Manuscripts under reviewed

[1] A. Jiao, Q. Yan, J. Harlim, and L. Lu
Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators [arXiv]

[2] J. Wilson Peoples and J. Harlim
A Higher Order Local Mesh Method for Approximating Laplacians on Unknown Manifolds [arXiv]

[3] Y. Yu, J. Harlim, D. Huang, and Y. Li
Learning Coarse-Grained Dynamics on Graph [arXiv]

[4] J. Wilson Peoples and J. Harlim
Spectral convergence of symmetrized graph Laplacian on manifolds with boundary [arXiv]

Books

[2] J. Harlim
Data-driven computational methods: Parameter and operator estimations
Cambridge University Press, UK, 2018. 
Chapter 1 [arXiv] 

[1] A.J. Majda and J. Harlim
Filtering complex turbulent systems
Cambridge University Press, UK, 2012.

Book Chapters

[2] J. Harlim
Model error in data assimilation
Nonlinear and Stochastic Climate Dynamics, Eds. C.L.E. Franzke and T.J. O'Kane, Cambridge University Press, pp.276-317, 2017. [arXiv]

[1] J. Harlim
Framework and mathematical strategies for filtering or data assimilation
Encyclopedia of Applied and Computational Mathematics, Ed. B. Engquist, Springer, pp.559-563, 2015.

Journal Publications

2024

[66] S. Liang, S.W. Jiang, J. Harlim, and H. Yang
Solving PDEs on unknown manifolds with machine learning
Appl. Comput. Harmon. Anal. 71, 101652, 2024. [arXiv]

[65] S.W. Jiang, R. Li, Q. Yan, and J. Harlim
Generalized finite difference method on unknown manifolds
J. Comput. Phys. 502, 112812, 2024. [arXiv]

2023

[64] J. Harlim, S.W. Jiang, and J. Wilson Peoples
Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning
J. Mach. Learn. Res. 24(345): 1-85, 2023. [arXiv]

[63] Q. Yan, S.W. Jiang, and J. Harlim
Spectral methods for solving elliptic PDEs on unknown manifolds
J. Comput. Phys. 486, 112132, 2023. [arXiv]

[62] D. Qi and J. Harlim
A Data-Driven Statistical-Stochastic Surrogate Modeling Strategy for Complex Nonlinear Non-stationary Dynamics
J. Comput. Phys. 485, 112085, 2023. [arXiv]

[61] Y. Gu, J. Harlim, S. Liang, and H. Yang
Stationary Density Estimation of Itô Diffusions Using Deep Learning
SIAM J. Numer. Anal. 61(1) 45-82, 2023. [arXiv]

[60] S.W. Jiang and J. Harlim
Ghost point diffusion maps for solving elliptic PDEs on manifolds with classical boundary conditions
Comm. Pure Appl. Math. 76(2) 337-405, 2023. [arXiv]

[59] Q. Yan, S.W. Jiang, and J. Harlim
Kernel-based methods for solving time-dependent advection-diffusion equations on manifolds
J. Sci. Comput. 94 (5), 2023. [arXiv]

2022

[58] D. Qi and J. Harlim
Machine Learning-Based Statistical Closure Models for Turbulent Dynamical systems
Philos. Trans. R. Soc. A. 380:20210205, 2022. [arXiv]

[57] J. Harlim, S.W. Jiang, H. Kim, and D. Sanz-Alonso
Graph-based prior and forward models for inverse problems on manifolds with boundaries
Inverse Problems 38, 035006, 2022. [arXiv]

2021

[56] H. Zhang, J. Harlim, and X. Li
Error bounds of the invariant statistics in machine learning of ergodic Itô diffusions
Physica D 427, 133022, 2021. [arXiv]

[55] N. Chen, F. Gilani, and J. Harlim
A Bayesian Machine Learning Algorithm for predicting ENSO using short observational time series
Geophys. Res. Lett. 48, e2021GL093704, 2021. [arXiv]

[54] H. Antil, T. Berry, and J. Harlim
Fractional diffusion maps
Appl. Comput. Harmon. Anal. 54, 145-175, 2021. [arXiv]

[53] H. Zhang, J. Harlim, and X. Li
Linear response based parameter estimation in the presence of model error
J Comput. Phys. 430, 110112, 2021. [arXiv]

[52] F. Gilani, D. Giannakis, and J. Harlim
Kernel-based prediction of non-Markovian time series
Physica D 418, 132829, 2021. [arXiv]

[51] J. Harlim, S.W. Jiang, S. Liang, and H. Yang
Machine learning for prediction with missing dynamics
J. Comput. Phys. 428, 109922, 2021. [arXiv]

2020

[50] H. Zhang, J. Harlim, and X. Li
Estimating linear response statistics using orthogonal polynomials: An RKHS formulation
Foundations of Data Science 2(4), 443-485, 2020. [arXiv]

