Low-Order Modeling and Machine Learning in Fluid Dynamics: Methods II

ORAL · J10 · ID: 3583409

Presentations

  • Development of reduced-order modeling of a multiphase flow in an ejector

    ORAL

    –

    Publication: 1. Bhaduri, Sreetam, Leonard J. Peltier, David Ladd, Eckhard A. Groll, and Davide Ziviani. "Turbulence and Interface Physics of a Carbon-Dioxide Jet in an Ejector." Physics of Fluids (Under Review).
    2. Bhaduri, Sreetam, Leonard J. Peltier, David Ladd, Eckhard A. Groll, and Davide Ziviani. "Regimes of a Decelerating Wall-bounded Multiphase Jet inside Ejectors." Physics of Fluids 37 (2025).
    3. Bhaduri, Sreetam, Junyan Ren, Leonard J. Peltier, David Ladd, Eckhard A. Groll, and Davide Ziviani. "Flow physics of a subcritical carbon dioxide jet in a multiphase ejector." Applied Thermal Engineering 256 (2024): 124043.

    Presenters

    • Sreetam Bhaduri

      Purdue University

    Authors

    • Sreetam Bhaduri

      Purdue University

    • Leonard J Peltier

      Bechtel Nuclear, Security, & Environmental, 12011 Sunset Hills Road, Reston, 20190, Virginia, United States

