Publications

+++ Data Assimilation: A Mathematical Introduction.  K. J. H. Law, A. M. Stuart, and K. Zygalakis. Springer Texts in Applied Mathematics (2015).

+++ The accompanying MATLAB code for this book is available here.

• Fast Deep Mixtures of Gaussian Process Experts. C. Etienam, K. J. H. Law, S. Wade, and V. Zankin. Machine Learning (2024). 

• A randomized multi-index sequential Monte Carlo method. S. Cotter, K.J.H. Law, X. Liang, S. Yang. Stat. and Comp. 33, 97, (2023).

• Multi-index sequential Monte Carlo ratio estimators for Bayesian inverse problems. K. J.H. Law, N. Walton, S. Yang, and A. Jasra. Found. Comp. Math. (2023).

• Core-Pedestal Plasma Configurations in Advanced Tokamaks. E. Hassan etal. Fusion Sci. & Tech. 79:3, 189-212 (2023).

• Digital Fingerprinting of Microstructures. M. White, A. Tarakanov, C. P. Race, P. J. Withers, and K. J. H. Law. Comp. Mat. Sci. 218, 111985 (2023).

• On Unbiased Estimation for Discretized Models. J. Heng, A. Jasra, K. J. H. Law, and A. Tarakanov. To appear in SIAM/ASA J. Unc. Quant. 11:2, 616-645 (2023).

• Bayesian Estimation of Oscillator Parameters: Toward Anomaly Detection and Cyber-Physical System Security. J. M. Lukens, A. Passian, S. Yoginath, K. J. H. Law, J. A. Dawson. Sensors, 22(16), 6112 (2022).

• Strain-Induced asymmetry and on-site dynamics of silicon defects in graphene. O. Dyck, F. Bao, M. Ziatdinov, A. Yousefzadi Nobakht, K. J. H. Law, A. Maksov, B. G. Sumpter, R. Archibald, S. Jesse, S. V. Kalinin, D. B. Lingerfelt. Carbon Trends, 9, 100189 (2022).

• Sparse online variational Bayesian regression. K. J.H. Law and V. Zankin. SIAM/ASA J. Unc. Quant. 10(3), 1070-1100 (2022).

• Certified dimension reduction in nonlinear Bayesian inverse problems. O. Zahm, T. Cui, K. J. H. Law, A. Spantini, Y. M. Marzouk. Mathematics of Computation 91, 1789-1835 (2022).

• Randomized multilevel Monte Carlo for embarrassingly parallel inference. A. Jasra, K. J. H. Law, A. Tarakanov, and F. Yu. In: Nichols J. et al. (eds) Driving Scientific and Engineering Discoveries Through the Integration of Experiment, Big Data, and Modeling and Simulation. Communications in Computer and Information Science, vol 1512. Springer, Cham. https://doi.org/10.1007/978-3-030-96498-6_1 SMC21 (2022).

•  Unbiased Filtering of a Class of Partially Observed Diffusions. A. Jasra, K. J. H. Law, and F. Yu. Advances in Applied Probability 54(3), 661 - 687 (2022). 

• A Bayesian analysis of classical shadows. J. M. Lukens, K. J.H. Law, and R. S. Bennink. Nature pj Quantum Information 7(1), 1-10 (2021).

• Materials Fingerprinting Classification.  A. Spannaus, K. J.H. Law, P. Luszczekc, F. Nasrin, C. P. Micuccie, P. K. Liaw, L. J. Santodonato, D. J. Keffer, V. Maroulas. Comp. Phys. Comm. 266, 108019 (2021).

• Unbiased inference for discretely observed hidden Markov model diffusions. N. Chada, J. Franks, A. Jasra, K. J. H. Law, and M. Vihola. SIAM/ASA J. Unc. Quant. 9(2), 763–787 (2021).

• Markov chain simulation for MLMC. A. Jasra, K. J. H. Law,  & Y. Xu. Found. Data Sci. 3(1), 27-47 (2021).

• Unbiased Estimation of the Gradient of the Log-Likelihood in Inverse Problems. A. Jasra, K. J. H. Law, and D. Lu. Stat. and Comp., 31, 21 (2021).

