Information Systems; Signal Processing; Datasets; Fluid Dynamics
Abstract :
[en] Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Ohana, Ruben ✱; Polymathic AI ; Flatiron Institute, United States
McCabe, Michael ✱; Polymathic AI
Meyer, Lucas; Polymathic AI
Morel, Rudy; Polymathic AI ; Flatiron Institute, United States
Agocs, Fruzsina J.; Flatiron Institute, United States ; University of Colorado, Boulder, United States
Beneitez, Miguel; University of Cambridge, United Kingdom
Berger, Marsha; Flatiron Institute, United States ; New York University, United States
Burkhart, Blakesley; Flatiron Institute, United States ; Rutgers University, United States
Dalziel, Stuart B.; University of Cambridge, United Kingdom
Fielding, Drummond B.; Flatiron Institute, United States ; Cornell University, United States
Fortunato, Daniel; Flatiron Institute, United States
Goldberg, Jared A.; Flatiron Institute, United States
Hirashima, Keiya; Polymathic AI ; Flatiron Institute, United States ; University of Tokyo, Japan
Jiang, Yan-Fei; Flatiron Institute, United States
Kerswell, Rich R.; University of Cambridge, United Kingdom
Maddu, Suryanarayana; Flatiron Institute, United States
Miller, Jonah; Los Alamos National Laboratory, United States
Mukhopadhyay, Payel; University of California, Berkeley, United States
Nixon, Stefan S.; University of Cambridge, United Kingdom
Shen, Jeff; Princeton University, United States
Watteaux, Romain; CEA DAM, France
Blancard, Bruno Régaldo-Saint; Polymathic AI ; Flatiron Institute, United States
Rozet, François ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Big Data ; Polymathic AI
Parker, Liam H.; Polymathic AI ; Flatiron Institute, United States ; University of California, Berkeley, United States
Cranmer, Miles; Polymathic AI ; University of Cambridge, United Kingdom
Ho, Shirley; Polymathic AI ; Flatiron Institute, United States ; New York University, United States ; Princeton University, United States
The authors would like to thank the Scientific Computing Core, a division of the Flatiron Institute, a division of the Simons Foundation, and more specifically Geraud Krawezik for the computing support, the members of Polymathic AI for the insightful discussions, and especially Michael Eickenberg for his input on the paper. Polymathic AI acknowledges funding from the Simons Foundation and Schmidt Sciences, LLC. Additionally, we gratefully acknowledge the support of NVIDIA Corporation for the donation of the DGX Cloud node hours used in this research. The authors would like to thank Aaron Watters, Alex Meng and Lucy Reading-Ikkanda for their help on the visuals, as well as Keaton Burns for his help on using Dedalus. M.B and R.R.K acknowledge Dr Jacob Page and Dr Yves Dubief for their valuable discussions about the multistability of viscoelastic states, and are grateful to EPSRC for supporting this work via grant EP/V027247/1. B.B. acknowledges the generous support of the Flatiron Institute Simons Foundation for hosting the CATS database and the support of NASA award 19-ATP19-0020. R.M. would like to thank Keaton Burns for his advice on using the Dedalus package for generating data. J.S, J.A.G, Y-F J. would like to thank Lars Bildsten, William C. Schultz, and Matteo Cantiello for valuable discussions instrumental to the development of the global RSG simulation setup. These calculations were supported in part by NASA grants ATP-80NSSC18K0560 and ATP-80NSSC22K0725, and computational resources were provided by the NASA High-End Computing (HEC) program through the NASA Advanced Supercomputing (NAS) Division at Ames. J.M.M's work was supported through the Laboratory Directed Research and Development program under project number 20220564ECR at Los Alamos National Laboratory (LANL). LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). P.M. acknowledges the continued support of the Neutrino Theory Network Program Grant under award number DE-AC02-07CHI11359. P.M. expresses gratitude to the Institute of Astronomy at the University of Cambridge for hosting them as a visiting researcher, during which the idea for this contribution was conceived and initiated. S.S.N would like to acknowledge that their work is funded and supported by the CEA. K.H. acknowledges support of Grants-in-Aid for JSPS Fellows (22KJ1153) and MEXT as \u201CProgram for Promoting Researches on the Supercomputer Fugaku\u201D (Structure and Evolution of the Universe Unraveled by Fusion of Simulation and AI; Grant Number JPMXP1020230406). These calculations are partially carried out on Cray XC50 CPU-cluster at the Center for Computational Astrophysics (CfCA) of the National Astronomical Observatory of Japan.
V. Eyring, S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor. Overview of the coupled model intercomparison project phase 6 (cmip6) experimental design and organization. Geoscientific Model Development, 9(5):1937-1958, 2016.
Marsha J. Berger and Randall J. LeVeque. Implicit adaptive mesh refinement for dispersive tsunami propagation, 2024.
Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Ferran Alet, Suman Ravuri, Timo Ewalds, Zach Eaton-Rosen, Weihua Hu, et al. Graphcast: Learning skillful medium-range global weather forecasting. arXiv preprint arXiv:2212.12794, 2022.
Lorenz T Biegler, Omar Ghattas, Matthias Heinkenschloss, and Bart van Bloemen Waanders. Large-scale pde-constrained optimization: an introduction. In Large-scale PDE-constrained optimization, pages 3-13. Springer, 2003.
Bijan Mohammadi and Olivier Pironneau. Shape optimization in fluid mechanics. Annu. Rev. Fluid Mech., 36:255-279, 2004.
Kyle Cranmer, Johann Brehmer, and Gilles Louppe. The frontier of simulation-based inference. Proceedings of the National Academy of Sciences, 117(48):30055-30062, 2020.
Pablo Lemos, Liam Parker, ChangHoon Hahn, Shirley Ho, Michael Eickenberg, Jiamin Hou, Elena Massara, Chirag Modi, Azadeh Moradinezhad Dizgah, Bruno Regaldo-Saint Blancard, and David Spergel. Simbig: Field-level simulation-based inference of galaxy clustering, 2023.
