A list of main papers

Please see c.v. for more information.

Selected (see Longer list below for details)

• Convergence of Kinetic Langevin Monte Carlo on Lie groups
  Lingkai Kong and Molei Tao.
  submitted, 2024

• Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion
  Ye He, Kevin Rojas, and Molei Tao.
  submitted 2024

• Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult
  Yuqing Wang, Zhenghao Xu, Tuo Zhao, and Molei Tao.
  submitted (short version published in NeurIPS’23 Workshop) 2023

• Mirror Diffusion Models for Constrained and Watermarked Generation
  Guan-Horng Liu, Tianrong Chen, Evangelos A. Theodorou, and Molei Tao.
  NeurIPS 2023

• Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transport
  Lingkai Kong, Yuqing Wang, and Molei Tao.
  ICLR 2023
  code

• gDDIM: generalized denoising diffusion implicit models
  Qinsheng Zhang, Molei Tao, and Yongxin Chen.
  ICLR, 2023

• Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect
  Yuqing Wang, Minshuo Chen, Tuo Zhao, and Molei Tao.
  ICLR 2022

• Sqrt(d) Dimension Dependence of Langevin Monte Carlo
  Ruilin Li, Hongyuan Zha, and Molei Tao.
  ICLR 2022

• The Mirror Langevin Algorithm Converges with Vanishing Bias
  Ruilin Li, Molei Tao, Santosh S. Vempala, and Andre Wibisono.
  International Conference on Algorithmic Learning Theory 2022
  

• Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
  Renyi Chen and Molei Tao.
  ICML 2021

• Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
  Lingkai Kong and Molei Tao.
  NeurIPS 2020

• Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
  Molei Tao and Tomoki Ohsawa.
  AISTATS 2020 (best paper award)

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

• Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
  Molei Tao.
  Physical Review E 2016

• 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

• 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

Longer list

(number of pages included for ML conference papers per suggestion from my mathematician friends)

• Quantum State Generation with Structure-Preserving Diffusion Model
  Yuchen Zhu, Tianrong Chen, Evangelos A. Theodorou, Xie Chen, Molei Tao.
  TBA, 2024
  arXiv       machine learning,   stochastic,   structure preserving,   physics
  

• Convergence of Kinetic Langevin Monte Carlo on Lie groups
  Lingkai Kong and Molei Tao.
  TBA, 2024
  arXiv 53 pages       stochastic,   structure preserving,   nonlinear,   numerical analysis
  

• Can Specific THz Fields Induce Collective Base-Flipping in DNA? A Stochastic Averaging and Resonant Enhancement Investigation Based on a New Mesoscopic Model
  Wang Sang Koon, Houman Owhadi, Molei Tao, and Tomohiro Yanao (alphabetical, led by Koon).
  TBA, 2024
  arXiv       stochastic,   nonlinear,   multiscale
  

• Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion
  Ye He, Kevin Rojas, and Molei Tao.
  TBA, 2024
  arXiv       machine learning,   stochastic,   nonlinear,   numerical analysis
  

• Extragradient Type Methods for Riemannian Variational Inequality Problems
  Zihao Hu, Guanghui Wang, Xi Wang, Andre Wibisono, Jacob Abernethy, Molei Tao.
  AISTATS, 2024
  arXiv       machine learning,   optimization,   numerical analysis

• Automated construction of effective potential via algorithmic implicit bias
  Xingjie Li and Molei Tao.
  TBA, 2024
  arXiv       machine learning,   stochastic,   multiscale

• Appropriate State-Dependent Friction Coefficient Accelerates Kinetic Langevin Dynamics
  Keunwoo Lim and Molei Tao.
  TBA, 2024
  arXiv       stochastic,   nonlinear

• Explicit Energy-Preserving Momentum-Scaling Schemes for Hamiltonian Systems
  Molei Tao and Andy T.S. Wan (alphabetical, lead by Wan).
  TBA, 2024
  TBA       structure preserving,   nonlinear,   numerical analysis

• Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult
  Yuqing Wang, Zhenghao Xu, Tuo Zhao, and Molei Tao.
  NeurIPS workshop (short version, long version in review), 2023
  arXiv       machine learning,   nonlinear,   optimization

• Dual Fourier Unet: scale-robust diffusion model for zero-shot super-resolution image generation
  Alexander Havrilla, Kevin Rojas, Wenjing Liao, and Molei Tao.
  NeurIPS workshop, 2023
  arXiv       machine learning, stochastic