• Multilevel ensemble Kalman filtering for spatio-temporal processes.  A. Chernov, H. Hoel, K. J. H. Law, F. Nobile, and R. Tempone.  Numerische Mathematik, 147, 71–125 (2021). 

• Probing potential energy landscapes via electron-beam-induced single atom dynamics. O. Dyck, M. Ziatdinov, S. Jesse, F. Bao, A. Yousefzadi Nobakht, A. Maksov, B.G. Sumpter, R. Archibald, K.J.H. Law, S.V. Kalinin. Acta Materialia 203, 116508 (2021).

• Multi-Index Sequential Monte Carlo Methods for Partially Observed Stochastic Partial Differential Equations. A. Jasra, K. J. H. Law, and Y. Xu. Int. J. UQ 11(3) 1-25 (2021).

• Computationally efficient Bayesian quantum state tomography. J. M. Lukens, K. J. H. Law, A. Jasra, and P. Lougovski. 2020 IEEE Photonics Conference (IPC), pp. 1-2. IEEE, (2020).

• Reconstruction of effective potential from statistical analysis of dynamic trajectories. A. Yousefzadi Nobakht, O. Dyck, D. B. Lingerfelt, F. Bao, M. Ziatdinov, A. Maksov, B. G. Sumpter, R. Archibald, S. Jesse, S. V. Kalinin, and K. J. H. Law.  AIP Advances 10(6), 065034 (2020). 

• Advanced Multilevel Monte Carlo methods.  A. Jasra, K. J. H. Law, and C. Suciu. Int. Stat. Rev. 88(3), 548-579 (2020). 

• A practical and efficient approach for Bayesian quantum state estimation. J. M. Lukens, K. J. H.  Law, A. Jasra, and P. Lougovski. New J. Phys. 22, 063038 (2020).

• Machine learning for analysis of atomic spectral data. M. Cianciosa, K. J. H. Law, E. H. Martin and D. L. Green. J. Quant. Spec. and Rad. Trans. 240, 106671 (2020).

• Cluster, Classify, Regress: A General Method For Learning Discountinous Functions.  D. E. Bernholdt, M. R. Cianciosa, C. Etienam, D. L. Green, K. J. H. Law, and J. M. Park. Found. Data Sci. 1(4), 491-506 (2019).

• Multilevel Particle Filters for Levy-driven stochastic differential equations. A. Jasra, K. J. H. Law, and P. P. Osei. Stat. and Comp. 29(4), 775–789 (2019).

• A multilevel approach for partially observed deterministic systems.  A. Jasra, K. J. H. Law,  & Y. Xu. Int. J. Unc. Quant. 9(4), 321-330 (2019).

• Estimation and uncertainty quantification for the output from quantum simulators. Ryan Bennink, Ajay Jasra, Kody J. H. Law, and Pavel Lougovski. Found. of Data Sci. 1(2), 157-176 (2019).

• Bayesian Point Set Registration. A. Spannaus, V. Maroulas, D. J. Keffer, and K. J. H. Law. 2017 Matrix Annals,  99-120. Springer (2019).

• Comparing theory based and higher-order reduced models for fusion simulation data. D. E. Bernholdt, M. R. Cianciosa, D. L. Green, K. J.H. Law, A. Litvinenko, and J. M. Park. Big Data and Info. Anal. 3(2), 41-53 (2018). 

• Accuracy of some approximate Gaussian Filters for the Navier-Stokes equation in the presence of model error. M. Branicki, A. J. Majda, and K. J. H. Law. SIAM Mult. Mod. Sim. 16(4), 1756--1794 (2018).

• Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals. A. Beskos, A. Jasra, K. J. H. Law, Y. M. Marzouk, and Y. Zhou. SIAM/ASA J. Unc. Quant. 6(2) 762–786 (2018).

• Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo. A. Jasra, K. Kamatani, K. J. H. Law, and Y. Zhou. SIAM J. Sci. Comp., 40, A887-A902 (2018).

• A multi-index Markov chain Monte Carlo method.  A. Jasra, K. Kamatani, K. J. H. Law, and Y. Zhou. Int. J. Unc. Quant. 8(1), 61-73 (2018).