Lawrence C Evans. Partial differential equations, volume 19. American Mathematical Society, 2022.
Nestor V. Queipo, Raphael T. Haftka, Wei Shyy, Tushar Goel, Rajkumar Vaidyanathan, and P. Kevin Tucker. Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41(1):1-28, 2005.
A. Forrester, A. Sóbester, and A. Keane. Engineering Design via Surrogate Modelling: A Practical Guide. Wiley, 2008.
Luning Sun, Han Gao, Shaowu Pan, and Jian-Xun Wang. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Computer Methods in Applied Mechanics and Engineering, 361:112732, 2020.
Jun Tao and Gang Sun. Application of deep learning based multi-fidelity surrogate model to robust aerodynamic design optimization. Aerospace Science and Technology, 92:722-737, 2019.
Ehsan Haghighat, Maziar Raissi, Adrian Moure, Hector Gomez, and Ruben Juanes. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 379:113741, 2021.
Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo. Neural-network quantum state tomography. Nature Physics, 14(5):447-450, 2018.
Kevin Ryczko, David A Strubbe, and Isaac Tamblyn. Deep learning and density-functional theory. Physical Review A, 100(2):022512, 2019.
Kamal Choudhary, Brian DeCost, Chi Chen, Anubhav Jain, Francesca Tavazza, Ryan Cohn, Cheol Woo Park, Alok Choudhary, Ankit Agrawal, Simon JL Billinge, et al. Recent advances and applications of deep learning methods in materials science. npj Computational Materials, 8(1):59, 2022.
Ali Siahkoohi, Rudy Morel, Randall Balestriero, Erwan Allys, Grégory Sainton, Taichi Kawamura, and Maarten V de Hoop. Martian time-series unraveled: A multi-scale nested approach with factorial variational autoencoders. arXiv preprint arXiv:2305.16189, 2023.
Vignesh Gopakumar, Stanislas Pamela, Lorenzo Zanisi, Zongyi Li, Ander Gray, Daniel Brennand, Nitesh Bhatia, Gregory Stathopoulos, Matt Kusner, Marc Peter Deisenroth, Anima Anandkumar, JOREK Team, and MAST Team. Plasma surrogate modelling using fourier neural operators, 2023.
Shashank Subramanian, Peter Harrington, Kurt Keutzer, Wahid Bhimji, Dmitriy Morozov, Michael W. Mahoney, and Amir Gholami. Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior. In Thirty-seventh Conference on Neural Information Processing Systems, 2023.
Bogdan Raonić, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, and Emmanuel de Bézenac. Convolutional neural operators for robust and accurate learning of pdes, 2023.
Jared A. Goldberg, Yan-Fei Jiang, and Lars Bildsten. Numerical Simulations of Convective Three-dimensional Red Supergiant Envelopes. The Astrophysical Journal, 929(2):156, April 2022.
Yuichi Kodama, Martin Shumway, and Rasko Leinonen. The sequence read archive: explosive growth of sequencing data. Nucleic acids research, 40(D1):D54-D56, 2012.
Tony Hey and Anne Trefethen. The data deluge: An e-science perspective. Grid computing: Making the global infrastructure a reality, pages 809-824, 2003.
Lucas Thibaut Meyer, Marc Schouler, Robert Alexander Caulk, Alejandro Ribes, and Bruno Raffin. Training deep surrogate models with large scale online learning. In International Conference on Machine Learning, pages 24614-24630. PMLR, 2023.
Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023.
Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023.
Ebtesam Almazrouei, Hamza Alobeidli, Abdulaziz Alshamsi, Alessandro Cappelli, Ruxandra Cojocaru, Mérouane Debbah, Étienne Goffinet, Daniel Hesslow, Julien Launay, Quentin Malartic, et al. The falcon series of open language models. arXiv preprint arXiv:2311.16867, 2023.
Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. arXiv preprint arXiv:2403.03206, 2024.
Pedro Javier Ortiz Suárez, Benoît Sagot, and Laurent Romary. Asynchronous pipeline for processing huge corpora on medium to low resource infrastructures. In 7th Workshop on the Challenges in the Management of Large Corpora (CMLC-7). Leibniz-Institut für Deutsche Sprache, 2019.
Hugo Laurençon, Lucile Saulnier, Léo Tronchon, Stas Bekman, Amanpreet Singh, Anton Lozhkov, Thomas Wang, Siddharth Karamcheti, Alexander Rush, Douwe Kiela, et al. Obelics: An open web-scale filtered dataset of interleaved image-text documents. Advances in Neural Information Processing Systems, 36, 2024.
Leo Gao, Stella Biderman, Sid Black, Laurence Golding, Travis Hoppe, Charles Foster, Jason Phang, Horace He, Anish Thite, Noa Nabeshima, et al. The pile: An 800gb dataset of diverse text for language modeling. arXiv preprint arXiv:2101.00027, 2020.
Guilherme Penedo, Quentin Malartic, Daniel Hesslow, Ruxandra Cojocaru, Alessandro Cappelli, Hamza Alobeidli, Baptiste Pannier, Ebtesam Almazrouei, and Julien Launay. The refinedweb dataset for falcon llm: outperforming curated corpora with web data, and web data only. arXiv preprint arXiv:2306.01116, 2023.
Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. Laion-5b: An open large-scale dataset for training next generation image-text models. Advances in Neural Information Processing Systems, 35:25278-25294, 2022.
Jack W Rae, Sebastian Borgeaud, Trevor Cai, Katie Millican, Jordan Hoffmann, Francis Song, John Aslanides, Sarah Henderson, Roman Ring, Susannah Young, et al. Scaling language models: Methods, analysis & insights from training gopher. arXiv preprint arXiv:2112.11446, 2021.