    • David Ladd

      Bechtel Manufacturing & Technology, USA

    • Eckhard A Groll

      Purdue University, West Lafayette

    • Davide Ziviani

      Purdue University

    View abstract →

  • Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulence

    ORAL

    –

    Publication: Abernathey R, Rochanotes, Ross A, Jansen M, Ziwei Li, Poulin FJ, Constantinou NC, Anirban Sinha, Dhruv Balwada,
    SalahKouhen, Jones S, Rocha CB, Wolfe CLP, Chuizheng Meng, Van Kemenade H, Bourbeau J, Penn J, Busecke J,
    Bueti M and , Tobias (2022) pyqg/pyqg: v0.7.2. doi: 10.5281/ZENODO.6563667. Available at https://zenodo.org/record/
    6563667.
    Arakawa A and Lamb VR (1977) Computational Design of the Basic Dynamical Processes of the UCLA General Circulation
    Model. In General Circulation Models of the Atmosphere. Elsevier, 173–265. doi: 10.1016/b978-0-12-460817-7.50009-4.
    Available at http://dx.doi.org/10.1016/B978-0-12-460817-7.50009-4.
    Bracco A, Brajard J, Dijkstra HA, Hassanzadeh P, Lessig C and Monteleoni C (2025) Machine learning for the physics of
    climate. Nature Reviews Physics 7(1), 6–20.
    Bracco A, Brajard J, Dijkstra HA, Hassanzadeh P, Lessig C and Monteleoni C (2024) Machine learning for the physics of
    climate. Nature Reviews Physics 7(1), 6–20. issn: 2522-5820. doi: 10.1038/s42254-024-00776-3. http://dx.doi.org/10.1038/
    s42254-024-00776-3.
    Carati D, Ghosal S and Moin P (1995) On the representation of backscatter in dynamic localization models. Physics of Fluids
    7(3), 606–616. issn: 1089-7666. doi: 10.1063/1.868585. http://dx.doi.org/10.1063/1.868585.
    Chattopadhyay A, Gray M, Wu T, Lowe AB and He R (2024) OceanNet: A principled neural operator-based digital twin for
    regional oceans. Scientific Reports 14(1), 21181.
    Chattopadhyay A and Hassanzadeh P (2023) Long-term instabilities of deep learning-based digital twins of the climate system:
    The cause and a solution. arXiv preprint arXiv:2304.07029.
    Chattopadhyay A, Subel A and Hassanzadeh P (2020) Data-driven super-parameterization using deep learning: Experimen-
    tation with multiscale Lorenz 96 systems and transfer learning. Journal of Advances in Modeling Earth Systems 12(11),
    e2020MS002084.
    Chen X, Gong C, Wan Q, Deng L, Wan Y, Liu Y, Chen B and Liu J (2021) Transfer learning for deep neural network-based
    partial differential equations solving. Advances in Aerodynamics 3(1). issn: 2524-6992. doi: 10.1186/s42774-021-00094-7.
    http://dx.doi.org/10.1186/s42774-021-00094-7.
    Desai S, Mattheakis M, Joy H, Protopapas P and Roberts S (2021) One-Shot Transfer Learning of Physics-Informed Neural
    Networks. doi: 10.48550/ARXIV.2110.11286. Available at https://arxiv.org/abs/2110.11286.
    Dipankar A, Stevens B, Heinze R, Moseley C, Zängl G, Giorgetta M and Brdar S (2015) Large eddy simulation using
    the general circulation model ICON. Journal of Advances in Modeling Earth Systems 7(3), 963–986. issn:
    1942-2466. doi: 10.1002/2015ms000431. http://dx.doi.org/10.1002/2015MS000431.
    Domaradzki JA, Metcalfe RW, Rogallo RS and Riley JJ (1987) Analysis of subgrid-scale eddy viscosity with use of results
    from direct numerical simulations. Physical Review Letters 58(6), 547–550. issn: 0031-9007. doi: 10.1103/physrevlett.58.547.
    http://dx.doi.org/10.1103/PhysRevLett.58.547.
    Fox DG and Orszag SA (1973) Pseudospectral approximation to two-dimensional turbulence. Journal of Computational Physics
    11(4), 612–619.
    Fox RO (2012) Large-Eddy-Simulation Tools for Multiphase Flows. Annual Review of Fluid Mechanics 44(1), 47–76. issn:
    1545-4479. doi: 10.1146/annurev-fluid-120710-101118. http://dx.doi.org/10.1146/annurev-fluid-120710-101118.
    Fox-Kemper B and Menemenlis D (2008) Can large eddy simulation techniques improve mesoscale rich ocean models? In
    Geophysical Monograph Series. American Geophysical Union, 319–337. doi: 10.1029/177gm19. Available at http://dx.doi.
    org/10.1029/177GM19.
    Gallet B and Ferrari R (2021) A quantitative scaling theory for meridional heat transport in planetary atmospheres and oceans.