• Ultrafast current imaging by Bayesian inversion. S. Somnath, K. J. H. Law, A. N. Morozovska, P. Maksymovych, Y. Kim, X. Lu, M. Alexe, R. Archibald, S. V. Kalinin, S. Jesse, and R. K. Vasudevan. Nature Communications 9, 513 (2018).

• Multilevel particle filters.  A. Jasra, K. Kamatani, K. J. H. Law, and Y. Zhou. SIAM J. Numer. Anal., 55(6), 3068–3096 (2017).

• Multilevel sequential Monte Carlo samplers for normalizing constants.  P.  Del Moral, A. Jasra, K. J. H. Law, and Y. Zhou.  Trans. Mod. Comp. Sim. 27(3), 20 (2017).

• Multilevel Sequential Monte Carlo: Mean Square Error Bounds under Verifiable Conditions. P. Del Moral, A. Jasra, and K. J. H. Law. Stoch. Anal. and App. 35(3) 478-498 (2017). 

• Multilevel sequential Monte Carlo samplers.  A. Beskos, A. Jasra, K. J.H. Law, R. Tempone, and Y. Zhou.  Stoch. Proc. App. 127(5) 1417--1440 (2017). 

• Forward and Inverse Uncertainty Quantification using Multilevel Monte Carlo Algorithms for an Elliptic Nonlocal Equation.  A. Jasra, K. J.H. Law, and Y. Zhou. Int. J. Unc. Quant.  6(6) 501-514 (2016).

• Accelerated dimension-independent adaptive Metropolis.  Y. Chen, D. Keyes, K. J. H. Law, and H. Ltaief.  SIAM J. Sci. Comput., 38(5) S539-S565 (2016).

• Multilevel ensemble Kalman filter.  H. Hoel, K. J.H. Law, and R. Tempone. SIAM J. Numer. Anal., 54(3), 1813–1839 (2016).

• Controlling Unpredictability with Observations in the Partially Observed Lorenz ’96 Model.  K.J.H. Law, D. Sanz-Alonso, A. Shukla, and A.M. Stuart. Phys. D, 325, 1-13 (2016).

• Deterministic Mean-field Ensemble Kalman Filtering.  K. J. H. Law, H. Tembine, and R. Tempone. SIAM J. Sci. Comput., 38(3), A1251–A1279 (2016).

• Dimension-independent, likelihood-informed MCMC samplers for inverse problems.  T. Cui, K. J. H. Law, and Y.M. Marzouk. J. Comp. Phys., 304, 109-137 (2016).

• Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time.  D.B. Kelly, K. J. H. Law, and A.M. Stuart. Nonlinearity, 27, 2579-2603 (2014).

• Dynamic and energetic stabilization of persistent currents in Bose-Einstein condensates.  K. J. H. Law, T. W. Neeley, P. G. Kevrekidis, B. P. Anderson, R. Carretero-González, A. S. Bradley, and M. J. Davis.  Phys. Rev. A 89, 053606 (2014).

• Determining white noise forcing from Eulerian observations in the Navier-Stokes equation.  V. H Hoang, K.J.H. Law and A.M. Stuart. Stochastic Partial Differential Equations: Analysis and Computations 2:2, 233-261 (2014).

• Analysis of the 3DVAR Filter for the Partially Observed Lorenz 63 Model.  K. J. H. Law, A. Shukla, and A.M. Stuart. Discrete and Continuous Dynamical Systems A 34, 1061-1078 (2014).

• Proposals Which Speed-Up Function-Space MCMC.  K. J. H. Law. Journal of Computational and Applied Mathematics 262 127–138 (2014). 

• Evaluation of Gaussian approximations for data assimilation in reservoir models.  M. A. Iglesias, K. J.H. Law, and A. M. Stuart. Computational Geosciences 17:5, 851-885 (2013).

• Accuracy and Stability of The Continuous Time 3DVAR Filter for The Navier-Stokes Equation.  D. Bloemker, K.J.H. Law, A.M. Stuart, and K. Zygalakis. Nonlinearity 26 2193 (2013).