Yuanzhi Li, Sébastien Bubeck, Ronen Eldan, Allie Del Giorno, Suriya Gunasekar, and Yin Tat Lee. Textbooks are all you need ii: phi-1.5 technical report. arXiv preprint arXiv:2309.05463, 2023.
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Daniel MacKinlay, Francesco Alesiani, Dirk Pflüger, and Mathias Niepert. Pdebench: An extensive benchmark for scientific machine learning. Advances in Neural Information Processing Systems, 35:1596-1611, 2022.
Jayesh K Gupta and Johannes Brandstetter. Towards multi-spatiotemporal-scale generalized pde modeling. arXiv preprint arXiv:2209.15616, 2022.
Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, et al. Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving pdes. arXiv preprint arXiv:2306.08827, 2023.
Georg Kohl, Li-Wei Chen, and Nils Thuerey. Benchmarking autoregressive conditional diffusion models for turbulent flow simulation. arXiv, 2023.
Florent Bonnet, Jocelyn Mazari, Paola Cinnella, and Patrick Gallinari. Airfrans: High fidelity computational fluid dynamics dataset for approximating reynolds-averaged navier-stokes solutions. Advances in Neural Information Processing Systems, 35:23463-23478, 2022.
Artur Toshev, Gianluca Galletti, Fabian Fritz, Stefan Adami, and Nikolaus Adams. Lagrangebench: A lagrangian fluid mechanics benchmarking suite. Advances in Neural Information Processing Systems, 36, 2024.
Hans Hersbach, Bill Bell, Paul Berrisford, Shoji Hirahara, András Horányi, Joaquín Muñoz-Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Dinand Schepers, et al. The era5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730):1999-2049, 2020.
Sungduk Yu, Walter Hannah, Liran Peng, Jerry Lin, Mohamed Aziz Bhouri, Ritwik Gupta, Björn Lütjens, Justus Christopher Will, Gunnar Behrens, Julius Busecke, Nora Loose, Charles I Stern, Tom Beucler, Bryce Harrop, Benjamin R Hillman, Andrea Jenney, Savannah Ferretti, Nana Liu, Anima Anandkumar, Noah D Brenowitz, Veronika Eyring, Nicholas Geneva, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Akshay Subramaniam, Carl Vondrick, Rose Yu, Laure Zanna, Tian Zheng, Ryan Abernathey, Fiaz Ahmed, David C Bader, Pierre Baldi, Elizabeth Barnes, Christopher Bretherton, Peter Caldwell, Wayne Chuang, Yilun Han, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David Randall, Sara Shamekh, Mark A Taylor, Nathan Urban, Janni Yuval, Guang Zhang, and Michael Pritchard. Climsim: A large multi-scale dataset for hybrid physics-ml climate emulation, 2024.
Steeven Janny, Aurélien Benetteau, Madiha Nadri, Julie Digne, Nicolas Thome, and Christian Wolf. Eagle: Large-scale learning of turbulent fluid dynamics with mesh transformers. In International Conference on Learning Representations (ICLR), 2023.
Sheikh Md Shakeel Hassan, Arthur Feeney, Akash Dhruv, Jihoon Kim, Youngjoon Suh, Jaiyoung Ryu, Yoonjin Won, and Aparna Chandramowlishwaran. BubbleML: A multi-physics dataset and benchmarks for machine learning. In Advances in Neural Information Processing Systems, 2023.
Milad LEYLI ABADI, Antoine Marot, Jérôme Picault, David Danan, Mouadh Yagoubi, Benjamin Donnot, Seif Attoui, Pavel Dimitrov, Asma Farjallah, and Clement Etienam. Lips-learning industrial physical simulation benchmark suite. Advances in Neural Information Processing Systems, 35:28095-28109, 2022.
Wai Tong Chung, Bassem Akoush, Pushan Sharma, Alex Tamkin, Ki Sung Jung, Jacqueline H. Chen, Jack Guo, Davy Brouzet, Mohsen Talei, Bruno Savard, Alexei Y. Poludnenko, and Matthias Ihme. Turbulence in focus: Benchmarking scaling behavior of 3D volumetric super-resolution with BLASTNet 2.0 data. Advances in Neural Information Processing Systems (NeurIPS), 36, 2023.
Yi Li, Eric Perlman, Minping Wan, Yunke Yang, Charles Meneveau, Randal Burns, Shiyi Chen, Alexander Szalay, and Gregory Eyink. A public turbulence database cluster and applications to study lagrangian evolution of velocity increments in turbulence. Journal of Turbulence, (9):N31, 2008.
Michael McCabe, Bruno Régaldo-Saint Blancard, Liam Holden Parker, Ruben Ohana, Miles Cranmer, Alberto Bietti, Michael Eickenberg, Siavash Golkar, Geraud Krawezik, Francois Lanusse, et al. Multiple physics pretraining for physical surrogate models. arXiv preprint arXiv:2310.02994, 2023.
Liu Yang, Siting Liu, Tingwei Meng, and Stanley J. Osher. In-context operator learning with data prompts for differential equation problems. Proceedings of the National Academy of Sciences, 120(39), September 2023.
Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy, Daniel Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A Yeh, Jean Kossaifi, et al. Pretraining codomain attention neural operators for solving multiphysics pdes. arXiv preprint arXiv:2403.12553, 2024.
Jingmin Sun, Yuxuan Liu, Zecheng Zhang, and Hayden Schaeffer. Towards a foundation model for partial differential equation: Multi-operator learning and extrapolation. arXiv preprint arXiv:2404.12355, 2024.
Junhong Shen, Tanya Marwah, and Ameet Talwalkar. Ups: Towards foundation models for pde solving via cross-modal adaptation. arXiv preprint arXiv:2403.07187, 2024.
Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bézenac, and Siddhartha Mishra. Poseidon: Efficient foundation models for pdes, 2024.
Andrew Collette, Thomas Kluyver, Thomas A Caswell, James Tocknell, Jerome Kieffer, Aleksandar Jelenak, Anthony Scopatz, Darren Dale, Thomas VINCENT, Matt Einhorn, et al. h5py/h5py: 3.8. 0-aarch64-wheels. Zenodo, 2023.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library, 2019.