    AGU Advances 2(3), e2020AV000362.
    Gao Y, Cheung KC and Ng MK (2022) SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular
    Value Decomposition. In 2022 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE. doi: 10.1109/ssci51031.
    2022.10022281. Available at http://dx.doi.org/10.1109/SSCI51031.2022.10022281.
    Germano M, Piomelli U, Moin P and Cabot WH (1991) A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A:
    Fluid Dynamics 3(7), 1760–1765. issn: 0899-8213. doi: 10.1063/1.857955. http://dx.doi.org/10.1063/1.857955.
    Goswami S, Anitescu C, Chakraborty S and Rabczuk T (2020) Transfer learning enhanced physics informed neural network
    for phase-field modeling of fracture. Theoretical and Applied Fracture Mechanics 106, 102447. issn: 0167-8442. doi:
    10.1016/j.tafmec.2019.102447. http://dx.doi.org/10.1016/j.tafmec.2019.102447.
    Goswami S, Kontolati K, Shields MD and Karniadakis GE (2022) Deep transfer operator learning for partial differential
    equations under conditional shift. Nature Machine Intelligence 4(12), 1155–1164. issn: 2522-5839. doi: 10.1038/s42256-
    022-00569-2. http://dx.doi.org/10.1038/s42256-022-00569-2.
    Gray MA, Chattopadhyay A, Wu T, Lowe A and He R (2024) Long-term Prediction of the Gulf Stream Meander Using
    OceanNet: a Principled Neural Operator-based Digital Twin. EGUsphere 2024, 1–23.
    Grooms I (2023a) Backscatter in energetically-constrained Leith parameterizations. Ocean Modelling 186, 102265.
    Grooms I (2023b) Backscatter in energetically-constrained Leith parameterizations. Ocean Modelling 186, 102265. issn: 1463-
    5003. doi: 10.1016/j.ocemod.2023.102265. http://dx.doi.org/10.1016/j.ocemod.2023.102265.
    Guan Y, Chattopadhyay A, Subel A and Hassanzadeh P (2022a) Stable a posteriori LES of 2D turbulence using convolutional
    neural networks: Backscattering analysis and generalization to higher Re via transfer learning. Journal of Computational
    Physics 458, 111090.
    Guan Y, Hassanzadeh P, Schneider T, Dunbar O, Huang DZ, Wu J and Lopez-Gomez I (2024) Online learning of eddy-
    viscosity and backscattering closures for geophysical turbulence using ensemble Kalman inversion. doi: 10.48550/ARXIV.
    2409.04985. Available at https://arxiv.org/abs/2409.04985.
    Guan Y, Subel A, Chattopadhyay A and Hassanzadeh P (2023) Learning physics-constrained subgrid-scale closures in the
    small-data regime for stable and accurate LES. Physica D: Nonlinear Phenomena 443, 133568.
    Guo H, Zhuang X, Chen P, Alajlan N and Rabczuk T (2022) Analysis of three-dimensional potential problems in non-
    homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis.
    Engineering with Computers 38(6), 5423–5444. issn: 1435-5663. doi: 10.1007/s00366-022-01633-6. http://dx.doi.org/10.
    1007/s00366-022-01633-6.
    Haghighat E, Raissi M, Moure A, Gomez H and Juanes R (2021) A physics-informed deep learning framework for inversion
    and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering 379, 113741. issn:
    0045-7825. doi: 10.1016/j.cma.2021.113741. http://dx.doi.org/10.1016/j.cma.2021.113741.
    Hallberg R (2013) Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects. Ocean Modelling
    72, 92–103.
    Hanna JM, Aguado JV, Comas-Cardona S, Askri R and Borzacchiello D (2022) Residual-based adaptivity for two-phase
    flow simulation in porous media using Physics-informed Neural Networks. Computer Methods in Applied Mechanics and
    Engineering 396, 115100. issn: 0045-7825. doi: 10.1016/j.cma.2022.115100. http://dx.doi.org/10.1016/j.cma.2022.115100.
    Hornik K, Stinchcombe M and White H (1989) Multilayer feedforward networks are universal approximators. Neural Networks
    2(5), 359–366. issn: 0893-6080. doi: 10.1016/0893-6080(89)90020-8. http://dx.doi.org/10.1016/0893-6080(89)90020-8.
    Jakhar K, Guan Y, Mojgani R, Chattopadhyay A and Hassanzadeh P (2023) Learning Closed-form Equations for Subgrid-
    scale Closures from High-fidelity Data: Promises and Challenges. doi: 10.48550/ARXIV.2306.05014. Available at https:
    //arxiv.org/abs/2306.05014.

