My group attacks fundamental questions in ice-dynamics, geophysics, and fluid dynamics by integrating mathematical and machine-learned models with observational data. We use our findings to address challenges facing the world, such as advancing our scientific knowledge of ice dynamics under climate change. The length scale of the systems we are interested in varies broadly from a few microns to thousands of kilometers, because the governing physical principles are often universal across a range of length and time scales. We use mathematical models, simulations, and machine learning to study the complex interactions between fluids and elasticity and their interfacial dynamics, such as multiphase flows, flows in deformable structures, and cracks. We extend our findings to tackle emerging topics in climate science and geophysics, such as understand the missing physics that governs the flow of ice sheets in a warming climate. We welcome collaborations across disciplinary lines, from geophysics, engineering, physics, applied math to computer science, since we believe combining expertise and methodologies across fields is crucial for new discoveries.

Academic Appointments

Administrative Appointments

  • Executive Committee Member, Topical Group on the Physics of Climate, American Physical Society (APS) (2021 - 2023)

Honors & Awards

  • Sloan Research Fellowship, Alfred P. Sloan Foundation (2024-2026)
  • Research Scholar Award, Google Research (2023-2024)
  • Lamont Postdoctoral Fellowship, Lamont-Doherty Earth Observatory, Columbia University (2018-2019)

Professional Education

  • Ph.D., Princeton University, Mechanical and Aerospace Engineering (2018)
  • B.S., National Taiwan University, Physics (2013)

2023-24 Courses

Stanford Advisees

All Publications

  • Multi-stage neural networks: Function approximator of machine precision JOURNAL OF COMPUTATIONAL PHYSICS Wang, Y., Lai, C. 2024; 504
  • Realistic tropical cyclone wind and pressure fields can be reconstructed from sparse data using deep learning COMMUNICATIONS EARTH & ENVIRONMENT Eusebi, R., Vecchi, G. A., Lai, C., Tong, M. 2024; 5 (1)
  • One-dimensional ice shelf hardness inversion: Clustering behavior and collocation resampling in physics-informed neural networks JOURNAL OF COMPUTATIONAL PHYSICS Iwasaki, Y., Lai, C. 2023; 492
  • Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks. Physical review letters Wang, Y., Lai, C. Y., Gómez-Serrano, J., Buckmaster, T. 2023; 130 (24): 244002


    Whether there exist finite-time blow-up solutions for the 2D Boussinesq and the 3D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new numerical framework, employing physics-informed neural networks, that discover, for the first time, a smooth self-similar blow-up profile for both equations. The solution itself could form the basis of a future computer-assisted proof of blow-up for both equations. In addition, we demonstrate physics-informed neural networks could be successfully applied to find unstable self-similar solutions to fluid equations by constructing the first example of an unstable self-similar solution to the Córdoba-Córdoba-Fontelos equation. We show that our numerical framework is both robust and adaptable to various other equations.

    View details for DOI 10.1103/PhysRevLett.130.244002

    View details for PubMedID 37390436

  • Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages. Nature communications Lai, C. Y., Stevens, L. A., Chase, D. L., Creyts, T. T., Behn, M. D., Das, S. B., Stone, H. A. 2021; 12 (1): 3955


    Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 [Formula: see text] to 215 ± 90.2 [Formula: see text]) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.

    View details for DOI 10.1038/s41467-021-24186-6

    View details for PubMedID 34172733

    View details for PubMedCentralID PMC8233380

  • Vulnerability of Antarctica's ice shelves to meltwater-driven fracture. Nature Lai, C. Y., Kingslake, J., Wearing, M. G., Chen, P. C., Gentine, P., Li, H., Spergel, J. J., van Wessem, J. M. 2020; 584 (7822): 574-578


    Atmospheric warming threatens to accelerate the retreat of the Antarctic Ice Sheet by increasing surface melting and facilitating 'hydrofracturing'1-7, where meltwater flows into and enlarges fractures, potentially triggering ice-shelf collapse3-5,8-10. The collapse of ice shelves that buttress11-13 the ice sheet accelerates ice flow and sea-level rise14-16. However, we do not know if and how much of the buttressing regions of Antarctica's ice shelves are vulnerable to hydrofracture if inundated with water. Here we provide two lines of evidence suggesting that many buttressing regions are vulnerable. First, we trained a deep convolutional neural network (DCNN) to map the surface expressions of fractures in satellite imagery across all Antarctic ice shelves. Second, we developed a stability diagram of fractures based on linear elastic fracture mechanics to predict where basal and dry surface fractures form under current stress conditions. We find close agreement between the theoretical prediction and the DCNN-mapped fractures, despite limitations associated with detecting fractures in satellite imagery. Finally, we used linear elastic fracture mechanics theory to predict where surface fractures would become unstable if filled with water. Many regions regularly inundated with meltwater today are resilient to hydrofracture-stresses are low enough that all water-filled fractures are stable. Conversely, 60 ± 10 per cent of ice shelves (by area) both buttress upstream ice and are vulnerable to hydrofracture if inundated with water. The DCNN map confirms the presence of fractures in these buttressing regions. Increased surface melting17 could trigger hydrofracturing if it leads to water inundating the widespread vulnerable regions we identify. These regions are where atmospheric warming may have the largest impact on ice-sheet mass balance.

