A list of main papers

Please see c.v. for more information.

  • Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect
    Yuqing Wang, Minshuo Chen, Tuo Zhao, and Molei Tao.
    preprint, 2021
    arXiv       machine learning,   nonlinear,   optimization

  • Parametric resonance for enhancing the rate of metastable transition
    Ying Chao and Molei Tao.
    preprint, 2021
    arXiv       stochastic,   nonlinear,   multiscale

  • The Mirror Langevin Algorithm Converges with Vanishing Bias
    Ruilin Li, Molei Tao, Santosh S. Vempala, and Andre Wibisono (alphabetical).
    preprint, 2021
    arXiv       machine learning,   stochastic,   numerical analysis

  • Sqrt(d) Dimension Dependence of Langevin Monte Carlo
    Ruilin Li, Hongyuan Zha, and Molei Tao.
    preprint, 2021
    arXiv       machine learning,   stochastic,   numerical analysis

  • Improving sampling accuracy of SG-MCMC methods via non-uniform subsampling of gradients
    Ruilin Li, Xin Wang, Hongyuan Zha, and Molei Tao.
    Discrete & Continuous Dynamical SystemsS, 2021
    arXiv       machine learning,   stochastic,   optimization,   multiscale

  • Obliquity Variations of Circumbinary Planets
    Renyi Chen, Gongjie Li, and Molei Tao.
    preprint, 2021
    submitted       nonlinear,   multiscale,   physics

  • Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials
    Molei Tao and Shi Jin.
    preprint, 2021
    arXiv       structure preserving,   nonlinear,   numerical analysis

  • Hessian-Free High-Resolution Nesterov Acceleration for Sampling
    Ruilin Li, Hongyuan Zha, and Molei Tao.
    preprint, 2021
    arXiv       machine learning,   stochastic

  • Variational Symplectic Accelerated Optimization on Lie Groups
    Taeyoung Lee, Molei Tao, and Melvin Leok.
    Conference on Decision and Control (CDC), 2021
    arXiv       structure preserving,   optimization,   nonlinear,   numerical analysis

  • GRIT: a package for structure-preserving simulations of gravitationally interacting rigid-bodies
    Renyi Chen, Gongjie Li, and Molei Tao.
    The Astrophysical Journal, 2021
    arXiv       structure preserving,   nonlinear,   numerical analysis,   multiscale,   physics

  • Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
    Renyi Chen and Molei Tao.
    ICML 2021
    arXiv       machine learning,   data,   nonlinear,   structure preserving,   numerical analysis
    a 5-min talk for this work

  • Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? -A Neural Tangent Kernel Perspective
    Kaixuan Huang^, Yuqing Wang^, Molei Tao, and Tuo Zhao (^ joint first author).
    NeurIPS 2020
    pdf       machine learning,   nonlinear
    a 3-min talk for this work by my student Yuqing Wang

  • A Derivative-Free Optimization Method with Application to Functions with Exploding and Vanishing Gradients
    Said Al-Abri, Tony X. Lin, Molei Tao, and Fumin Zhang
    IEEE Control Systems Letters, 2020
    pdf       optimization,   nonlinear,   multiscale

  • Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
    Molei Tao and Tomoki Ohsawa.
    AISTATS, 2020 (best paper award)
    pdf       machine learning,   optimization,   structure preserving,   numerical analysis,   stochastic
    a 13-min talk for this work

  • AhKin: a modular and efficient code for the Doppler Shift Attenuation Method
    Alejandro Garzon, Wilmar Rodriguez, Fernando Cristancho, and Molei Tao.
    Computer Physics Communications, 2020
    pdf       stochastic,   physics

  • Space-time phononic crystals with anomalous topological edge states
    Mourad Oudich, Yuanchen Deng, Molei Tao, and Yun Jing.
    Physical Review Research, 2019
    pdf       nonlinear,   multiscale,   engineering

  • Dynamic mode decomposition for multiscale nonlinear physics
    Daniel Dylewsky, Molei Tao, and J. Nathan Kutz.
    Physical Review E, 2019
    pdf       data,   multiscale,   nonlinear

  • Parametric resonant control of macroscopic behaviors of multiple oscillators
    Pengcheng Xie and Molei Tao.
    American Control Conference, 2019
    pdf       multiscale,   nonlinear

  • Simply improved averaging of coupled oscillators and weakly nonlinear waves
    Molei Tao.
    Communications in Nonlinear Science and Numerical Simulation, 2019
    pdf       nonlinear,   multiscale

  • Analysis and design of capacitive parametric ultrasonic transducers for efficient ultrasonic power transfer based on a 1D lumped model
    Sushruta Surappa, Molei Tao, and F. Levent Degertekin.
    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2018
    pdf       multiscale,   engineering

  • Metastable transitions in inertial Langevin systems: what can be different from the overdamped case?
    Andre Souza and Molei Tao.
    European Journal of Applied Mathematics, 2018
    pdf       stochastic,   nonlinear

  • Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions
    Molei Tao.
    Physica D, 2018
    pdf       stochastic,   nonlinear

  • Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
    Molei Tao.
    Physical Review E, 2016
    pdf       symplectic,   multiscale,   nonlinear,   numerical analysis

  • Uncovering circumbinary planetary architectural properties from selection biases
    Gongjie Li, Matthew J. Holman, and Molei Tao.
    The Astrophysical Journal, 2016
    pdf       exoplanetary,   nonlinear

  • Explicit high-order symplectic integrators for charged particles in general electromagnetic fields
    Molei Tao.
    Journal of Computational Physics, 2016
    pdf       symplectic,   nonlinear,   numerical analysis

  • Temporal homogenization of linear ODEs, with applications to parametric super-resonance and energy harvest
    Molei Tao and Houman Owhadi.
    Archive for Rational Mechanics and Analysis, 2016
    pdf       multiscale,   engineering,   nonlinear

  • Variational and linearly-implicit integrators, with applications
    Molei Tao and Houman Owhadi.
    IMA Journal of Numerical Analysis, 2016
    pdf       symplectic,   multiscale,   numerical analysis

  • Convex optimal uncertainty quantification
    Shuo Han, Molei Tao, Ufuk Topcu, Houman Owhadi, and Richard M. Murray.
    SIAM Journal on Optimization, 2015
    pdf       optimization,   stochastic

  • An improved wave-vector-frequency-domain method for nonlinear wave modeling
    Yun Jing, Molei Tao, and Jonathan Cannata.
    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2014
    pdf       multiscale,   engineering,   numerical analysis

  • Convex optimal uncertainty quantification: algorithms and a case study in energy storage placement
    Shuo Han, Ufuk Topcu, Molei Tao, Houman Owhadi, and Richard M. Murray.
    American Control Conference, 2013
    pdf       optimization,   stochastic,   engineering

  • Variational integrators for electric circuits
    Sina Ober-Bloebaum, Molei Tao, Mulin Cheng, Houman Owhadi, and Jerrold E. Marsden.
    Journal of Computational Physics, 2013
    pdf       symplectic,   multiscale,   numerical analysis,   engineering

  • Control of a Model of DNA Division via Parametric Resonance
    Wang Sang Koon, Houman Owhadi, Molei Tao, and Tomohiro Yanao.
    Chaos, 2013
    pdf       nonlinear,   multiscale

  • Statistics of Dislocation Slip Avalanches in Nanosized Single Crystals Show Tuned Critical Behavior Predicted by a Simple Mean Field Model
    Nir Friedman, Andrew T. Jennings, Georgios Tsekenis, Ju-Young Kim, Molei Tao, Jonathan T. Uhl, Julia R. Greer, and Karin A. Dahmen.
    Physical Review Letters, 2012
    pdf       nonlinear,   physics,   experiment

  • From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials
    Molei Tao, Houman Owhadi, and Jerrold E. Marsden.
    Applied Mathematics Research eXpress, 2011
    pdf       symplectic,   numerical analysis,   multiscale

  • Space-time FLAVORS: finite difference, multisymplectic, and pseudospectral integrators for multiscale PDEs
    Molei Tao, Houman Owhadi, and Jerrold E. Marsden.
    Dynamics of Partial Differential Equations, 2011
    pdf       symplectic,   multiscale,   numerical analysis

  • Evaluation of a wave vector frequency domain method for nonlinear wave propagation
    Yun Jing, Molei Tao, and Gregory T. Clement.
    The Journal of the Acoustical Society of America, 2011
    pdf       multiscale,   engineering

  • Nonintrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging
    Molei Tao, Houman Owhadi, and Jerrold E. Marsden.
    SIAM: Multiscale Modeling and Simulation, 2010
    pdf       multiscale,   numerical analysis,   symplectic,   stochastic

  • A fast and reliable two-sequence local alignment algorithm
    Qiming Hou, Molei Tao, and Yanda Li.
    China National Computer Conference, 2005
    (in Chinese)       bioinformatics

Not peer-reviewed

  • Multiscale symplectic integration of deterministic and stochastic systems
    Molei Tao.
    Caltech Ph.D. Dissertation, 2011
    link       multiscale,   numerical analysis,   symplectic,   stochastic

  • Structure preserving stochastic impulse methods for stiff Langevin systems with a uniform global error of order 1 or 1/2 on position
    Molei Tao, Houman Owhadi, and Jerrold E. Marsden.
    arXiv supplement to [Tao et al. AMRX 2011], 2010
    arXiv       multiscale,   numerical analysis,   symplectic,   stochastic

  • Temperature and Friction Accelerated Sampling of Boltzmann-Gibbs Distribution
    Molei Tao, Houman Owhadi, and Jerrold E. Marsden.
    unpublished but not wrong, 2010
    arXiv       numerical analysis,   symplectic,   stochastic

  • Thermodynamic and structural consensus principle predicts mature miRNA location and structure, categorizes conserved interspecies miRNA subgroups, and hints new possible mechanisms of miRNA maturization
    Molei Tao.
    Tsinghua Bachelor Thesis, 2007
    arXiv       bioinformatics,   data

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