Altosaar, Jaan, Rajesh Ranganath, and Kyle Cranmer. 2019. “Hierarchical Variational Models for Statistical Physics.” In, 5.
Asher, M. J., B. F. W. Croke, A. J. Jakeman, and L. J. M. Peeters. 2015. “A Review of Surrogate Models and Their Application to Groundwater Modeling.” Water Resources Research
51 (8): 5957–73.
Atkinson, Steven, Waad Subber, and Liping Wang. 2019. “Data-Driven Discovery of Free-Form Governing Differential Equations.” In, 7.
Ayed, Ibrahim, and Emmanuel de Bézenac. 2019. “Learning Dynamical Systems from Partial Observations.” In Advances In Neural Information Processing Systems, 12.
Baker, Ruth E., Jose-Maria Peña, Jayaratnam Jayamohan, and Antoine Jérusalem. 2018. “Mechanistic Models Versus Machine Learning, a Fight Worth Fighting for the Biological Community?” Biology Letters
14 (5): 20170660.
Bar-Sinai, Yohai, Stephan Hoyer, Jason Hickey, and Michael P. Brenner. 2019. “Learning Data-Driven Discretizations for Partial Differential Equations.” Proceedings of the National Academy of Sciences
116 (31): 15344–49.
Brehmer, Johann, Kyle Cranmer, Siddharth Mishra-Sharma, Felix Kling, and Gilles Louppe. 2019. “Mining Gold: Improving Simulation-Based Inference with Latent Information.” In, 7.
Brunton, Steven L., and Jose Nathan Kutz. 2019. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
. Cambridge: Cambridge University Press.
Brunton, Steven L., Joshua L. Proctor, and J. Nathan Kutz. 2016. “Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems.” Proceedings of the National Academy of Sciences
113 (15): 3932–37.
Carleo, Giuseppe, and Matthias Troyer. 2017. “Solving the Quantum Many-Body Problem with Artificial Neural Networks.” Science
355 (6325): 602–6.
Chang, Michael B., Tomer Ullman, Antonio Torralba, and Joshua B. Tenenbaum. 2017. “A Compositional Object-Based Approach to Learning Physical Dynamics.”
In Proceedings of ICLR
Cranmer, Miles D, Rui Xu, Peter Battaglia, and Shirley Ho. 2019. “Learning Symbolic Physics with Graph Networks.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), 6.
Cui, Tao, Luk Peeters, Dan Pagendam, Trevor Pickett, Huidong Jin, Russell S. Crosbie, Matthias Raiber, David W. Rassam, and Mat Gilfedder. 2018. “Emulator-Enabled Approximate Bayesian Computation (ABC) and Uncertainty Analysis for Computationally Expensive Groundwater Models.” Journal of Hydrology
564 (September): 191–207.
Deiana, Allison McCarn, Nhan Tran, Joshua Agar, Michaela Blott, Giuseppe Di Guglielmo, Javier Duarte, Philip Harris, et al. 2021. “Applications and Techniques for Fast Machine Learning in Science.” arXiv:2110.13041 [Physics]
Filippi, Jean-Baptiste, Vivien Mallet, and Bahaa Nader. 2014. “Representation and Evaluation of Wildfire Propagation Simulations.” International Journal of Wildland Fire
23 (1): 46.
Girolami, Mark, Eky Febrianto, Ge Yin, and Fehmi Cirak. 2021. “The Statistical Finite Element Method (statFEM) for Coherent Synthesis of Observation Data and Model Predictions.” Computer Methods in Applied Mechanics and Engineering
375 (March): 113533.
Gladish, Daniel W., Daniel E. Pagendam, Luk J. M. Peeters, Petra M. Kuhnert, and Jai Vaze. 2018. “Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models.” Journal of Agricultural, Biological and Environmental Statistics
23 (1): 39–62.
Goldstein, Evan B., and Giovanni Coco. 2015. “Machine Learning Components in Deterministic Models: Hybrid Synergy in the Age of Data.” Frontiers in Environmental Science
Gulian, Mamikon, Ari Frankel, and Laura Swiler. 2020. “Gaussian Process Regression Constrained by Boundary Value Problems.” arXiv:2012.11857 [Cs, Math, Stat]
He, QiZhi, David Barajas-Solano, Guzel Tartakovsky, and Alexandre M. Tartakovsky. 2020. “Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport.” Advances in Water Resources
141 (July): 103610.