[49] T. Berry, D. Giannakis, and J. Harlim
Bridging data science and dynamical systems theory
Notices of the American Mathematical Society 67(9), 1336-1349, 2020. [arXiv]

[48] J. Harlim, D. Sanz-Alonso, and R. Yang
Kernel methods for Bayesian elliptic inverse problems on manifolds
SIAM/ASA J Uncertainty Quantification 8(4), 1414-1445, 2020. [arXiv]

[47] S.W. Jiang and J. Harlim
Modeling of missing dynamical systems: Deriving parametric models using a nonparametric framework
Res. Math. Sci. 7, 16, 2020. [arXiv]

2019

[46] F. Gilani and J. Harlim
Approximating solutions of linear elliptic PDE's on smooth manifold using local kernels
J. Comput. Phys. 395, 563-582, 2019. [arXiv]

[45] S.W. Jiang and J. Harlim
Parameter estimation with data-driven nonparametric likelihood functions
Entropy 21(6), 559, 2019. [arXiv]

[44] H. Zhang, X. Li, and J. Harlim
A parameter estimation method using the linear response statistics: Numerical scheme
Chaos 29, 033101, 2019. [arXiv]

2018

[43] M. De La Chevrotière and J. Harlim
Data-driven localization mappings in filtering the monsoon-Hadley multicloud convective flows
Mon. Wea. Rev. 146(4), 1197-1218, 2018. [arXiv]

[42] W. Hao and J. Harlim
An equation-by-equation algorithm for solving the multidimensional moment constrained maximum entropy problem
Comm. App. Math. Comp. Sci. 13(2), 189-214, 2018. [arXiv]
Supplementary movies, Supplementary codes (in Matlab)

[41] J. Harlim and H. Yang
Diffusion forecasting model with basis functions from QR decomposition
J. Nonlinear Sci. 28(3), 847-872, 2018. [arXiv]

[40] T. Berry and J. Harlim
Iterated diffusion maps for feature identification
Appl. Comput. Harmon. Anal. 45(1), 84-119, 2018. [arXiv]

2017

[39] J. Harlim, X. Li, and H. Zhang
A parameter estimation method using the linear response statistics
J. Stat. Phys. 168(1), 146-170, 2017. [arXiv]

[38] T. Berry and J. Harlim
Correcting biased observation model error in data assimilation
Mon. Wea. Rev. 145(7), 2833-2853, 2017.  [arXiv]

[37] M. De La Chevrotière and J. Harlim
A data-driven method for improving the correlation estimation in serial ensemble Kalman filters
Mon. Wea. Rev. 145(3), 985-1001, 2017. [arXiv]

2016

[36] T. Berry, D. Giannakis, and J. Harlim
Reply to "Comments on 'Nonparametric forecasting of low-dimensional dynamical systems' "
Phys. Rev. E 93, 036202, 2016.

[35] T. Berry and J. Harlim
Forecasting turbulent modes with nonparametric models: Learning from noisy data
Physica D 320, 57-76, 2016. [arXiv]

[34] T. Berry and J. Harlim
Semiparametric modeling: Correcting low-dimensional model error in parametric models
J. Comput. Phys. 308, 305-321, 2016. [arXiv]

[33] T. Berry and J. Harlim
Variable bandwidth diffusion kernels
Appl. Comput. Harmon. Anal. 40, 68-96, 2016. [arXiv]

2015

[32] T. Berry and J. Harlim
Nonparametric uncertainty quantification for stochastic gradient flows
SIAM/ASA J. Uncertainty Quantification 3(1), 484-508, 2015. [arXiv]
Supplementary movies

[31] J. Harlim and X. Li
Parametric reduced models for the nonlinear Schrödinger equation
Phys. Rev. E 91 053306, 2015. [arXiv]

[30] Y. Zhen and J. Harlim
Adaptive error covariance estimation methods for ensemble Kalman filtering
J. Comput. Phys. 294, 619-638, 2015. [arXiv]

[29] T. Berry, D. Giannakis, and J. Harlim
Nonparametric forecasting of low-dimensional dynamical systems
Phys. Rev. E 91 032915, 2015. [arXiv]
Supplementary movies

[28] J. Harlim, H. Hong, and J.L. Robbins
An algebraic method for constructing stable and consistent autoregressive filters
J. Comput. Phys. 283, 241-257, 2015. [arXiv]
Supplementary code (in MAPLE)

2014

[27] T. Berry and J. Harlim
Linear theory for filtering nonlinear multiscale systems with model error
Proc. R. Soc. A (2014) 470, 20140168 [arXiv]

