{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T14:50:02Z","timestamp":1776351002531,"version":"3.51.2"},"reference-count":59,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSF","award":["1934721"],"award-info":[{"award-number":["1934721"]}]},{"name":"Department of the Interior Midwest Climate Adaptation Science Center"},{"name":"North Temperate Lakes Long-Term Ecological Research"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM\/IMS Trans. Data Sci."],"published-print":{"date-parts":[[2021,8,31]]},"abstract":"<jats:p>\n                    Physics-based models are often used to study engineering and environmental systems. The ability to model these systems is the key to achieving our future environmental sustainability and improving the quality of human life. This article focuses on simulating lake water temperature, which is critical for understanding the impact of changing climate on aquatic ecosystems and assisting in aquatic resource management decisions.\n                    <jats:bold>General Lake Model (GLM)<\/jats:bold>\n                    is a state-of-the-art physics-based model used for addressing such problems. However, like other physics-based models used for studying scientific and engineering systems, it has several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This article proposes a\n                    <jats:bold>physics-guided recurrent neural network model (PGRNN)<\/jats:bold>\n                    that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models (by over 20% even with very little training data), while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where physics-based (also known as mechanistic) models are used.\n                  <\/jats:p>","DOI":"10.1145\/3447814","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T10:45:29Z","timestamp":1621334729000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":213,"title":["Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles"],"prefix":"10.1145","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8544-5233","authenticated-orcid":false,"given":"Xiaowei","family":"Jia","sequence":"first","affiliation":[{"name":"University of Pittsburgh, Pittsburgh, PA"}]},{"given":"Jared","family":"Willard","sequence":"additional","affiliation":[{"name":"University of Minnesota, Twin Cities, Minneapolis, MN"}]},{"given":"Anuj","family":"Karpatne","sequence":"additional","affiliation":[{"name":"Virginia Tech, Blacksburg, VA"}]},{"given":"Jordan S.","family":"Read","sequence":"additional","affiliation":[{"name":"U.S. Geological Survey, Middleton, WI"}]},{"given":"Jacob A.","family":"Zwart","sequence":"additional","affiliation":[{"name":"U.S. Geological Survey, Middleton, WI"}]},{"given":"Michael","family":"Steinbach","sequence":"additional","affiliation":[{"name":"University of Minnesota, Minneapolis, MN"}]},{"given":"Vipin","family":"Kumar","sequence":"additional","affiliation":[{"name":"University of Minnesota, Twin Cities, Minneapolis, MN"}]}],"member":"320","published-online":{"date-parts":[[2021,5,18]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/72.279181"},{"key":"e_1_2_1_2_1","unstructured":"T. Beucler S. Rasp M. Pritchard and P. Gentine. 2019. Achieving conservation of energy in neural network emulators for climate modeling. arXiv:1906.06622 (2019)."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0609476104"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.envsoft.2017.11.016"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113"},{"key":"e_1_2_1_6_1","volume-title":"Machine learning for molecular and materials science. Nature 559, 7715","author":"Butler Keith T.","year":"2018","unstructured":"Keith T. Butler, Daniel W. Davies, Hugh Cartwright, Olexandr Isayev, and Aron Walsh. 2018. Machine learning for molecular and materials science. Nature 559, 7715 (2018), 547."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207179208934317"},{"key":"e_1_2_1_8_1","volume-title":"McNamara","author":"Crutchfield James P.","year":"1987","unstructured":"James P. Crutchfield and Bruce S. McNamara. 1987. Equations of motions a data series. Complex Systems 1 (01 1987)."},{"key":"e_1_2_1_9_1","volume-title":"IFAC Proceedings Volumes","author":"Forssell Urban","year":"1997","unstructured":"Urban Forssell and Peter Lindskog. 1997. Combining semi-physical and neural network modeling: An example of its usefulness. IFAC Proceedings Volumes (1997)."