Quantum search by local adiabatic evolution. Physical Review A 65, 042308, 2002. References |
| [53] | Cohen, T. and Welling, M. Group equivariant convolutional neural networks. In Interna-tional Conference on machine learning, pages 2990-2999. PLMR, 2016. |
| [54] | Dimitrienko, Y. Tensor Analysis and Nonlinear Tensor Functions. Springer Dordrecht, 1 edition, June 2013. |
| [55] | Gregory, W., Hogg, D.W., Blum-Smith, B., Arias, M.T., Wong, K. and Villar, S. Ge-ometricImageNet: Extending convolutional neural networks to vector and tensor images arxiv.org/abs/2305.12585 Preprint, 2023. |
| [56] | Kondor, R. and Trivedi, S. On the generalization of equivariance and convolution in neural networks to the action of compact groups. Proceedings of the 35th International Conference on Machine Learning, 2018. |
| [57] | LeCun, Y., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W. and Jackel, L.D. Backpropagation applied to handwritten zip code recognition. Neural Computation, 1(4):541-551, 1989. |
| [58] | Ricci, M.M.G. and Levi-Civita, T. Méthodes de calcul differentiel absolu et leurs applica-tions. Mathematische Annalen, 54(1):125-201, 1900. · JFM 31.0297.01 |
| [59] | Thorne, K.S. and Blandford, R.d. Modern Classical Physics: Optics, Fluids, Plasmas, Elas-ticity, Relativity, and Statistical Physics. Princeton University Press, 2017. · Zbl 1398.82004 |
| [60] | Weiler, M. and Cesa, G.. General e(2)-equivariant steerable, cnns, 2021. References |
| [61] | Klami, A., Damoulas, T., Rinke, P., and Kaski, S. Virtual Laboratories: Transforming research with AI. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.20412540.v1, 2022. · doi:10.36227/techrxiv.20412540.v1 |
| [62] | Mikkola, P., Todorovic, M., Järvi, J., Rinke, P., and Kaski, S. Projective preferential Bayesian optimization. In Proc. ICML 2020, the 37th International Conference on Machine Learning, vol 119 of PMLR, pp 6884-6892, 2020. |
| [63] | Sundin, I., Voronov, A., Xiao, H., Papadopoulos, K., Bjerrum, E.J., Heinonen, M., Patronov, A., Kaski, S., and Engkvist, O. Human-in-the-loop assisted de novo molecular design. Jour-nal of Cheminformatics, 14:86, 2022. |
| [64] | Mikkola, P., Martinelli, J., Filstroff, L., and Kaski, S. Multi-fidelity Bayesian optimiza-tion with unreliable information sources. In Proc. AISTATS 2023, the 26th International Conference on Artificial Intelligence and Statistics, vol 206 of PMLR, pp 7425-7454, 2023. |
| [65] | Celikok, M.M., Murena, P-A., and Kaski, S. Modelling needs user modelling. Frontiers in Artificial Intelligence, 6:1097891, 2023. |
| [66] | Lintusaari, J., Vuollekoski, H., Kangasrääsiö, Skytén, K., Järvenpää, Marttinen, P., Gut-mann, M., Vehtari, A., Corander, J. and Kaski, S. ELFI: engine for likelihood-free inference. Journal of Machine Learning Research, 19(16):1-7, 2018. |
| [67] | Hämäläinen, A., Celikok, M.M., and Kaski, S. Amortized surrogates for user models. In Proc. UAI 2023, in press. . |
| [68] | De Peuter, S., Oulasvirta, A., and Kaski, S. Toward AI assistants that let designers design. AI Magazine, 44(1):85-96, 2023. |
| [69] | De Peuter, S. and Kaski, S. Zero-shot assistance in sequential decision problems. In Proc. AAAI-23, in press, 2023. Beyond Simulation-based inference Jakob Macke References |
| [70] | Deistler, M., Macke, J. and Goncalves, P.J. Energy efficient network activity from disparate circuit parameters, PNAS 2022. |