Charles R Harris, K Jarrod Millman, Stéfan J Van Der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J Smith, et al. Array programming with numpy. Nature, 585(7825):357-362, 2020.
Jared A. Goldberg, Yan-Fei Jiang, and Lars Bildsten. Shock Breakout in Three-dimensional Red Supergiant Envelopes. The Astrophysical Journal, 933(2):164, July 2022.
E. Böhm-Vitense. Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen. Zeitschrift für Astrophysik, 46:108, January 1958.
J. P. Cox and R. T. Giuli. Principles of stellar structure. 1968.
Meridith Joyce and Jamie Tayar. A Review of the Mixing Length Theory of Convection in 1D Stellar Modeling. Galaxies, 11(3):75, June 2023.
A. Chiavassa, R. Norris, M. Montargès, R. Ligi, L. Fossati, L. Bigot, F. Baron, P. Kervella, J. D. Monnier, D. Mourard, N. Nardetto, G. Perrin, G. H. Schaefer, T. A. ten Brummelaar, Z. Magic, R. Collet, and M. Asplund. Asymmetries on red giant branch surfaces from CHARA/MIRC optical interferometry. Astronomy & Astrophysics, 600:L2, April 2017.
A. Chiavassa, B. Freytag, and M. Schultheis. Heading Gaia to measure atmospheric dynamics in AGB stars. Astronomy & Astrophysics, 617:L1, September 2018.
A. Chiavassa, K. Kravchenko, F. Millour, G. Schaefer, M. Schultheis, B. Freytag, O. Creevey, V. Hocdé, F. Morand, R. Ligi, S. Kraus, J. D. Monnier, D. Mourard, N. Nardetto, N. Anugu, J. B. Le Bouquin, C. L. Davies, J. Ennis, T. Gardner, A. Labdon, C. Lanthermann, B. R. Setterholm, and T. ten Brummelaar. Optical interferometry and Gaia measurement uncertainties reveal the physics of asymptotic giant branch stars. Astronomy & Astrophysics, 640:A23, August 2020.
Andrea Chiavassa, Kateryna Kravchenko, and Jared A. Goldberg. Signatures of convection in the atmospheres of cool evolved stars. Living Reviews in Computational Astrophysics, 10(1):2, March 2024.
Peter D. Lax and Xu-Dong Liu. Solution of two-dimensional riemann problems of gas dynamics by positive schemes. SIAM Journal on Scientific Computing, 19(2):319-340, 1998.
Alan M. Turing. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B, 237(641):37-72, 1952.
P. Gray and S. K. Scott. Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A+2B→3B; B→C. Chemical Engineering Science, 39(6):1087-1097, 1984.
David L. Williamson, John B. Drake, James J. Hack, Rüdiger Jakob, and Paul N. Swarztrauber. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics, 102(1):211-224, 1992.
J. M. Lattimer and D. N. Schramm. The tidal disruption of neutron stars by black holes in close binaries. The Astrophysical Journal, 210:549-567, December 1976.
Li-Xin Li and Bohdan Paczyński. Transient Events from Neutron Star Mergers. Astrophysical Journal Letters, 507(1):L59-L62, 1998.
B. P. Abbott et al. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Physical Review Letters, 119(16):30-33, 2017.
B. P. Abbott et al. Multi-messenger Observations of a Binary Neutron Star Merger. Astrophysical Journal Letters, 848:L12, 2017.
K. D. Alexander et al. The electromagnetic counterpart of the binary neutron star merger ligo/virgo gw170817. vi. radio constraints on a relativistic jet and predictions for late-time emission from the kilonova ejecta. The Astrophysical Journal Letters, 848(2):L21, oct 2017.
P. S. Cowperthwaite et al. The electromagnetic counterpart of the binary neutron star merger LIGO/VIRGO GW170817. II. UV, optical, and near-ir light curves and comparison to kilonova models. Astrophysical Journal Letters, 848:L17, 2017.
V. A. Villar et al. The combined ultraviolet, optical, and near-infrared light curves of the kilonova associated with the binary neutron star merger gw170817: unified data set, analytic models, and physical implications. Astrophysical Journal Letters, 851(1):L21, 2017.
Lord Rayleigh. Lix. on convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 32(192):529-546, 1916.
Baole Wen, David Goluskin, and Charles R Doering. Steady rayleigh-bénard convection between no-slip boundaries. Journal of Fluid Mechanics, 933:R4, 2022.
Gerald Schubert, Donald Lawson Turcotte, and Peter Olson. Mantle convection in the Earth and planets. Cambridge University Press, 2001.
Gerold Siedler, John Gould, and John A Church. Ocean circulation and climate: observing and modelling the global ocean. Elsevier, 2001.
James R Holton and Gregory J Hakim. An introduction to dynamic meteorology, volume 88. Academic press, 2013.
Sadik Kakaç, Hafit Yüncü, and Kunio Hijikata. Cooling of electronic systems, volume 258. Springer Science & Business Media, 2012.
David R Poirier and G Geiger. Transport phenomena in materials processing. Springer, 2016.
Carl J Hansen, Steven D Kawaler, and Virginia Trimble. Stellar interiors: physical principles, structure, and evolution. Springer Science & Business Media, 2012.
Geoffrey Ingram Taylor. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. i. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 201(1065):192-196, 1950.
Pijush K Kundu, Ira M Cohen, and David R Dowling. Fluid mechanics. Academic press, 2015.
Ting Wu and Guowei He. Space-time energy spectra in turbulent shear flows. Physical Review Fluids, 6(10):100504, 2021.
Prathmesh Vinze and Sebastien Michelin. Self-organization of autophoretic suspensions in confined shear flows. Physical Review Fluids, 9(1):014202, 2024.