[26] J. Harlim, A. Mahdi, and A.J. Majda
An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models
J. Comput. Phys. 257, Part A, 782-812, 2014. [pdf]

2013

[25] G.A. Gottwald and J. Harlim
The role of additive and multiplicative noise in filtering complex dynamical systems
Proc. R. Soc. A (2013) 469, 20130096. [pdf]

[24] E.S. Bakunova and J. Harlim
Optimal filtering of complex turbulent systems with memory depth through consistency constraints
J. Comput. Phys. 237, 320-343, 2013. [pdf]

[23] J. Harlim and A.J. Majda
Test models for filtering with superparameterization
Multiscale Model. Simul. 11(1), 282-308, 2013. [pdf]

[22] K.A. Brown and J. Harlim
Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters
J. Comput. Phys. 235, 143-160, 2013. [pdf]

[21] A.J. Majda and J. Harlim [in Mathematics of Planet Earth Highlights]
Physics constrained nonlinear regression models for time series
Nonlinearity 26(1), 201-217, 2013. [pdf]

[20] E.L. Kang, J. Harlim and A.J. Majda
Regression models with memory for the linear response of turbulent dynamical systems
Comm. Math. Sci. 11(2), 481-498, 2013. [pdf]

[19] J. Harlim and A.J. Majda
Test models for filtering and prediction of moisture-coupled tropical waves
Q. J. R. Meteorol. Soc. 139, 119-136, 2013. [pdf]

2012

[18] E.L. Kang and J. Harlim
Filtering nonlinear spatio-temporal chaos with autoregressive linear stochastic models
Physica D 241(12), 1099-1113, 2012. [pdf]

[17] E.L. Kang and J. Harlim
Filtering partially observed multiscale systems with heterogeneous multiscale methods-based reduced climate models
Mon. Wea. Rev. 140(3), 860-873, 2012. [pdf]

2011

[16] J. Harlim
Interpolating irregularly spaced observations for filtering turbulent complex systems
SIAM J. Sci. Comput. 33(5), 2620-2640, 2011. [pdf]

[15] J. Harlim
Numerical strategies for filtering partially observed stiff stochastic differential equations
J. Comput. Phys. 230(3), 744-762, 2011.

2010

[14] A.J. Majda, J. Harlim, and B. Gershgorin
Mathematical strategies for filtering turbulent dynamical systems
Discrete Contin. Dynam. Syst. A 27(2), 441-486, 2010.

[13] J. Harlim and A.J. Majda
Filtering turbulent sparsely observed geophysical flows
Mon. Wea. Rev. 138(4), 1050-1083, 2010.

[12] B. Gershgorin, J. Harlim, and A.J. Majda
Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation
J. Comput. Phys. 229(1), 32-57, 2010.

[11] B. Gershgorin, J. Harlim, and A.J. Majda
Test models for improving filtering with model errors through stochastic parameter estimation
J. Comput. Phys. 229(1), 1-31, 2010.

[10] J. Harlim and A.J. Majda
Catastrophic filter divergence in filtering nonlinear dissipative systems
Comm. Math. Sci. 8(1), 27-42, 2010.

2008

[9] J. Harlim and A.J. Majda
Filtering nonlinear dynamical systems with linear stochastic models
Nonlinearity 21(6), 1281-1306, 2008.

[8] J. Harlim and A.J. Majda
Mathematical strategies for filtering complex systems: Regularly spaced sparse observations
J. Comput. Phys. 227(10), 5304-5341, 2008.

[7] E. Castronovo, J. Harlim, and A.J. Majda
Mathematical test criteria for filtering complex systems: Plentiful observations
J. Comput. Phys. 227(7), 3678-3714, 2008.

2007

[6] J. Harlim and B.R. Hunt
Four-dimensional local ensemble transform Kalman filter: Numerical experiments with a global circulation model
Tellus A 59(5), 731-748, 2007.

[5] J. Harlim and W.F. Langford
The cusp-Hopf bifurcation
Int. J Bif. Chaos 17(8), 2547-2570, 2007.

[4] A.J. Majda and J. Harlim
Information flow between subspaces of complex dynamical systems
Proc. Nat. Acad. Sci. 104(23), 9558-9562, 2007.

[3] J. Harlim and B.R. Hunt
A non-Gaussian ensemble filter for assimilating infrequent noisy observations
Tellus A 59(2), 225-237, 2007.

[2] E.J. Fertig, J. Harlim, and B.R. Hunt
A comparative study of 4D-VAR and 4D ensemble Kalman filter: Perfect model simulations with Lorenz-96
Tellus A 59(1), 96-100, 2007.

2005

[1] J. Harlim, M. Oczkowski, J.A. Yorke, E. Kalnay, and B.R. Hunt
Convex error growth patterns in a global weather model
Phys. Rev. Lett. 94, 228501, 2005.