| [71] | Greenberg, D., Nonnenmacher, M. and Macke, J. Automatic posterior transformation for likelihood-free inference. International Conference on Machine Learning, 2404-2414, PMLR, 2019. |
| [72] | Gonçalves, P. J., Lueckmann, J. M., Deistler, M., Nonnenmacher, M.,Öcal, K., Bassetto, G., ... and Macke, J. H. Training deep neural density estimators to identify mechanistic models of neural dynamics. Elife, 9, e56261, 2020. References |
| [73] | Ailer, E., Hartford, J., and Kilbertus, N. Sequential Underspecified Instrument Selection for Cause-Effect Estimation. Proceedings of the 40th International Conference on Machine Learning, 2023. |
| [74] | Janzing, D. Causal regularization. Advances in Neural Information Processing Systems, 32, 2019. |
| [75] | Pfister, N., and Peters, J. Identifiability of sparse causal effects using instrumental variables. In Uncertainty in Artificial Intelligence, 1613-1622, PMLR, 2022. References |
| [76] | Beucler, T., Pritchard, M., Yuval, J., Gupta, A., Peng, L., Rasp, S., Ahmed, F., O’Gorman, P.A., Neelin, J.D., Lutsko, N.J., Gentine, P., Climate-Invariant Machine Learn-ing, https://doi.org/10.48550/arxiv.2112.08440, 2021. · doi:10.48550/arxiv.2112.08440 |
| [77] | Eyring, V., Bony, S., Meehl, G.A., Senior, C.A., Stevens, B., Stouffer, R.J., Taylor, K.E.: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) ex-perimental design and organization. Geoscientific Model Development 9(5), 1937-1958, https://doi.org/10.5194/gmd-9-1937-2016, 2016. · doi:10.5194/gmd-9-1937-2016 |
| [78] | Eyring, V., N.P. Gillett, K.M. Achuta Rao, R. Barimalala, M. Barreiro Parrillo, N. Bellouin, C. Cassou, P.J. Durack, Y. Kosaka, S. McGregor, S. Min, O. Morgenstern, and Y. Sun, 2021: Human Influence on the Climate System. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. |
| [79] | Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 423-552, doi:10.1017/9781009157896.005, 2021a. · doi:10.1017/9781009157896.005 |
| [80] | Eyring, V., Mishra, V., Griffith, G., Chen, L., Keenan, T. F., Turetsky, M. R., Brown, S., Jotzo, F., Moore, F. C. and van der Linden, S. Reflections and projections on a decade of climate science. Nat. Clim. Chang. 11, 279-285. https://doi.org/10.1038/s41558-021-01020-x, 2021b. · doi:10.1038/s41558-021-01020-x |
| [81] | Gentine, P., Pritchard, M., Rasp, S., Reinaudi, G., and Yacalis, G. Could machine learning break the convection parameterization deadlock? Geophysical Research Letters, 45(11), 5742-5751, 2018. |
| [82] | Gentine, P., Eyring, V. and Beucler, T. Deep Learning for the Parametrization of Subgrid Processes in Climate Models. In Deep learning for the Earth Sciences (eds G. Camps-Valls, D. Tuia, X.X. Zhu and M. Reichstein), https://doi.org/10.1002/9781119646181.ch21, 2021. · doi:10.1002/9781119646181.ch21 |
| [83] | Grundner, A., Beucler, T., Gentine, P., Iglesias-Suarez, F., Giorgetta, M. A., and Eyring, V. Deep learning based cloud cover parameterization for ICON. Journal of Advances in Mod-eling Earth Systems, 14, e2021MS002959. https://doi.org/10.1029/2021MS002959, 2022. · doi:10.1029/2021MS002959,2022 |
| [84] | Grundner, A., T. Beucler, P. Gentine and V. Eyring, Data-Driven Equation Discovery of a Cloud Cover Parameterization, arXiv preprint, http://arxiv.org/abs/2304.08063, JAMES, subm., 2023. |
| [85] | Iglesias-Suarez, F., P. Gentine, Solino-Fernandez, B., Beucler, T., Pritchard, M., Runge, J. and Eyring, V. Causally-informed deep learning to improve climate models and projections, arXiv preprint, https://arxiv.org/abs/2304.12952, JGR, subm., 2023. |