Hoffimann, Júlio, Maciel Zortea, Breno de Carvalho, and Bianca Zadrozny. 2021. “Geostatistical Learning: Challenges and Opportunities.” Frontiers in Applied Mathematics and Statistics
Holl, Philipp, Nils Thuerey, and Vladlen Koltun. 2020. “Learning to Control PDEs with Differentiable Physics.”
Hu, Yuanming, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand. 2020. “DiffTaichi: Differentiable Programming for Physical Simulation.”
Hu, Yuanming, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Frédo Durand. 2019. “Taichi: A Language for High-Performance Computation on Spatially Sparse Data Structures.” ACM Transactions on Graphics
38 (6): 1–16.
Innes, Mike, Alan Edelman, Keno Fischer, Chris Rackauckas, Elliot Saba, Viral B. Shah, and Will Tebbutt. 2019. “A Differentiable Programming System to Bridge Machine Learning and Scientific Computing.”
Karniadakis, George Em, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. 2021. “Physics-Informed Machine Learning.” Nature Reviews Physics
, May, 1–19.
Kashinath, K., M. Mustafa, A. Albert, J-L. Wu, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, et al. 2021. “Physics-Informed Machine Learning: Case Studies for Weather and Climate Modelling.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
379 (2194): 20200093.
Kasim, M. F., D. Watson-Parris, L. Deaconu, S. Oliver, P. Hatfield, D. H. Froula, G. Gregori, et al. 2020. “Up to Two Billion Times Acceleration of Scientific Simulations with Deep Neural Architecture Search.” arXiv:2001.08055 [Physics, Stat]
Kasim, Muhammad, J Topp-Mugglestone, P Hatﬁeld, D H Froula, G Gregori, M Jarvis, E Viezzer, and Sam Vinko. 2019. “A Million Times Speed up in Parameters Retrieval with Deep Learning.” In, 5.
Kimura, Nobuaki, Ikuo Yoshinaga, Kenji Sekijima, Issaku Azechi, and Daichi Baba. 2020. “Convolutional Neural Network Coupled with a Transfer-Learning Approach for Time-Series Flood Predictions.” Water
12 (1): 96.
Li, Yunzhu, Antonio Torralba, Animashree Anandkumar, Dieter Fox, and Animesh Garg. 2020. “Causal Discovery in Physical Systems from Videos.” arXiv:2007.00631 [Cs, Stat]
Liu, Xiao, Kyongmin Yeo, and Siyuan Lu. 2020. “Statistical Modeling for Spatio-Temporal Data From Stochastic Convection-Diffusion Processes.” Journal of the American Statistical Association
0 (0): 1–18.
Liu, Yunjie, Evan Racah, Prabhat, Joaquin Correa, Amir Khosrowshahi, David Lavers, Kenneth Kunkel, Michael Wehner, and William Collins. 2016. “Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasets.” arXiv:1605.01156 [Cs]
Lu, Peter Y., Joan Ariño, and Marin Soljačić. 2021. “Discovering Sparse Interpretable Dynamics from Partial Observations.” arXiv:2107.10879 [Physics]
Medasani, Bharat, Anthony Gamst, Hong Ding, Wei Chen, Kristin A. Persson, Mark Asta, Andrew Canning, and Maciej Haranczyk. 2016. “Predicting Defect Behavior in B2 Intermetallics by Merging Ab Initio Modeling and Machine Learning.” Npj Computational Materials
2 (1): 1.
Meng, Chuizheng, Sungyong Seo, Defu Cao, Sam Griesemer, and Yan Liu. 2022. “When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning.” arXiv:2203.16797 [Cs, Stat]
Merwe, Rudolph van der, Todd K. Leen, Zhengdong Lu, Sergey Frolov, and Antonio M. Baptista. 2007. “Fast Neural Network Surrogates for Very High Dimensional Physics-Based Models in Computational Oceanography.” Neural Networks
, Computational Intelligence in Earth and Environmental Sciences, 20 (4): 462–78.
