The Cusp-hopf bifurcation. - John Harlim; William F. Langford (Int. J. Bifurc. Chaos, 2007)

Mathematical test criteria for filtering complex systems: Plentiful observations. - Emilio Castronovo; John Harlim; Andrew J. Majda (J. Comput. Phys., 2008)

Mathematical strategies for filtering complex systems: Regularly spaced sparse observations. - John Harlim; Andrew J. Majda (J. Comput. Phys., 2008)

Test models for improving filtering with model errors through stochastic parameter estimation. - Boris Gershgorin; John Harlim; Andrew J. Majda (J. Comput. Phys., 2010)

Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation. - Boris Gershgorin; John Harlim; Andrew J. Majda (J. Comput. Phys., 2010)

Numerical strategies for filtering partially observed stiff stochastic differential equations. - John Harlim (J. Comput. Phys., 2011)

Interpolating Irregularly Spaced Observations for Filtering Turbulent Complex Systems. - John Harlim (SIAM J. Sci. Comput., 2011)

Optimal filtering of complex turbulent systems with memory depth through consistency constraints. - Eugenia S. Bakunova; John Harlim (J. Comput. Phys., 2013)

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters. - Kristen A. Brown; John Harlim (J. Comput. Phys., 2013)

Test Models for Filtering with Superparameterization. - John Harlim; Andrew J. Majda (Multiscale Model. Simul., 2013)

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models. - John Harlim; Adam Mahdi; Andrew J. Majda (J. Comput. Phys., 2014)

An algebraic method for constructing stable and consistent autoregressive filters. - John Harlim; Hoon Hong; Jacob L. Robbins (J. Comput. Phys., 2015)

Adaptive error covariances estimation methods for ensemble Kalman filters. - Yicun Zhen; John Harlim (J. Comput. Phys., 2015)

Nonparametric Uncertainty Quantification for Stochastic Gradient Flows. - Tyrus Berry; John Harlim (SIAM/ASA J. Uncertain. Quantification, 2015)

Semiparametric modeling: Correcting low-dimensional model error in parametric models. - Tyrus Berry; John Harlim (J. Comput. Phys., 2016)

Diffusion Forecasting Model with Basis Functions from QR-Decomposition. - John Harlim; Haizhao Yang (J. Nonlinear Sci., 2018)

Kernel Embedding Linear Response. - He Zhang; John Harlim; Xiantao Li (CoRR, 2019)

Parameter Estimation with Data-Driven Nonparametric Likelihood Functions. - Shixiao W. Jiang; John Harlim (Entropy, 2019)

Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernel. - Faheem Gilani; John Harlim (J. Comput. Phys., 2019)

Ghost Point Diffusion Maps for solving elliptic PDE's on Manifolds with Classical Boundary Conditions. - Shixiao W. Jiang; John Harlim (CoRR, 2020)

Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds. - John Harlim; Daniel Sanz-Alonso; Ruiyi Yang (SIAM/ASA J. Uncertain. Quantification, 2020)

Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions. - He Zhang; John Harlim; Xiantao Li (CoRR, 2021)

Solving PDEs on Unknown Manifolds with Machine Learning. - Senwei Liang; Shixiao W. Jiang; John Harlim; Haizhao Yang (CoRR, 2021)

Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries. - John Harlim; Shixiao W. Jiang; Hwanwoo Kim; Daniel Sanz-Alonso (CoRR, 2021)

Spectral Convergence of Symmetrized Graph Laplacian on manifolds with boundary. - J. Wilson Peoples; John Harlim (CoRR, 2021)

Machine learning for prediction with missing dynamics. - John Harlim; Shixiao W. Jiang; Senwei Liang; Haizhao Yang (J. Comput. Phys., 2021)

Linear response based parameter estimation in the presence of model error. - He Zhang; John Harlim; Xiantao Li (J. Comput. Phys., 2021)

A data-driven statistical-stochastic surrogate modeling strategy for complex nonlinear non-stationary dynamics. - Di Qi; John Harlim (J. Comput. Phys., 2023)

Spectral methods for solving elliptic PDEs on unknown manifolds. - Qile Yan; Shixiao Willing Jiang; John Harlim (J. Comput. Phys., 2023)

Radial Basis Approximation of Tensor Fields on Manifolds: From Operator Estimation to Manifold Learning. - John Harlim; Shixiao Willing Jiang; John Wilson Peoples (J. Mach. Learn. Res., 2023)

Kernel-Based Methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds. - Qile Yan; Shixiao W. Jiang; John Harlim (J. Sci. Comput., 2023)

Stationary Density Estimation of Itô Diffusions Using Deep Learning. - Yiqi Gu; John Harlim; Senwei Liang; Haizhao Yang (SIAM J. Numer. Anal., 2023)

Learning Coarse-Grained Dynamics on Graph. - Yin Yu; John Harlim; Daning Huang; Yan Li (CoRR, 2024)

A Higher Order Local Mesh Method for Approximating Laplacians on Unknown Manifolds. - John Wilson Peoples; John Harlim (CoRR, 2024)

Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators. - Anran Jiao; Qile Yan; John Harlim; Lu Lu 010 (CoRR, 2024)

Generalized finite difference method on unknown manifolds. - Shixiao Willing Jiang; Rongji Li; Qile Yan; John Harlim (J. Comput. Phys., 2024)

Learning vector fields of differential equations on manifolds with geometrically constrained operator-valued kernels. - Daning Huang; Hanyang He; John Harlim; Yan Li (ICLR, 2025)