    View details for DOI 10.1038/s41586-020-2627-8

    View details for PubMedID 32848224

    View details for PubMedCentralID 6374411

  • Bubble Bursting: Universal Cavity and Jet Profiles. Physical review letters Lai, C. Y., Eggers, J., Deike, L. 2018; 121 (14): 144501


    After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a nondimensional number that compares capillary inertia and viscous forces, i.e., the Laplace number La=ργR_{0}/μ^{2}, where ρ, μ, γ, and R_{0} are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this Letter, we show that the time-dependent profiles of cavity collapse (tt_{0}) both obey a |t-t_{0}|^{2/3} inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.

    View details for DOI 10.1103/PhysRevLett.121.144501

    View details for PubMedID 30339416

  • Foam-driven fracture. Proceedings of the National Academy of Sciences of the United States of America Lai, C. Y., Rallabandi, B., Perazzo, A., Zheng, Z., Smiddy, S. E., Stone, H. A. 2018; 115 (32): 8082-8086


    In hydraulic fracturing, water is injected at high pressure to crack shale formations. More sustainable techniques use aqueous foams as injection fluids to reduce the water use and wastewater treatment of conventional hydrofractures. However, the physical mechanism of foam fracturing remains poorly understood, and this lack of understanding extends to other applications of compressible foams such as fire-fighting, energy storage, and enhanced oil recovery. Here we show that the injection of foam is much different from the injection of incompressible fluids and results in striking dynamics of fracture propagation that are tied to the compressibility of the foam. An understanding of bubble-scale dynamics is used to develop a model for macroscopic, compressible flow of the foam, from which a scaling law for the fracture length as a function of time is identified and exhibits excellent agreement with our experimental results.

    View details for DOI 10.1073/pnas.1808068115

    View details for PubMedID 30049705

    View details for PubMedCentralID PMC6094105

  • Suppressing viscous fingering in structured porous media. Proceedings of the National Academy of Sciences of the United States of America Rabbani, H. S., Or, D., Liu, Y., Lai, C. Y., Lu, N. B., Datta, S. S., Stone, H. A., Shokri, N. 2018; 115 (19): 4833-4838


    Finger-like protrusions that form along fluid-fluid displacement fronts in porous media are often excited by hydrodynamic instability when low-viscosity fluids displace high-viscosity resident fluids. Such interfacial instabilities are undesirable in many natural and engineered displacement processes. We report a phenomenon whereby gradual and monotonic variation of pore sizes along the front path suppresses viscous fingering during immiscible displacement, that seemingly contradicts conventional expectation of enhanced instability with pore size variability. Experiments and pore-scale numerical simulations were combined with an analytical model for the characteristics of displacement front morphology as a function of the pore size gradient. Our results suggest that the gradual reduction of pore sizes act to restrain viscous fingering for a predictable range of flow conditions (as anticipated by gradient percolation theory). The study provides insights into ways for suppressing unwanted interfacial instabilities in porous media, and provides design principles for new engineered porous media such as exchange columns, fabric, paper, and membranes with respect to their desired immiscible displacement behavior.

    View details for DOI 10.1073/pnas.1800729115

    View details for PubMedID 29686067

    View details for PubMedCentralID PMC5948996

  • Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow. Physical review letters Lai, C. Y., Zheng, Z., Dressaire, E., Ramon, G. Z., Huppert, H. E., Stone, H. A. 2016; 117 (26): 268001


    Cracks filled with fluid propagation when the pressurized fluid is injected into the crack. Subsequently, when the fluid inlet is exposed to a lower pressure, the fluid flows backwards (backflow) and the crack closes due to the elastic relaxation of the solid. Here we study the dynamics of the crack closure during the backflow. We find that the crack radius remains constant and the fluid volume in the crack decreases with time in a power-law manner at late times. The balance between the viscous stresses in the fluid and elastic stresses in the fluid and the elastic stresses in the solid yields a scaling law that agrees with the experimental results for different fluid viscosities, Young's moduli of the solid, and initial radii of the cracks. Furthermore, we visualize the time-dependent crack shapes, and the convergence to a universal dimensionless shape demonstrates the self-similarity of the crack shapes during the backflow process.

    View details for DOI 10.1103/PhysRevLett.117.268001

    View details for PubMedID 28059547