Arthur Rizzi. Separated and vortical flow in aircraft aerodynamics: a cfd perspective. The Aeronautical Journal, 127(1313):1065-1103, 2023.
William D Smyth and James N Moum. Ocean mixing by kelvin-helmholtz instability. Oceanography, 25(2):140-149, 2012.
Romana Perinajová, Joe F Juffermans, Jonhatan Lorenzo Mercado, Jean-Paul Aben, Leon Ledoux, Jos JM Westenberg, Hildo J Lamb, and Saša Kenjereš. Assessment of turbulent blood flow and wall shear stress in aortic coarctation using image-based simulations. Biomedical engineering online, 20(1):84, 2021.
Max Gronke and S. Peng Oh. The growth and entrainment of cold gas in a hot wind. Monthly Notices of the Royal Astronomical Society: Letters, 480(1):L111-L115, October 2018.
Matthew W. Abruzzo, Drummond B. Fielding, and Greg L. Bryan. Taming the TuRMoiL: The Temperature Dependence of Turbulence in Cloud-Wind Interactions. The Astrophysical Journal, 966(2):181, May 2024.
Drummond B. Fielding, Eve C. Ostriker, Greg L. Bryan, and Adam S. Jermyn. Multiphase Gas and the Fractal Nature of Radiative Turbulent Mixing Layers. The Astrophysical Journal Letters, 894(2):L24, May 2020.
Miguel Beneitez, Jacob Page, Yves Dubief, and Rich R Kerswell. Multistability of elasto-inertial two-dimensional channel flow. Journal of Fluid Mechanics, 981:A30, 2024.
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895, 2020.
Jean Kossaifi, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, and Anima Anandkumar. Multi-grid tensorized fourier neural operator for high resolution PDEs, 2023.
Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention-MICCAI 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, pages 234-241. Springer, 2015.
Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. A convnet for the 2020s, 2022.
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research, 24(89):1-97, 2023.
Nadim Saad, Gaurav Gupta, Shima Alizadeh, and Danielle Maddix Robinson. Guiding continuous operator learning through physics-based boundary constraints. In ICLR 2023, 2023.
N. Sukumar and Ankit Srivastava. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering, 389:114333, February 2022.
Antonio Alguacil, Wagner Gonçalves Pinto, Michael Bauerheim, Marc C. Jacob, and Stéphane Moreau. Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics, 2021.
Derek Hansen, Danielle Maddix Robinson, Shima Alizadeh, Gaurav Gupta, and Michael Mahoney. Learning physical models that can respect conservation laws. In ICML 2023, 2023.
Nick McGreivy and Ammar Hakim. Invariant preservation in machine learned pde solvers via error correction, 2023.
Kim Stachenfeld, Drummond Buschman Fielding, Dmitrii Kochkov, Miles Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter Battaglia, and Alvaro Sanchez-Gonzalez. Learned simulators for turbulence. In International Conference on Learning Representations, 2022.
Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E. Turner, and Johannes Brandstetter. Pde-refiner: Achieving accurate long rollouts with neural pde solvers, 2023.
Mubashara Akhtar, Omar Benjelloun, Costanza Conforti, Pieter Gijsbers, Joan Giner-Miguelez, Nitisha Jain, Michael Kuchnik, Quentin Lhoest, Pierre Marcenac, Manil Maskey, Peter Mattson, Luis Oala, Pierre Ruyssen, Rajat Shinde, Elena Simperl, Goeffry Thomas, Slava Tykhonov, Joaquin Vanschoren, Jos van der Velde, Steffen Vogler, and Carole-Jean Wu. Croissant: A metadata format for ml-ready datasets. DEEM'24, page 1-6, New York, NY, USA, 2024. Association for Computing Machinery.
Clawpack Development Team. Clawpack software. http://www.clawpack.org, 2021.
James M. Stone, Kengo Tomida, Christopher J. White, and Kyle G. Felker. The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers. The Astrophysical Journal Supplement Series, 249(1):4, July 2020.
Keaton J Burns, Geoffrey M Vasil, Jeffrey S Oishi, Daniel Lecoanet, and Benjamin P Brown. Dedalus: A flexible framework for numerical simulations with spectral methods. Physical Review Research, 2(2):023068, 2020.
Jonah M. Miller, Ben. R. Ryan, and Joshua C. Dolence. νbhlight: Radiation grmhd for neutrino-driven accretion flows. The Astrophysical Journal Supplement Series, 241(2):30, apr 2019.
Romain Watteaux. Détection des grandes structures turbulentes dans les couches de mélange de type Rayleigh-Taylor en vue de la validation de modèles statistiques turbulents bi-structure. Theses, École normale supérieure de Cachan - ENS Cachan, September 2011.
Masaki Iwasawa, Ataru Tanikawa, Natsuki Hosono, Keigo Nitadori, Takayuki Muranushi, and Junichiro Makino. Implementation and performance of FDPS: a framework for developing parallel particle simulation codes. Publications of the Astronomical Society of Japan, 68(4):54, August 2016.
Barath Ezhilan, Michael J Shelley, and David Saintillan. Instabilities and nonlinear dynamics of concentrated active suspensions. Physics of Fluids, 25(7), 2013.
Tong Gao, Meredith D Betterton, An-Sheng Jhang, and Michael J Shelley. Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid. Physical Review Fluids, 2(9):093302, 2017.
David Saintillan and Michael J Shelley. Theory of active suspensions. Complex Fluids in Biological Systems: Experiment, Theory, and Computation, pages 319-355, 2015.
Scott Weady, David B Stein, and Michael J Shelley. Thermodynamically consistent coarse-graining of polar active fluids. Physical Review Fluids, 7(6):063301, 2022.
Suryanarayana Maddu, Scott Weady, and Michael J Shelley. Learning fast, accurate, and stable closures of a kinetic theory of an active fluid. Journal of Computational Physics, page 112869, 2024.