| [86] | Lee, J.-Y., J. Marotzke, G. Bala, L. Cao, S. Corti, J.P. Dunne, F. Engelbrecht, E. Fischer, J.C. Fyfe, C. Jones, A. Maycock, J. Mutemi, O. Ndiaye, S. Panickal, and T. Zhou, Fu-ture Global Climate: Scenario-Based Projections and NearTerm Information. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Wa-terfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. |
| [87] | Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 553-672, doi:10.1017/9781009157896.006, 2021. · doi:10.1017/9781009157896.006 |
| [88] | Rasp, S., Pritchard, M. S., and Gentine, P. Deep learning to represent subgrid processes in climate models. Proceedings of the National Academy of Sciences, 115(39), 9684-9689, 2018. |
| [89] | Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J., Carvalhais, N., Prab-hat, Deep learning and process understanding for data-driven Earth system science. Nature 566(7743), 195-204, https://doi.org/10.1038/s41586-019-0912-1, 2019. · doi:10.1038/s41586-019-0912-1 |
| [90] | Stevens, B., Satoh, M., Auger, L. et al. DYAMOND: the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains. Prog Earth Planet Sci 6, 61 (2019). https://doi.org/10.1186/s40645-019-0304-z. · doi:10.1186/s40645-019-0304-z |
| [91] | Camps-Valls, G., Svendsen, D., Martino, L., Muñoz-Marí, J., Laparra, V., Campos-Taberner, M. and Luengo, D. Physics-aware Gaussian processes in remote sensing. Applied Soft Computing 68:69-82, 2018. |
| [92] | Cortés-Andrés, J., Camps-Valls, G., Sippel, S., Székely, E., Sejdinovic, D., Diaz, E. Pérez-Suay, A., Li, Z., Mahecha, M. and Reichstein, M. Physics-aware Nonparametric Regression Models for Earth Data Analysis. Environmental Research Letters 17 (5) 2022. |
| [93] | Winkler, A., Myneni, R., Reimers, C., Reichstein, M. et al. Carbon System State Determines Warming Potential of Emissions, in review: DOI: 10.21203/rs.3.rs-2865911/v1, 2023. · doi:10.21203/rs.3.rs-2865911/v1 |
| [94] | Liu, G., ..., Reimers, C., Winkler, A. et al. Data-driven modeling of canopy geenness dy-namics accounting for environmental memory effects for vegetation phenology. in prep, 2023. |
| [95] | Reimers, C. Rachti, D.H. et al. Understanding Vegetation Phenology using Interpretable Machine Learning based on Wavelet Transform of Meteorological Drivers in preparation, (www.bgc-jena.mpg.de/ creimers), 2023. |
| [96] | ElGhawi, R., Kraft, B., Reimers, C., Reichstein, M., Körner, M., Gentine, P. and Winkler, A.J. Hybrid modeling of evapotranspiration: inferring stomatal and aerodynamic resistances using combined physics-based and machine learning. Environ. Res. Lett. 18, 034039, 2023 https://doi.org/10.1088/1748-9326/acbbe0. · doi:10.1088/1748-9326/acbbe0 |
| [97] | Reimers, C., Winkler, A., Humphrey, V., and Reichstein, M. Disentangling direct and indi-rect soil moisture effects on ecosystem carbon uptake with Causal Modeling. In EGU General Assembly Conference Abstracts (pp. EGU22-11148), 2022 (May). |
| [98] | Zhan, C., Orth, R., Migliavacca, M., Zaehle, S., Reichstein, M., Engel, J., ... and Winkler, A. J. Emergence of the physiological effects of elevated CO2 on land-atmosphere exchange of carbon and water. Global Change Biology, 28(24), 7313-7326, 2022. |
| [99] | Liu, G., Migliavacca, M., Reimers, C., Bastos, A., Linscheid, N., Reichstein, M., and Win-kler, A. J. Compound effects of extreme spring temperature fluctuations on vegetation phe-nology (No. EGU23-14577). Copernicus Meetings. 2023. Reporter: Jessica Montgomery |
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.