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.24764"},{"key":"e_1_2_1_11_1","first-page":"8","article-title":"Big data: Science in the petabyte era","volume":"455","author":"Graham-Rowe D.","year":"2008","unstructured":"D. Graham-Rowe, D. Goldston, C. Doctorow, M. Waldrop, C. Lynch, F. Frankel, R. Reid, S. Nelson, D. Howe, S. Y. Rhee, et\u00a0al. 2008. Big data: Science in the petabyte era. Nature 455, 7209 (2008), 8\u20139.","journal-title":"Nature"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/2013WR015096"},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","first-page":"e1005655","DOI":"10.1371\/journal.pcbi.1005655","article-title":"Hybrid modeling and prediction of dynamical systems","volume":"13","author":"Hamilton Franz","year":"2017","unstructured":"Franz Hamilton, Alun L. Lloyd, and Kevin B. Flores. 2017. Hybrid modeling and prediction of dynamical systems. PLoS Computational Biology 13, 7 (2017), e1005655.","journal-title":"PLoS Computational Biology"},{"key":"e_1_2_1_14_1","first-page":"109","article-title":"Predicting lake surface water phosphorus dynamics using process-guided machine learning","volume":"430","author":"Hanson Paul C.","year":"2020","unstructured":"Paul C. Hanson, Aviah B. Stillman, Xiaowei Jia, Anuj Karpatne, Hilary A. Dugan, Cayelan C. Carey, Joseph Stachelek, Nicole K. Ward, Yu Zhang, Jordan S. Read, and Vipin Kumar. 2020. Predicting lake surface water phosphorus dynamics using process-guided machine learning. Ecological Modelling 430 (2020), 109\u2013136.","journal-title":"Ecological Modelling"},{"key":"e_1_2_1_15_1","volume-title":"Graham","author":"Harris Ted D.","year":"2017","unstructured":"Ted D. Harris and Jennifer L. Graham. 2017. Predicting cyanobacterial abundance, microcystin, and geosmin in a eutrophic drinking-water reservoir using a 14-year dataset. Lake and Reservoir Management (2017)."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02033919"},{"key":"e_1_2_1_17_1","unstructured":"M. R. Hipsey L. C. Bruce and D. P. Hamilton. 2014. GLM-general lake model: Model overview and user information. The University of Western Perth Perth Australia."},{"key":"e_1_2_1_18_1","volume-title":"Michael Weber, et\u00a0al.","author":"Hipsey Matthew R.","year":"2019","unstructured":"Matthew R. Hipsey, Louise C. Bruce, Casper Boon, Brendan Busch, Cayelan C. Carey, David P. Hamilton, Paul C. Hanson, Jordan S. Read, Eduardo De Sousa, Michael Weber, et\u00a0al. 2019. A general lake model (GLM 3.0) for linking with high-frequency sensor data from the global lake ecological observatory network (GLEON). (2019)."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975673.63"},{"key":"e_1_2_1_20_1","unstructured":"J. Kani and A. Elsheikh. 2017. DR-RNN: A deep residual recurrent neural network for model reduction. arXiv:1709.00939 (2017)."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2017.2720168"},{"key":"e_1_2_1_22_1","volume-title":"Physics-guided neural networks (PGNN): An application in lake temperature modeling. arXiv preprint arXiv:1710.11431","author":"Karpatne Anuj","year":"2017","unstructured":"Anuj Karpatne, William Watkins, Jordan Read, and Vipin Kumar. 2017b. Physics-guided neural networks (PGNN): An application in lake temperature modeling. arXiv preprint arXiv:1710.11431 (2017)."},{"key":"e_1_2_1_23_1","volume-title":"Kingma and Jimmy Ba","author":"Diederik","year":"2014","unstructured":"Diederik P. Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2783258.2783380"},{"key":"e_1_2_1_25_1","volume-title":"Debates\u2014The future of hydrological sciences: A (common) path forward? One water. One world. Many climes. Many souls. WRR","author":"Lall Upmanu","year":"2014","unstructured":"Upmanu Lall. 2014. Debates\u2014The future of hydrological sciences: A (common) path forward? One water. One world. Many climes. Many souls. WRR (2014)."},{"key":"e_1_2_1_26_1","volume-title":"The parable of Google Flu: Traps in big data analysis. Science","author":"\u00a0al David Lazer","year":"2014","unstructured":"David Lazer et\u00a0al. 2014. The parable of Google Flu: Traps in big data analysis. Science (2014)."},{"key":"e_1_2_1_27_1","volume-title":"Loong Fah Cheong, and Robby T. Tan","author":"Li Ruotent","year":"2019","unstructured":"Ruotent Li, Loong Fah Cheong, and Robby T. Tan. 2019. Heavy rain image restoration: Integrating physics model and conditional adversarial learning. arXiv preprint arXiv:1904.05050 (2019)."