    Jansen MF, Adcroft A, Khani S and Kong H (2019) Toward an Energetically Consistent, Resolution Aware Parameterization
    of Ocean Mesoscale Eddies. Journal of Advances in Modeling Earth Systems 11(8), 2844–2860. issn: 1942-2466. doi:
    10.1029/2019ms001750. http://dx.doi.org/10.1029/2019MS001750.
    Jansen MF and Held IM (2014) Parameterizing subgrid-scale eddy effects using energetically consistent backscatter. Ocean
    Modelling 80, 36–48. issn: 1463-5003. doi: 10.1016/j.ocemod.2014.06.002. http://dx.doi.org/10.1016/j.ocemod.2014.06.002.
    Kent J, Jablonowski C, Thuburn J and Wood N (2016) An energy-conserving restoration scheme for the shallow-water
    equations. Quarterly Journal of the Royal Meteorological Society 142(695), 1100–1110. issn: 1477-870X. doi: 10.1002/qj.
    2713. http://dx.doi.org/10.1002/qj.2713.
    Kerr RM, Domaradzki JA and Barbier G (1996) Small-scale properties of nonlinear interactions and subgrid-scale energy
    transfer in isotropic turbulence. Physics of Fluids 8(1), 197–208. issn: 1089-7666. doi: 10.1063/1.868827. http://dx.doi.org/
    10.1063/1.868827.
    Khani S and Waite ML (2016) Backscatter in stratified turbulence. European Journal of Mechanics - B/Fluids 60, 1–12. issn:
    0997-7546. doi: 10.1016/j.euromechflu.2016.06.012. http://dx.doi.org/10.1016/j.euromechflu.2016.06.012.
    Kingma DP and Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.
    Knaepen B and Moin P (2004) Large-eddy simulation of conductive flows at low magnetic Reynolds number. Physics of Fluids
    16(5), 1255–1261. issn: 1089-7666. doi: 10.1063/1.1651484. http://dx.doi.org/10.1063/1.1651484.
    Krueger D, Caballero E, Jacobsen JH, Zhang A, Binas J, Zhang D, Priol RL and Courville A (2020) Out-of-Distribution
    Generalization via Risk Extrapolation (REx). doi: 10.48550/ARXIV.2003.00688. Available at https://arxiv.org/abs/2003.
    00688.
    Larraondo PR, Renzullo LJ, Inza I and Lozano JA (2019) A data-driven approach to precipitation parameterizations using
    convolutional encoder-decoder neural networks. doi: 10.48550/ARXIV.1903.10274. Available at https://arxiv.org/abs/1903.
    10274.
    Leslie DC and Quarini GL (1979) The application of turbulence theory to the formulation of subgrid modelling procedures.
    Journal of Fluid Mechanics 91(01), 65. issn: 1469-7645. doi: 10.1017/s0022112079000045. http://dx.doi.org/10.1017/
    S0022112079000045.
    Li Z, Zheng H, Kovachki N, Jin D, Chen H, Liu B, Azizzadenesheli K and Anandkumar A (2021) Physics-Informed Neural
    Operator for Learning Partial Differential Equations. doi: 10.48550/ARXIV.2111.03794. Available at https://arxiv.org/abs/
    2111.03794.
    Lund T (1997) On the use of discrete filters for large eddy simulation. Annual Research Briefs, 83–95.
    Lupin-Jimenez L, Darman M, Hazarika S, Wu T, Gray M, He R, Wong A and Chattopadhyay A (2025) Simultane-
    ous emulation and downscaling with physically-consistent deep learning-based regional ocean emulators. arXiv preprint
    arXiv:2501.05058.