Yan-Fei Jiang. An Implicit Finite Volume Scheme to Solve the Time-dependent Radiation Transport Equation Based on Discrete Ordinates. The Astrophysical Journal Supplement Series, 253(2):49, April 2021.
Carlos A. Iglesias and Forrest J. Rogers. Updated Opal Opacities. The Astrophysical Journal, 464:943, June 1996.
Yan-Fei Jiang, Matteo Cantiello, Lars Bildsten, Eliot Quataert, and Omer Blaes. Local Radiation Hydrodynamic Simulations of Massive Star Envelopes at the Iron Opacity Peak. The Astrophysical Journal, 813(1):74, November 2015.
Yan-Fei Jiang, Matteo Cantiello, Lars Bildsten, Eliot Quataert, Omer Blaes, and James Stone. Outbursts of luminous blue variable stars from variations in the helium opacity. Nature, 561(7724):498-501, September 2018.
K.T.Mandli, A.J. Ahmadia, M.J. Berger, D.A. Calhoun, D.L. George, Y. Hadjimichael, D.I. Ketcheson, G.I Lemoine, and R.J. LeVeque. Clawpack: building an open source ecosystem for solving hyperbolic PDEs. PeerJ Computer Science 2:e68, 2016. https://doi.org/10.7717/peerj-cs.68.
Robert P. Munafo. Reaction-diffusion by the Gray-Scott model: Pearson's parametrization. https://www.mrob.com/pub/comp/xmorphia/.
B.J. Walker, A.K. Townsend, A.K. Chudasama, and A. L. Krause. VisualPDE: Rapid interactive simulations of partial differential equations, 2023.
T. A Driscoll, N. Hale, and L. N. Trefethen. Chebfun Guide. Pafnuty Publications, 2014.
Aly-Khan Kassam and Lloyd N. Trefethen. Fourth-Order Time-Stepping for Stiff PDEs. SIAM J. Sci. Comput., 26(4):1214-1233, 2005.
Fruzsina J Agocs and Alex H Barnett. Trapped acoustic waves and raindrops: high-order accurate integral equation method for localized excitation of a periodic staircase. arXiv preprint arXiv:2310.12486, 2023.
Armin Lechleiter and Ruming Zhang. A convergent numerical scheme for scattering of aperiodic waves from periodic surfaces based on the Floquet-Bloch transform. SIAM J. Numer. Anal., 55(2):713-736, 2017.
Ruming Zhang. A high order numerical method for scattering from locally perturbed periodic surfaces. SIAM J. Sci. Comput., 40(4):A2286-A2314, 2018.
Graeme Fairweather and Andreas Karageorghis. The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9:69-95, 1998.
Alexander HD Cheng and Yongxing Hong. An overview of the method of fundamental solutions-solvability, uniqueness, convergence, and stability. Engineering Analysis with Boundary Elements, 120:118-152, 2020.
Alex H Barnett and Timo Betcke. Stability and convergence of the method of fundamental solutions for helmholtz problems on analytic domains. Journal of Computational Physics, 227(14):7003-7026, 2008.
Carlos JS Alves and Svilen S Valtchev. Numerical comparison of two meshfree methods for acoustic wave scattering. Engineering Analysis with Boundary Elements, 29(4):371-382, 2005.
RF Millar. The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers. Radio Science, 8(8-9):785-796, 1973.
William C Meecham. On the use of the Kirchhoff approximation for the solution of reflection problems. Journal of Rational Mechanics and Analysis, 5(2):323-334, 1956.
J B Keller. A geometrical theory of diffraction. In L M Graves, editor, Calculus of Variations and its Applications, number 8 in Proceedings of Symposia in Applied Mathematics, pages 27-52, New York, 1958. McGraw-Hill.
Joseph B Keller. Geometrical theory of diffraction. Josa, 52(2):116-130, 1962.
Edward L Richards, HC Song, and WS Hodgkiss. Acoustic scattering comparison of Kirchhoff approximation to Rayleigh-fourier method for sinusoidal surface waves at low grazing angles. The Journal of the Acoustical Society of America, 144(3):1269-1278, 2018.
Jungyeon Cho and A. Lazarian. Compressible Magnetohydrodynamic Turbulence: mode coupling, scaling relations, anisotropy, new regime and astrophysical implications. MNRAS, 345:325-339, jan 2003.
G. Kowal, A. Lazarian, and A. Beresnyak. Density fluctuations in mhd turbulence: Spectral properties and intermittency. The Astrophysical Journal, 658:423-445, 2007.
BICEP2 Collaboration. BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales. The Astrophysical Journal Letters, 785:L1, April 2014.
Blakesley Burkhart, A. Lazarian, and B. M. Gaensler. Properties of interstellar turbulence in the galactic halo from structure function analysis of rotation measure maps. The Astrophysical Journal, 785(1):123, 2014.
S. K. N. Portillo and D. P. Finkbeiner. Applying the Wasserstein Distance to Astronomical Catalogs. The Astrophysical Journal, 862:119, August 2018.
Alex S. Hill, Robert A. Benjamin, Grzegorz Kowal, Ronald J. Reynolds, L. Matthew Haffner, and Alex Lazarian. The turbulent warm ionized medium: Emission measure distribution and mhd simulations. The Astrophysical Journal, 686:363-378, 2008.
Christopher F. McKee and Eve C. Ostriker. Theory of star formation. Annual Review of Astronomy and Astrophysics, 45:565-687, 2007.
Blakesley Burkhart, Diego Falceta-Goncalves, Grzegorz Kowal, and A. Lazarian. Density studies of mhd interstellar turbulence: Statistical moments, correlations and bispectrum. The Astrophysical Journal, 693:250-266, 2009.
B. Burkhart, S. M. Appel, S. Bialy, J. Cho, A. J. Christensen, D. Collins, C. Federrath, D. B. Fielding, D. Finkbeiner, A. S. Hill, J. C. Ibáñez-Mejía, M. R. Krumholz, A. Lazarian, M. Li, P. Mocz, M. M. Mac Low, J. Naiman, S. K. N. Portillo, B. Shane, Z. Slepian, and Y. Yuan. The Catalogue for Astrophysical Turbulence Simulations (CATS). The Astrophysical Journal, 905(1):14, December 2020.