• Two-Dimensional Turbulence in a Compressible Quantum Fluid.  T. W. Neely, etal. Physical Review Letters 11 235301 (2013).

• Map Estimators for Bayesian Nonparametrics.  M. Dashti, K.J.H. Law, A.M. Stuart and J. Voss. Inverse Problems 29 095017 (2013).

• Ensemble Kalman Methods for Inverse Problems.  M. A. Iglesias, K. J. H. Law and A. M. Stuart. Inverse Problems 29 045001 (2013).

• Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates.  Chang Wang, Kody J. H. Law, Panayotis. G. Kevrekidis, and Mason A. Porter. Phys Rev A 87(2) 023621 (2013).

• Accuracy and Stability of Filters for Dissipative PDEs.  C. E. A. Brett, K. F. Lam, K. J. H. Law, D. S. McCormick, M. R. Scott and A. M. Stuart. Physica D245, 1, 34-45 (2013).

• Evaluating Data Assimilation Algorithms.  K. J. H. Law and A. M. Stuart. Monthly Weather Review 140, 3757-3782 (2012).

• Stable structures with high topological charge in nonlinear photonic quasicrystals.  K. J. H. Law, Avadh Saxena, P. G. Kevrekidis, and A. R. Bishop. Phys. Rev. A 82, 035802 (2010).

• Stable Vortex-Bright Soliton Structures in Two-Component Bose Einstein Condensates.  K. J. H. Law, P. G. Kevrekidis, Laurette S. Tuckerman. Phys. Rev. Lett. 105, 160405 (2010).

• Existence and stability of multisite breathers in honeycomb and hexagonal lattices.  V. Koukouloyannis, P. G. Kevrekidis, K. J. H. Law, I. Kourakis, D. J. Frantzeskakis. J. Phys. A: Math. Theor. 43, 235101 (2010).

• Self-trapping of optical vortices at the surface of an induced semi-infinite photonic lattice.  Daohong Song, Cibo Lou, Kody J. H. Law, Liqin Tang, Zhuoyi Ye, P.G. Kevrekidis, Jingjun Xu, and Zhigang Chen. Opt. Exp. 18, 5873 (2010).

• Interaction of excited states in two-species Bose-Einstein condensates: a case study.  Todd Kapitula, K.J.H. Law and P.G. Kevrekidis. SIAM J. Appl. Dyn. Syst. 9, Issue 1, 34 (2010).

• Mapping between generalized nonlinear Schroedinger equations and neutral scalar field theories and new solutions of the cubic-quintic NLS equation.  Avinash Khare, Avadh Saxena and K. J. H. Law. J. Phys. A: Math. Theor. 42, 475404 (2009).

• Geometric stabilization of S=2 vortices in lattices: theoretical analysis, numerical computation and experimental results.  K.J.H. Law, D. Song, P.G. Kevrekidis, and Z. Chen. Phys. Rev. A 80, 063817 (2009).

• Manipulation of Vortices by Localized Impurities in Bose-Einstein Condensates.  M.C. Davis, R Carretero-Gonzalez, Z. Shi, K.J.H. Law, P.G. Kevrekidis,and B.P. Anderson. Phys. Rev. A 80, 023604 (2009).

• A two-dimensional paradigm for symmetry breaking: the nonlinear Schroedinger equation with a four-well potential.  C. Wang, G. Theocharis, P. G. Kevrekidis, N. Whitaker, K. J. H. Law, D. J. Frantzeskakis, and B.A. Malomed. Phys. Rev. E 80, 046611 (2009).

• Numerical Methods in DNLS.  K.J.H. Law, P.G. Kevrekidis. Chapter in Discrete Nonlinear Schroedinger Equation : Mathematical Analysis, Numerical Computations, and Physical Perspectives. P.G. Kevrekidis. Springer Tracts in Modern Physics, Vol. 232 (2009).

• The Dynamics of Unstable Waves.  Kody J.H. Law and Q. Enam Hoq. Chapter in Discrete Nonlinear Schroedinger Equation : Mathematical Analysis, Numerical Computations, and Physical Perspectives. P.G. Kevrekidis. Springer Tracts in Modern Physics, Vol. 232 (2009).