},{"key":"e_1_2_1_28_1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1093\/icb\/19.1.331","article-title":"Temperature as an ecological resource","volume":"19","author":"\u00a0al John J.","year":"1979","unstructured":"John J. Magnuson et\u00a0al. 1979. Temperature as an ecological resource. American Zoologist 19, 1 (1979), 331\u2013343.","journal-title":"American Zoologist"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/26\/1\/201"},{"key":"e_1_2_1_30_1","volume-title":"McDonnell and Keith Beven","author":"Jeffrey","year":"2014","unstructured":"Jeffrey J. McDonnell and Keith Beven. 2014. Debates\u2014The future of hydrological sciences: A (common) path forward? A call to action aimed at understanding velocities, celerities and residence time distributions of the headwater hydrograph. WRR (2014)."},{"key":"e_1_2_1_31_1","volume-title":"Proceedings of the Workshop on Deep Learning for Physical Sciences (DLPS 2017), NIPS 2017.","author":"McGregor Sean","year":"2017","unstructured":"Sean McGregor, Dattaraj Dhuri, Anamaria Berea, and Andr\u00e9s Mu\u00f1oz-Jaramillo. 2017. FlareNet: A deep learning framework for solar phenomena prediction. In Proceedings of the Workshop on Deep Learning for Physical Sciences (DLPS 2017), NIPS 2017."},{"key":"e_1_2_1_32_1","doi-asserted-by":"crossref","unstructured":"N. Muralidhar M. R. Islam M. Marwah A. Karpatne and N. Ramakrishnan. 2018. Incorporating prior domain knowledge into deep neural networks. In IEEE Big Data. IEEE.","DOI":"10.1109\/BigData.2018.8621955"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/3093338.3093340"},{"key":"e_1_2_1_34_1","volume-title":"Paerl and Jef Huisman","author":"Hans","year":"2008","unstructured":"Hans W. Paerl and Jef Huisman. 2008. Blooms like it hot. Science 320, 5872 (2008), 57\u201358."},{"key":"e_1_2_1_35_1","unstructured":"Jinshan Pan Yang Liu Jiangxin Dong Jiawei Zhang Jimmy Ren Jinhui Tang Yu-Wing Tai and Ming-Hsuan Yang. 2018. Physics-based generative adversarial models for image restoration and beyond. arXiv e-prints Article arxiv:cs.CV\/1808.00605"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/4801012"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1523-1739.2008.00950.x"},{"key":"e_1_2_1_38_1","volume-title":"Deep hidden physics models: Deep learning of nonlinear partial differential equations. arXiv:1801.06637 [cs, math, stat] (Jan","author":"Raissi Maziar","year":"2018","unstructured":"Maziar Raissi. 2018. Deep hidden physics models: Deep learning of nonlinear partial differential equations. arXiv:1801.06637 [cs, math, stat] (Jan. 2018). http:\/\/arxiv.org\/abs\/1801.06637arXiv: 1801.06637."},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.01.060"},{"key":"e_1_2_1_40_1","unstructured":"Maziar Raissi Paris Perdikaris and George Em Karniadakis. 2018a. Multistep neural networks for data-driven discovery of nonlinear dynamical systems. arXiv e-prints Article arxiv:math.DS\/1801.01236"},{"key":"e_1_2_1_41_1","volume-title":"Hidden fluid mechanics: A Navier-Stokes informed deep learning framework for assimilating flow visualization data. arXiv preprint arXiv:1808.04327","author":"Raissi Maziar","year":"2018","unstructured":"Maziar Raissi, Alireza Yazdani, and George Em Karniadakis. 2018b. Hidden fluid mechanics: A Navier-Stokes informed deep learning framework for assimilating flow visualization data. arXiv preprint arXiv:1808.04327 (2018)."},{"key":"e_1_2_1_42_1","volume-title":"Read et\u00a0al","author":"Emily","year":"2017","unstructured":"Emily K. Read et\u00a0al. 2017. Water quality data for national-scale aquatic research: The Water Quality Portal. Water Resources Research (2017)."},{"key":"e_1_2_1_43_1","volume-title":"et\u00a0al","author":"Read Jordan S.","year":"2019","unstructured":"Jordan S. Read, Xiaowei Jia, Jared Willard, Alison P. Appling, Jacob A. Zwart, Samantha K. Oliver, Anuj Karpatne, Gretchen J. A. Hansen, Paul C. Hanson, William Watkins, et\u00a0al. 2019. Process-guided deep learning predictions of lake water temperature. Water Resources Research (2019)."},{"key":"e_1_2_1_44_1","volume-title":"Learning with weak supervision from physics and data-driven constraints.AI Magazine","author":"\u00a0al Hongyu Ren","year":"2018","unstructured":"Hongyu Ren et\u00a0al. 2018. Learning with weak supervision from physics and data-driven constraints.AI Magazine (2018)."},{"key":"e_1_2_1_45_1","volume-title":"Roberts et\u00a0al","author":"James","year":"2013","unstructured":"James J. Roberts et\u00a0al. 2013. Fragmentation and thermal risks from climate change interact to affect persistence of native trout in the Colorado River basin. Global Change Biology (2013)."