Uri M. Ascher, Steven J. Ruuth, and Raymond J. Spiteri. Implicit-explicit runge-kutta methods for time-dependent partial differential equations. Applied Numerical Mathematics, 25(2):151-167, 1997. Special Issue on Time Integration.
Michael McCabe, Peter Harrington, Shashank Subramanian, and Jed Brown. Towards stability of autoregressive neural operators. Transactions on Machine Learning Research, 2023.
Jonah M. Miller, Benjamin R. Ryan, Joshua C. Dolence, Adam Burrows, Christopher J. Fontes, Christopher L. Fryer, Oleg Korobkin, Jonas Lippuner, Matthew R. Mumpower, and Ryan T. Wollaeger. Full transport model of GW170817-like disk produces a blue kilonova. Physical Review D, 100(2):23008, 2019.
Jonah M Miller, Trevor M Sprouse, Christopher L Fryer, Benjamin R Ryan, Joshua C Dolence, Matthew R Mumpower, and Rebecca Surman. Full transport general relativistic radiation magnetohydrodynamics for nucleosynthesis in collapsars. The Astrophysical Journal, 902(1):66, 2020.
Sanjana Curtis, Jonah M Miller, Carla Fröhlich, Trevor Sprouse, Nicole Lloyd-Ronning, and Matthew Mumpower. Nucleosynthesis in outflows from black hole-neutron star merger disks with full gr (ν) rmhd. The Astrophysical Journal Letters, 945(1):L13, 2023.
Kelsey A Lund, Gail C McLaughlin, Jonah M Miller, and Matthew R Mumpower. Magnetic field strength effects on nucleosynthesis from neutron star merger outflows. The Astrophysical Journal, 964(2):111, 2024.
E.P. Velikhov. Stability of an ideally conducting liquid flowing between rotating cylinders in a magnetic field. Zhur. Eksptl'. i Teoret. Fiz., 36(5), 5 1959.
S. A. Balbus and J. F. Hawley. A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution. The Astrophysical Journal, 376:214-233, July 1991.
N. I. Shakura and R. A. Sunyaev. Black holes in binary systems. Observational appearance. Proceedings of the American Astronomical Society, 24:337-355, January 1973.
Charles F. Gammie, Jonathan C. McKinney, and Gabor Toth. Harm: A numerical scheme for general relativistic magnetohydrodynamics. The Astrophysical Journal, 589(1):444-457, May 2003.
Joshua C. Dolence, Charles F. Gammie, Monika Moś cibrodzka, and Po Kin Leung. grmonty: A MONTE CARLO CODE FOR RELATIVISTIC RADIATIVE TRANSPORT. The Astrophysical Journal Supplement Series, 184(2):387-397, oct 2009.
B. R. Ryan, J. C. Dolence, and C. F. Gammie. bhlight: General relativistic radiation magnetohydrodynamics with monte carlo transport. The Astrophysical Journal, 807(1):31, jun 2015.
Oliver Porth et al. The event horizon general relativistic magnetohydrodynamic code comparison project. The Astrophysical Journal Supplement Series, 243(2):26, aug 2019.
Jonathan C. McKinney and Charles F. Gammie. A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole. The Astrophysical Journal, 611(2):977-995, August 2004.
Alexander Tchekhovskoy, Jonathan C. McKinney, and Ramesh Narayan. WHAM: a WENO-based general relativistic numerical scheme - I. Hydrodynamics. Monthly Notices of the Royal Astronomical Society, 379(2):469-497, August 2007.
A. Mignone and Jonathan C. McKinney. Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index. Monthly Notices of the Royal Astronomical Society, 378(3):1118-1130, July 2007.
S. M. Ressler, A. Tchekhovskoy, E. Quataert, M. Chandra, and C. F. Gammie. Electron thermodynamics in GRMHD simulations of low-luminosity black hole accretion. Monthly Notices of the Royal Astronomical Society, 454(2):1848-1870, 10 2015.
Roy P. Kerr. Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics. Physical Review Letters, 11(5):237-238, September 1963.
L. G. Fishbone and V. Moncrief. Relativistic fluid disks in orbit around Kerr black holes. The Astrophysical Journal, 207:962-976, August 1976.
A. W. Steiner, M. Hempel, and T. Fischer. Core-collapse supernova equations of state based on neutron star observations. Astrophysical Journal, 774(1), 2013.
M. Aaron Skinner, Joshua C. Dolence, Adam Burrows, David Radice, and David Vartanyan. Fornax: A flexible code for multiphysics astrophysical simulations. The Astrophysical Journal Supplement Series, 241(1):7, feb 2019.
A. Burrows, S. Reddy, and T. A. Thompson. Neutrino opacities in nuclear matter. Nuclear Physics A, 777:356-394, October 2006.
Evan O'Connor and Christian D Ott. A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes. Classical and Quantum Gravity, 27(11):114103, 2010.
Erik Lindborg. Reynolds-number scaling and convergence time scale in two-dimensional rayleigh-bénard convection. Journal of Fluid Mechanics, 973:A9, 2023.
Guy Dimonte, D. L Youngs, A Dimits, S Weber, M Marinak, S Wunsch, C Garasi, A Robinson, M. J Andrews, P Ramaprabhu, A. C Calder, B Fryxell, J Biello, L Dursi, P MacNeice, K Olson, P Ricker, R Rosner, F Timmes, H Tufo, Y.-N Young, and M Zingale. A comparative study of the turbulent Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration. Physics of fluids (1994), 16(5):1668-1693, 2004.