Mo, Shaoxing, Dan Lu, Xiaoqing Shi, Guannan Zhang, Ming Ye, Jianfeng Wu, and Jichun Wu. 2017. “A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling.” Water Resources Research
53 (12): 10802–23.
Nabian, Mohammad Amin, and Hadi Meidani. 2019. “A Deep Learning Solution Approach for High-Dimensional Random Differential Equations.” Probabilistic Engineering Mechanics
57 (July): 14–25.
Nair, Suraj, Yuke Zhu, Silvio Savarese, and Li Fei-Fei. 2019. “Causal Induction from Visual Observations for Goal Directed Tasks.” arXiv:1910.01751 [Cs, Stat]
Ng, Ignavier, Shengyu Zhu, Zhitang Chen, and Zhuangyan Fang. 2019. “A Graph Autoencoder Approach to Causal Structure Learning.”
In Advances In Neural Information Processing Systems
Otness, Karl, Arvi Gjoka, Joan Bruna, Daniele Panozzo, Benjamin Peherstorfer, Teseo Schneider, and Denis Zorin. 2021. “An Extensible Benchmark Suite for Learning to Simulate Physical Systems.”
Paleyes, Andrei, Mark Pullin, Maren Mahsereci, Neil Lawrence, and Javier Gonzalez. 2019. “Emulation of Physical Processes with Emukit.”
In Advances In Neural Information Processing Systems
Park, Ji Hwan, Shinjae Yoo, and Balu Nadiga. 2019. “Machine Learning Climate Variability.” In, 5.
Partee, Sam, Michael Ringenburg, Benjamin Robbins, and Andrew Shao. 2019. “Model Parameter Optimization: ML-Guided Trans-Resolution Tuning of Physical Models.” In. Zenodo.
Pathak, Jaideep, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott. 2018. “Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.” Physical Review Letters
120 (2): 024102.
Pathak, Jaideep, Zhixin Lu, Brian R. Hunt, Michelle Girvan, and Edward Ott. 2017. “Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data.” Chaos: An Interdisciplinary Journal of Nonlinear Science
27 (12): 121102.
Pestourie, Raphaël, Youssef Mroueh, Christopher Vincent Rackauckas, Payel Das, and Steven Glenn Johnson. 2021. “Data-Efficient Training with Physics-Enhanced Deep Surrogates.”
Portwood, Gavin D, Peetak P Mitra, Mateus Dias Ribeiro, Tan Minh Nguyen, Balasubramanya T Nadiga, Juan A Saenz, Michael Chertkov, and Animesh Garg. 2019. “Turbulence Forecasting via Neural ODE.” In, 7.
Qian, Elizabeth, Boris Kramer, Benjamin Peherstorfer, and Karen Willcox. 2020. “Lift & Learn: Physics-Informed Machine Learning for Large-Scale Nonlinear Dynamical Systems.” Physica D: Nonlinear Phenomena
406 (May): 132401.
Rackauckas, Chris, Alan Edelman, Keno Fischer, Mike Innes, Elliot Saba, Viral B Shah, and Will Tebbutt. 2020. “Generalized Physics-Informed Learning Through Language-Wide Differentiable Programming.” MIT Web Domain
Raghu, Maithra, and Eric Schmidt. 2020. “A Survey of Deep Learning for Scientific Discovery.” arXiv:2003.11755 [Cs, Stat]
Raissi, Maziar, Alireza Yazdani, and George Em Karniadakis. 2020. “Hidden Fluid Mechanics: Learning Velocity and Pressure Fields from Flow Visualizations.” Science
367 (6481): 1026–30.
Ramsundar, Bharath, Dilip Krishnamurthy, and Venkatasubramanian Viswanathan. 2021. “Differentiable Physics: A Position Piece.” arXiv:2109.07573 [Physics]
Razavi, Saman, Bryan A. Tolson, and Donald H. Burn. 2012. “Review of Surrogate Modeling in Water Resources.” Water Resources Research
Rezende, Danilo J, Sébastien Racanière, Irina Higgins, and Peter Toth. 2019. “Equivariant Hamiltonian Flows.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), 6.