    Mason PJ and Thomson DJ (1992) Stochastic backscatter in large-eddy simulations of boundary layers. Journal of Fluid
    Mechanics 242, 51–78. issn: 1469-7645. doi: 10.1017/s0022112092002271. http://dx.doi.org/10.1017/S0022112092002271.
    Mathieu M, Henaff M and LeCun Y (2013) Fast training of convolutional networks through ffts. arXiv preprint arXiv:1312.5851.
    Mattheakis M, Joy H and Protopapas P (2021) Unsupervised Reservoir Computing for Solving Ordinary Differential Equations.
    doi: 10.48550/ARXIV.2108.11417. Available at https://arxiv.org/abs/2108.11417.
    Meneveau C and Katz J (2000) Scale-Invariance and Turbulence Models for Large-Eddy Simulation. Annual Review of Fluid
    Mechanics 32(1), 1–32. issn: 1545-4479. doi: 10.1146/annurev.fluid.32.1.1. http://dx.doi.org/10.1146/annurev.fluid.32.1.1.
    Orszag SA (1971) On the elimination of aliasing in finite-difference schemes by filtering high-wavenumber components. Journal
    of Atmospheric Sciences 28(6), 1074–1074.
    Pahlavan HA, Hassanzadeh P and Alexander MJ (2024a) Explainable Offline-Online Training of Neural Networks for
    Parameterizations: A 1D Gravity Wave-QBO Testbed in the Small-Data Regime. Geophysical Research Letters 51(2),
    e2023GL106324.
    Pahlavan HA, Hassanzadeh P and Alexander MJ (2024b) Explainable Offline-Online Training of Neural Networks for
    Parameterizations: A 1D Gravity Wave-QBO Testbed in the Small-Data Regime. Geophysical Research Letters 51(2). issn:
    1944-8007. doi: 10.1029/2023gl106324. http://dx.doi.org/10.1029/2023GL106324.
    Piomelli U (1999) Large-eddy simulation: achievements and challenges. Progress in Aerospace Sciences 35(4), 335–362. issn:
    0376-0421. doi: 10.1016/s0376-0421(98)00014-1. http://dx.doi.org/10.1016/S0376-0421(98)00014-1.
    Pope S (2000) Turbulent flows. Cambridge university press.
    Porta Mana P and Zanna L (2014) Toward a stochastic parameterization of ocean mesoscale eddies. Ocean Modelling 79, 1–20.
    issn: 1463-5003. doi: 10.1016/j.ocemod.2014.04.002. http://dx.doi.org/10.1016/j.ocemod.2014.04.002.
    Pressel KG, Mishra S, Schneider T, Kaul CM and Tan Z (2017) Numerics and subgrid-scale modeling in large eddy
    simulations of stratocumulus clouds. Journal of Advances in Modeling Earth Systems 9(2), 1342–1365. issn: 1942-2466. doi:
    10.1002/2016ms000778. http://dx.doi.org/10.1002/2016MS000778.
    Rasp S, Pritchard MS and Gentine P (2018) Deep learning to represent subgrid processes in climate models. Proceedings of
    the National Academy of Sciences 115(39), 9684–9689. issn: 1091-6490. doi: 10.1073/pnas.1810286115. http://dx.doi.org/
    10.1073/pnas.1810286115.
    Ross A, Li Z, Perezhogin P, Fernandez-Granda C and Zanna L (2023) Benchmarking of machine learning ocean subgrid
    parameterizations in an idealized model. Journal of Advances in Modeling Earth Systems 15(1), e2022MS003258.
    Sagaut P (2005) Large eddy simulation for incompressible flows: an introduction. Springer Science & Business Media.