},{"key":"e_1_2_1_46_1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1080\/02755947.2016.1264507","article-title":"Nonnative trout invasions combined with climate change threaten persistence of isolated cutthroat trout populations in the southern Rocky Mountains","volume":"37","author":"Roberts James J.","year":"2017","unstructured":"James J. Roberts, Kurt D. Fausch, Mevin B. Hooten, and Douglas P. Peterson. 2017. Nonnative trout invasions combined with climate change threaten persistence of isolated cutthroat trout populations in the southern Rocky Mountains. North American Journal of Fisheries Management 37, 2 (2017), 314\u2013325.","journal-title":"North American Journal of Fisheries Management"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1602614"},{"key":"e_1_2_1_48_1","doi-asserted-by":"crossref","unstructured":"O. San and R. Maulik. 2018. Machine learning closures for model order reduction of thermal fluids. Applied Mathematical Modelling (2018).","DOI":"10.1016\/j.apm.2018.03.037"},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33712-3_27"},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.5555\/3298483.3298610"},{"key":"e_1_2_1_51_1","volume-title":"A domainguided CNN architecture for predicting age from structural brain images. arXiv preprint arXiv:1808.04362","author":"Sturmfels Pascal","year":"2018","unstructured":"Pascal Sturmfels, Saige Rutherford, Mike Angstadt, Mark Peterson, Chandra Sripada, and Jenna Wiens. 2018. A domainguided CNN architecture for predicting age from structural brain images. arXiv preprint arXiv:1808.04362 (2018)."},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1227079"},{"key":"e_1_2_1_53_1","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1175\/1520-0450(1973)012<1410:ASBAFF>2.0.CO;2","article-title":"A simple but accurate formula for the saturation vapor pressure over liquid water","volume":"12","author":"Tabata S.","year":"1973","unstructured":"S. Tabata. 1973. A simple but accurate formula for the saturation vapor pressure over liquid water. Journal of Applied Meteorology 12, 8 (1973), 1410\u20131411.","journal-title":"Journal of Applied Meteorology"},{"key":"e_1_2_1_54_1","volume-title":"D. Tartakovsky, and David Barajas-Solano.","author":"Tartakovsky Alexandre M.","year":"2018","unstructured":"Alexandre M. Tartakovsky, Carlos Ortiz Marrero, D. Tartakovsky, and David Barajas-Solano. 2018. Learning parameters and constitutive relationships with physics informed deep neural networks. arXiv preprint arXiv:1808.03398 (2018)."},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0197704"},{"key":"e_1_2_1_56_1","volume-title":"Integrating physics-based modeling with machine learning: A survey. arXiv preprint arXiv:2003.04919","author":"Willard Jared","year":"2020","unstructured":"Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar. 2020a. Integrating physics-based modeling with machine learning: A survey. arXiv preprint arXiv:2003.04919 (2020)."},{"key":"e_1_2_1_57_1","volume-title":"Predicting water temperature dynamics of unmonitored lakes with meta transfer learning. arXiv preprint arXiv:2011.05369","author":"Willard Jared D.","year":"2020","unstructured":"Jared D. Willard, Jordan S. Read, Alison P. Appling, Samantha K. Oliver, Xiaowei Jia, and Vipin Kumar. 2020b. Predicting water temperature dynamics of unmonitored lakes with meta transfer learning. arXiv preprint arXiv:2011.05369 (2020)."},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cageo.2015.05.016"},{"key":"e_1_2_1_59_1","doi-asserted-by":"crossref","unstructured":"Kun Yao John E. Herr David W. Toth Ryker Mckintyre and John Parkhill. 2018. The TensorMol-0.1 model chemistry: A neural network augmented with long-range physics. https:\/\/pubs.rsc.org\/en\/content\/articlehtml\/2018\/sc\/c7sc04934j.","DOI":"10.1039\/C7SC04934J"}],"container-title":["ACM\/IMS Transactions on Data Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3447814","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3447814","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3447814","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T13:56:03Z","timestamp":1776347763000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3447814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,18]]},"references-count":59,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,8,31]]}},"alternative-id":["10.1145\/3447814"],"URL":"https:\/\/doi.org\/10.1145\/3447814","relation":{},"ISSN":["2691-1922"],"issn-type":[{"value":"2691-1922","type":"print"}],"subject":[],"published":{"date-parts":[[2021,5,18]]},"assertion":[{"value":"2019-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}