Saemundsson, Steindor, Alexander Terenin, Katja Hofmann, and Marc Peter Deisenroth. 2020. “Variational Integrator Networks for Physically Structured Embeddings.” arXiv:1910.09349 [Cs, Stat]
Sanchez-Gonzalez, Alvaro, Victor Bapst, Peter Battaglia, and Kyle Cranmer. 2019. “Hamiltonian Graph Networks with ODE Integrators.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), 11.
Sanchez-Gonzalez, Alvaro, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter W. Battaglia. 2020. “Learning to Simulate Complex Physics with Graph Networks.”
In arXiv:2002.09405 [Physics, Stat]
Sargsyan, Khachik, Bert Debusschere, Habib Najm, and Youssef Marzouk. 2009. “Bayesian Inference of Spectral Expansions for Predictability Assessment in Stochastic Reaction Networks.” Journal of Computational and Theoretical Nanoscience
6 (10): 2283–97.
Sarkar, Soumalya, and Michael Joly. 2019. “Multi-FIdelity Learning with Heterogeneous Domains.”
Särkkä, Simo. 2011. “Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression.”
In Artificial Neural Networks and Machine Learning – ICANN 2011
, edited by Timo Honkela, Włodzisław Duch, Mark Girolami, and Samuel Kaski, 6792:151–58. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer.
Sun, Alexander Y., Hongkyu Yoon, Chung-Yan Shih, and Zhi Zhong. 2021. “Applications of Physics-Informed Scientific Machine Learning in Subsurface Science: A Survey.” arXiv:2104.04764 [Physics]
Tait, Daniel J., and Theodoros Damoulas. 2020. “Variational Autoencoding of PDE Inverse Problems.” arXiv:2006.15641 [Cs, Stat]
Tartakovsky, Alexandre M., Carlos Ortiz Marrero, Paris Perdikaris, Guzel D. Tartakovsky, and David Barajas-Solano. 2018. “Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks,”
Thuerey, Nils, Philipp Holl, Maximilian Mueller, Patrick Schnell, Felix Trost, and Kiwon Um. 2021. Physics-Based Deep Learning
Tompson, Jonathan, Kristofer Schlachter, Pablo Sprechmann, and Ken Perlin. 2017. “Accelerating Eulerian Fluid Simulation with Convolutional Networks.”
In Proceedings of the 34th International Conference on Machine Learning - Volume 70
, 3424–33. ICML’17. Sydney, NSW, Australia: JMLR.org.
Willard, Jared, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar. n.d. “Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems” 1 (1): 35.
Witteveen, Jeroen A. S., and Hester Bijl. 2006. “Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos.”
In 44th AIAA Aerospace Sciences Meeting and Exhibit
. American Institute of Aeronautics and Astronautics.
Yang, Liu, Dongkun Zhang, and George Em Karniadakis. 2020. “Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations.” SIAM Journal on Scientific Computing
42 (1): A292–317.
Yu, Xiayang, Tao Cui, J. Sreekanth, Stephane Mangeon, Rebecca Doble, Pei Xin, David Rassam, and Mat Gilfedder. 2020. “Deep Learning Emulators for Groundwater Contaminant Transport Modelling.” Journal of Hydrology
, August, 125351.
Zammit-Mangion, Andrew, and Christopher K. Wikle. 2020. “Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting.” Spatial Statistics
37 (June): 100408.
Zang, Yaohua, Gang Bao, Xiaojing Ye, and Haomin Zhou. 2020. “Weak Adversarial Networks for High-Dimensional Partial Differential Equations.” Journal of Computational Physics
411 (June): 109409.
Zhang, Dongkun, Ling Guo, and George Em Karniadakis. 2020. “Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks.” SIAM Journal on Scientific Computing
42 (2): A639–65.
Zhang, Dongkun, Lu Lu, Ling Guo, and George Em Karniadakis. 2019. “Quantifying Total Uncertainty in Physics-Informed Neural Networks for Solving Forward and Inverse Stochastic Problems.” Journal of Computational Physics
397 (November): 108850.
Zhu, Yinhao, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, and Paris Perdikaris. 2019. “Physics-Constrained Deep Learning for High-Dimensional Surrogate Modeling and Uncertainty Quantification Without Labeled Data.” Journal of Computational Physics
394 (October): 56–81.