• Vortex solutions of the discrete Gross-Pitaevskii equation.  J. Cuevas, G. James, P.G. Kevrekidis, and K.J.H. Law. Physica D: Nonlinear Phenomena 238, Issue 15, 15 July 2009, Pages 1422-1431.

• Localized structures in Kagome lattices.  K.J.H. Law, Avadh Saxena, P.G. Kevrekidis, and A.R. Bishop. Phys. Rev. A 79, 053818 (2009).

• Observation of double-charge discrete vortex solitons in hexagonal photonic lattices.  Bernd Terhalle, etal. Phys. Rev. A 79, 043821 (2009).

• Stable higher-charge discrete vortices in hexagonal photonic lattices.  K. J.H. Law, Panayotis G. Kevrekidis, Tristram J. Alexander, Wieslaw Krolikowski, and Yuri S. Kivshar. Phys. Rev. A. 79, 025801 (2009).

• Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics.  K.J.H. Law, P.G. Kevrekidis, V. Koukouloyannis, I. Kourakis, D.J. Frantzeskakis, and A.R. Bishop. Phys. Rev. E 78, 066610 (2008).

• Dipole and quadrupole solitons in optically-induced two-dimensional defocusing photonic lattices.  H. Susanto, K.J.H. Law, P.G. Kevrekidis, L. Tang, C. Lou, X. Wang, and Z. Chen. Phys. D 237, 3123-3134 (2008).

• Self-trapping of optical vortices in photonic lattices optically induced with self-defocusing nonlinearity.  D.Song, L. Tang, C. Lou, X. Wang, J. Xu, Z. Chen, H. Susanto, K.J.H. Law and P.G. Kevrekidis. Opt. Exp. 16, 14, 10110 (2008).

• Averaging of Nonlinearity Management with Dissipation.  Shabnam Beheshti, Kody J. H. Law, Panayotis G. Kevrekidis, and Mason A. Porter. Phys. Rev. A 78, 025805 (2008).

• Solitons and vortices in honeycomb defocusing photonic lattices.  K.J.H. Law, H. Susanto, and P.G. Kevrekidis. Phys. Rev. A 78, 033802 (2008).

• Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations.  K.J.H. Law, P.G. Kevrekidis, D.J. Frantzeskakis, and A.R. Bishop. Phys. Lett. A 372, 658 (2008).

• Stability of Quantized Vortices in a Bose-Einstein condensate confined in an Optical Lattice.  K.J.H. Law, L. Qiao, P.G. Kevrekidis, and Y.G. Kevrekidis. Phys. Rev. A 77, 053612 (2008).

• Trapping of Two-component matter-wave solitons by mismatched optical lattices.  Z. Shi, K.J.H. Law, P.G. Kevrekidis, and B.A. Malomed. Phys. Lett. A372, 4021 (2008).

• Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement.  K.J.H. Law and P.G. Kevrekidis, B.P. Anderson, R. Carretero-Gonzalez, and D.J. Frantzeskakis. J. Phys. B: At. Mol. Opt. Phys. 41 195303 (2008).

• Observation of dipole-like gap solitons in self-defocusing waveguide lattices.  Liqin Tang, Cibo Lou, Xiaosheng Wang, Zhigang Chen, H. Susanto, K.J.H. Law and P.G. Kevrekidis. Opt. Lett. 32, 20, 3011 (2007).

Papers under review

• SMC Is All You Need: Parallel Strong Scaling. X. Liang, S. Lohani, J. M. Lukens, B. T. Kirby, T. A. Searles, K. J. H. Law. Submitted.

• Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need. S. Yang, V. Zankin, M. Balandat, S. Scherer, K. Carlberg, N. Walton, and K. J. H. Law. Submitted.

• Multilevel Bayesian Neural Networks. N. Chada, A. Jasra, K. J. H. Law, and S. S. Singh. Submitted.

• Convergence Rates for Stochastic Approximation on a Boundary. K. J. H. Law, N. Walton, S. Yang. Submitted. 

• Mixtures of Gaussian Process Experts with SMC$^2$. T. Härkönen, S. Wade, K.J.H. Law, L. Roininen. Submitted.