P. Ramaprabhu, Guy Dimonte, P. Woodward, C. Fryer, G. Rockefeller, K. Muthuraman, P.-H. Lin, and J. Jayaraj. The late-time dynamics of the single-mode Rayleigh-Taylor instability. Physics of Fluids, 24(7):074107, 07 2012.
Malcolm J Andrews and Stuart B Dalziel. Small Atwood number Rayleigh-Taylor experiments. Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 368(1916):1663-1679, 2010.
R. Peyret and T.D. Taylor. Computational methods for fluid flow. The International journal of heat and fluid flow, 4(3):182-182, 1983.
A Harten. On a class of high resolution total-variation-stable finite-difference schemes. SIAM journal on numerical analysis, 21(1):1-23, 1984.
A Harten, B Engquist, S Osher, and Chakravarthy. Uniformly high order accurate essentially non-oscillatory schemes.3. (reprinted from journal of computational physics, vol 71, pg 231, 1987). Journal of computational physics, 131(1):3-47, 1997.
S. Gottlieb, C.-W. Shu, and E. Tadmor. Strong stability-preserving high-order time discretization methods. SIAM review, 43(1):89-112, 2001.
William L Briggs, Van Emden Henson, and Steve F McCormick. A multigrid tutorial, second edition. Society for Industrial and Applied Mathematics, Philadelphia, Pa, 2nd ed. edition, 2000.
William H. Press and Saul A. Teukolsky. Multigrid methods for boundary value problems. i. Computers in physics, 5(5):514, 1991.
William H. Press and Saul A. Teukolsky. Multigrid methods for boundary value problems. ii. Computers in physics, 5(6):626, 1991.
S.B. Pope. Turbulent flows, cambridge university press, cambridge, u.k., 2000, 771 pp. Combustion and flame, 125(4):1361-1362, 2000.
Olivier Soulard and Jérôme Griffond. Inertial-range anisotropy in Rayleigh-Taylor turbulence. Physics of fluids (1994), 24(2):025101-025101-25, 2012.
William Cabot and Andrew Cook. Reynolds number effects on Rayleigh-Taylor instability with possible implications for type Ia supernovae. Nature Physics, 2:562-568, 07 2006.
Michael Chertkov. Phenomenology of Rayleigh-Taylor Turbulence. Physical review letters, 91(11):1150011-1150014, 2003.
Thomas Berlok and Christoph Pfrommer. On the kelvin-helmholtz instability with smooth initial conditions-linear theory and simulations. Monthly Notices of the Royal Astronomical Society, 485(1):908-923, 2019.
L. I. Sedov. Similarity and Dimensional Methods in Mechanics. 1959.
Takayuki R. Saitoh, Hiroshi Daisaka, Eiichiro Kokubo, Junichiro Makino, Takashi Okamoto, Kohji Tomisaka, Keiichi Wada, and Naoki Yoshida. Toward First-Principle Simulations of Galaxy Formation: I. How Should We Choose Star-Formation Criteria in High-Resolution Simulations of Disk Galaxies? Publications of the Astronomical Society of Japan, 60(4):667-681, August 2008.
Keiya Hirashima, Kana Moriwaki, Michiko S. Fujii, Yutaka Hirai, Takayuki R. Saitoh, and Junichiro Makino. 3D-Spatiotemporal forecasting the expansion of supernova shells using deep learning towards high-resolution galaxy simulations. Monthly Notices of the Royal Astronomical Society, 526(3):4054-4066, December 2023.
Takayuki R. Saitoh and Junichiro Makino. A Density-independent Formulation of Smoothed Particle Hydrodynamics. The Astrophysical Journal, 768(1):44, May 2013.
Takayuki R. Saitoh and Junichiro Makino. A Necessary Condition for Individual Time Steps in SPH Simulations. The Astrophysical Journal Letters, 697(2):L99-L102, June 2009.
Keiya Hirashima, Kana Moriwaki, Michiko S. Fujii, Yutaka Hirai, Takayuki R. Saitoh, Junichiro Makino, and Shirley Ho. Surrogate Modeling for Computationally Expensive Simulations of Supernovae in High-Resolution Galaxy Simulations. arXiv e-prints, page arXiv:2311.08460, November 2023.
S. Portegies Zwart, S. L. W. McMillan, E. van Elteren, I. Pelupessy, and N. de Vries. Multiphysics simulations using a hierarchical interchangeable software interface. Computer Physics Communications, 184(3):456-468, March 2013.
F. I. Pelupessy, A. van Elteren, N. de Vries, S. L. W. McMillan, N. Drost, and S. F. Portegies Zwart. The Astrophysical Multipurpose Software Environment. Astronomy & Astrophysics, 557:A84, September 2013.
Simon Portegies Zwart and Steve McMillan. Astrophysical Recipes. 2514-3433. IOP Publishing, 2018.
G. J. Ferland, K. T. Korista, D. A. Verner, J. W. Ferguson, J. B. Kingdon, and E. M. Verner. CLOUDY 90: Numerical Simulation of Plasmas and Their Spectra. Publications of the Astronomical Society of the Pacific, 110(749):761-778, July 1998.
G. J. Ferland, R. L. Porter, P. A. M. van Hoof, R. J. R. Williams, N. P. Abel, M. L. Lykins, G. Shaw, W. J. Henney, and P. C. Stancil. The 2013 Release of Cloudy. Revista mexicana de astronomía y astrofísica, 49:137-163, April 2013.
G. J. Ferland, M. Chatzikos, F. Guzmán, M. L. Lykins, P. A. M. van Hoof, R. J. R. Williams, N. P. Abel, N. R. Badnell, F. P. Keenan, R. L. Porter, and P. C. Stancil. The 2017 Release Cloudy. Revista mexicana de astronomía y astrofísica, 53:385-438, October 2017.
Jean Kossaifi, Nikola Kovachki, Kamyar Azizzadenesheli, and Anima Anandkumar. Multi-grid tensorized fourier neural operator for high-resolution pdes. arXiv preprint arXiv:2310.00120, 2023.