• Mirror Diffusion Models for Constrained and Watermarked Generation
  Guan-Horng Liu, Tianrong Chen, Evangelos A. Theodorou, and Molei Tao.
  NeurIPS, 2023
  arXiv       machine learning, stochastic

• Deep Multi-Marginal Momentum Schrodinger Bridge
  Tianrong Chen, Guan-Horng Liu, Molei Tao, and Evangelos A. Theodorou.
  NeurIPS, 2023
  arXiv       machine learning, stochastic

• Markov chain Monte Carlo for Gaussian: A linear control perspective
  Bo Yuan, Jiaojiao Fan, Yuqing Wang, Molei Tao, and Yongxin Chen.
  IEEE Control Systems Letters, 2023
  paper       stochastic

• Landscape classification through coupling method
  Yao Li, Molei Tao, and Shirou Wang.
  submitted, 2023
  arXiv       stochastic,   nonlinear

• gDDIM: generalized denoising diffusion implicit models
  Qinsheng Zhang, Molei Tao, and Yongxin Chen.
  ICLR, 2023
  arXiv       machine learning,   stochastic,   numerical analysis

• Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transport
  Lingkai Kong, Yuqing Wang, and Molei Tao.
  ICLR, 2023
  arXiv       machine learning,   optimization,   structure preserving,   numerical analysis
  code

• Electromechanical frequency comb generation in fluid media with a parametrically driven capacitive microresonator
  Sushruta Surappa, Charles Wei, Molei Tao, and F Levent Degertekin.
  Physical Review Applied, 2023
  TBA       nonlinear, multiscale,   engineering

• NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
  Xingjie Li, Fei Lu, Molei Tao, Felix Ye (alphabetical).
  Journal of Computational Physics, 2022
  arXiv       machine learning,   stochastic,   structure preserving,   numerical analysis,   multiscale

• Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
  Oswin So, Gongjie Li, Evangelos A. Theodorou, Molei Tao.
  NeurIPS workshop, 2022
  pdf       machine learning,   structure preserving,   nonlinear,   multiscale,   physics

• Alternating Mirror Descent for Constrained Min-Max Games
  Andre Wibisono, Molei Tao, and Georgios Piliouras.
  NeurIPS, 2022
  arXiv, 45 pages       machine learning,   optimization,   numerical analysis

• Low spin-axis variations of circumbinary planets
  Renyi Chen, Gongjie Li, and Molei Tao.
  Monthly Notices of the Royal Astronomical Society, 2022
  arXiv       nonlinear,   multiscale,   physics

• Hessian-Free High-Resolution Nesterov Acceleration for Sampling
  Ruilin Li, Hongyuan Zha, and Molei Tao.
  ICML, 2022
  arXiv, 38 pages       machine learning,   stochastic,   numerical analysis

• Parametric resonance for enhancing the rate of metastable transition
  Ying Chao and Molei Tao.
  SIAM Applied Math, 2022
  arXiv       stochastic,   nonlinear,   multiscale

• Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect
  Yuqing Wang, Minshuo Chen, Tuo Zhao, and Molei Tao.
  ICLR, 2022
  arXiv, 45 pages       machine learning,   nonlinear,   optimization
  a 5-min talk for this work by my student Yuqing Wang; best fit in Chrome browser

• Sqrt(d) Dimension Dependence of Langevin Monte Carlo
  Ruilin Li, Hongyuan Zha, and Molei Tao.
  ICLR, 2022
  arXiv, 22 pages       machine learning,   stochastic,   numerical analysis
  a 5-min talk for this work; best fit in Chrome browser

• The Mirror Langevin Algorithm Converges with Vanishing Bias
  Ruilin Li, Molei Tao, Santosh S. Vempala, and Andre Wibisono (alphabetical).
  International Conference on Algorithmic Learning Theory, 2022
  pdf, 25 pages       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

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

• 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
  code

• Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
  Renyi Chen and Molei Tao.
  ICML 2021
  arXiv, 17 pages       machine learning,   data,   nonlinear,   structure preserving,   numerical analysis
  a 5-min talk for this work
  

• Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
  Lingkai Kong and Molei Tao.
  NeurIPS 2020
  pdf, 32 pages       machine learning,   nonlinear,   multiscale,   optimization,   stochastic
  a 55-min talk for this work
  a 20-min talk for this work
  a 3-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, 28 pages       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, 17 pages       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 (alphabetical).
  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 geometric 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