    Sagaut P, Terracol M and Deck S (2013) Multiscale and multiresolution approaches in turbulence-LES, DES and Hybrid
    RANS/LES Methods: Applications and Guidelines. World Scientific.
    Sarlak H, Meneveau C and Sørensen J (2015) Role of subgrid-scale modeling in large eddy simulation of wind turbine wake
    interactions. Renewable Energy 77, 386–399. issn: 0960-1481. doi: 10.1016/j.renene.2014.12.036. http://dx.doi.org/10.
    1016/j.renene.2014.12.036.
    Schneider T, Lan S, Stuart A and Teixeira J (2017) Earth System Modeling 2.0: A Blueprint for Models That Learn
    From Observations and Targeted High-Resolution Simulations. Geophysical Research Letters 44(24). issn: 1944-8007. doi:
    10.1002/2017gl076101. http://dx.doi.org/10.1002/2017GL076101.
    Shevchenko I and Berloff P (2021) On a minimum set of equations for parameterisations in comprehensive ocean circulation
    models. Ocean Modelling 168, 101913. issn: 1463-5003. doi: 10.1016/j.ocemod.2021.101913. http://dx.doi.org/10.1016/j.
    ocemod.2021.101913.
    Shinde V (2020) Proper orthogonal decomposition assisted subfilter-scale model of turbulence for large eddy simulation. Physical
    Review Fluids 5(1). issn: 2469-990X. doi: 10.1103/physrevfluids.5.014605. http://dx.doi.org/10.1103/PhysRevFluids.5.
    014605.
    Smagorinsky (1963) GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS: I. THE BASIC
    EXPERIMENT*. Monthly Weather Review 91(3), 99–164. issn: 1520-0493. doi: 10 . 1175 / 1520 - 0493(1963 ) 091<0099 :
    gcewtp>2.3.co;2. http://dx.doi.org/10.1175/1520-0493(1963)091%3C0099:GCEWTP%3E2.3.CO;2.
    Stevens RJ, Martínez-Tossas LA and Meneveau C (2018) Comparison of wind farm large eddy simulations using actuator disk
    and actuator line models with wind tunnel experiments. Renewable Energy 116, 470–478. issn: 0960-1481. doi: 10.1016/j.
    renene.2017.08.072. http://dx.doi.org/10.1016/j.renene.2017.08.072.
    Subel A, Chattopadhyay A, Guan Y and Hassanzadeh P (2021) Data-driven subgrid-scale modeling of forced Burgers
    turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning. Physics of Fluids 33(3),
    031702.
    Subel A, Guan Y, Chattopadhyay A and Hassanzadeh P (2023) Explaining the physics of transfer learning in data-driven
    turbulence modeling. PNAS Nexus, pgad015.
    Subramanian S, Harrington P, Keutzer K, Bhimji W, Morozov D, Mahoney M and Gholami A (2023) Towards Foundation
    Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior. doi: 10.48550/ARXIV.2306.00258.
    https://arxiv.org/abs/2306.00258.
    Sun YQ, Pahlavan HA, Chattopadhyay A, Hassanzadeh P, Lubis SW, Alexander MJ, Gerber E, Sheshadri A and
    Guan Y (2023) Data Imbalance, Uncertainty Quantification, and Generalization via Transfer Learning in Data-driven
    Parameterizations: Lessons from the Emulation of Gravity Wave Momentum Transport in WACCM. doi: 10.48550/ARXIV.
    2311.17078. Available at https://arxiv.org/abs/2311.17078.
    Tan Z, Schneider T, Teixeira J and Pressel KG (2017) Large-eddy simulation of subtropical cloud-topped boundary layers:
    2. Cloud response to climate change. Journal of Advances in Modeling Earth Systems 9(1), 19–38. issn: 1942-2466. doi:
    10.1002/2016ms000804. http://dx.doi.org/10.1002/2016MS000804.
    Thuburn J, Kent J and Wood N (2013) Cascades, backscatter and conservation in numerical models of two-dimensional
    turbulence. Quarterly Journal of the Royal Meteorological Society 140(679), 626–638. issn: 1477-870X. doi: 10.1002/qj.2166.
    http://dx.doi.org/10.1002/qj.2166.
    Xu C, Cao BT, Yuan Y and Meschke G (2023) Transfer learning based physics-informed neural networks for solving inverse prob-
    lems in engineering structures under different loading scenarios. Computer Methods in Applied Mechanics and Engineering
    405, 115852. issn: 0045-7825. doi: 10.1016/j.cma.2022.115852. http://dx.doi.org/10.1016/j.cma.2022.115852.
    Xu W, Lu Y and Wang L (2022) Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations. doi:
    10.48550/ARXIV.2212.04663. Available at https://arxiv.org/abs/2212.04663.
    Yosinski J, Clune J, Bengio Y and Lipson H (2014) How transferable are features in deep neural networks? doi: 10.48550/
    ARXIV.1411.1792. https://arxiv.org/abs/1411.1792.
    Zanna L and Bolton T (2020) Data-Driven Equation Discovery of Ocean Mesoscale Closures. Geophysical Research Letters
    47(17). issn: 1944-8007. doi: 10.1029/2020gl088376. http://dx.doi.org/10.1029/2020GL088376.
    Zhou Y (1991) Eddy damping, backscatter, and subgrid stresses in subgrid modeling of turbulence. Physical Review A 43(12),
    7049–7052. issn: 1094-1622. doi: 10.1103/physreva.43.7049. http://dx.doi.org/10.1103/PhysRevA.43.7049.
    Zhuang F, Qi Z, Duan K, Xi D, Zhu Y, Zhu H, Xiong H and He Q (2021) A Comprehensive Survey on Transfer Learning.
    Proceedings of the IEEE 109(1), 43–76. issn: 1558-2256. doi: 10.1109/jproc.2020.3004555. http://dx.doi.org/10.1109/
    JPROC.2020.3004555.

    Presenters

    • Moein Darman

      University of California, Santa Cruz

    Authors

    • Moein Darman

      University of California, Santa Cruz

    • Pedram Hassanzadeh

      University of Chicago

    • Ashesh K Chattopadhyay

      University of California, Santa Cruz

    • Laure Zanna

      Courant Institute of Mathematical Sciences

    View abstract →