Publications

Probabilistic forecasting and data assimilation (Cambridge University Press, published May 2015)

• S. Reich and C.J. Cotter, Intro and first chapter (pdf-file available here)

Books, Proceedings Volumes

• Computational Molecular Dynamics: Challenges, Methods, Ideas -- Proceedings of the 2nd International Symposium on Algorithms for Macromolecular Modelling, Berlin, May 21-24, 1997. P. Deuflhard, J. Hermans, B. Leimkuhler, A.E. Mark, S. Reich, R.D. Skeel (eds.), Lecture Notes in Computational Science and Engineering Vol. 4, Springer-Verlag, 1998.

• B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics. ISBN-0521772907

Thesis

• S. Reich, Beitrag zur Theorie der Algebrodifferentialgleichungen. Ph.D. thesis, TU Dresden, 1990.

• S. Reich, Dynamical systems, numerical integration, and exponentially small estimates. Habilitationsschrift, Freie Universitat Berlin, 1998. (ps.gz-file available here)

Papers

2019

• N. Nuesken, S. Reich, and P.J. Rozdeba, State and parameter estimation from observed signal increments. technical report, (pdf-file available from here)

• S. Pathiraja and S. Reich, Discrete gradients for comptuational Bayesian inference. technical report, (pdf-file available from here)

2018

• S. Reich, Data assimilation -- The Schroedinger perspective. technical report, to be submitted to Acta Numerica. (pdf-file available from here)

• M. Morzfeld and S. Reich, Data assimilation: mathematics for merging models and data. Snapshots of modern mathematics from Oberwolfach, No. 11/2018. (pdf-file available from here)

• P.J. van Leeuwen, H.-R. Kuensch, L. Nerger, R. Potthast and S. Reich, Particle filters for applications in geosciences. technical report, submitted to QJRMS. (pdf-file available from here)

• J. de Wiljes, S. Reich, W. Stannat, Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise. SIAM J. Appl. Dyn. Syst., 17, 1152--1181, 2018. (pdf-file available from here)

2017

• A. Taghvaei, J. de Wiljes, P.G. Mehta, S. Reich, Kalman filter and its modern extensions for the continuous-time filtering problem J. Dyn. Sys. Meas., Control, 140, 030904, 2017. (pdf-file available from here)

• H.H. Schuett, L. Rothkegel, H.A. Trukenbrod, S. Reich, F.A. Wichmann, R. Engbert, Likelihood-based parameter estimation and comparison of dynamical cognitive models. Psychological Review, 124, 505--524, 2017. (pdf-file available from here)

• J. de Wiljes, W. Acevedo, S. Reich, A second-order accuate ensemble transform particle filter. SIAM J. Sci. Comput., 39, A1834-A1850, 2017. (pdf-file available from here)

• M. Asgarimehr, J. Wickert, S. Reich, P. Jales, V. U. Zavorotny, Backscattering effects of raindrops beating the ocean surface on TechDemoSat-1 derived wind speeds: Toward an improved GNSS scatterometry (submitted to Geophysical Review Letters)

• M. Reinhardt, G. Hastermann, R. Klein and S. Reich, Balanced data assimilation for highly oscillatory mechanical systems. submitted to Nonlinear Science (pdf-file available from here)

2016

• A. Gregory, C. Cotter, S. Reich, Multilevel ensemble transform particle filter. SIAM J Scientific Computing, 38, A1317-A1338, 2016 (pdf-file available from here)

• N. Chustagulprom, S. Reich, M. Reinhardt, A hybrid ensemble transform filter for high dimensional dynamical systems. SIAM/ASA Journal on Uncertainty Quantification, 4, 552-591, 2016 (pdf-file available from here)

• W. Acevedo, S. Reich, U. Cubasch, Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques. Climate Dynamics, 46 , 1909-1920, 2016.

2015

• V. Aizinger, P. Korn, P. Giorgetta, S. Reich, Large-scale modelling via alpha-regularization for atmospheric simulations. Journal of Turbulence, 14, 367-391, 2015

• B. Escribano, E. Akhmatskaya, S. Reich, J.M. Azprioz, Multiple-time-stepping generalized hybrid Monte Carlo methods. Journal of Computational Physics, 280 , 1-20, 2015 (pdf-file available here)

• Y. Chen and S. Reich, Data assimilation: a dynamical system perspective. Frontiers in Applied Dynamical Systems: Reviews and Tutorials Vol 2, 75-118, 2015 (pdf-file available here)

2014

• V. Grewe, S. Brinkop, P. Joeckel, S. Shin, S. Reich, H. Yserentant, On the theory of mass conserving transformations for Lagrangian methods in 3D atmosphere-chemistry models. Meteorologische Zeitschrift, 23, 441-447, 2014 (pdf-fiel available here )

• S. Reich and S. Shin, On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics, 1, 177-189, 2014 (pdf-file available here)

• J. Amezcua, E. Kalnay, K. Ide, S. Reich, Ensemble transform Kalman-Bucy filter. Q.J. Royal Meteorological Soc., 140, 995-1004, 2014 (pdf-file available here)

2013

• S. Reich, A non-parametric ensemble transform method for Bayesian inference. SIAM J Sci Comput, 35 , A2013-A2014, 2013 (pdf-file available here)

• C.J. Cotter, S. Reich, Ensemble filter techniques for intermittent data assimilation. in Large Scale Inverse Problems. Computational Methods and Applications in the Earth Sciences, M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (eds), Radon Ser. Comput. Appl. Math., 13 , 91-134, 2013, Walter de Gruyter Verlag, Berlin (pdf-file available here)

• S. Reich, A guided sequential Monte Carlo method for the assimilation of data into stochastic dynamical systems. in Recent Trends in Dynamical Systems, A. Johann, H.-P. Kruse, F. Rupp, and S. Schmitz (eds), Springer Proceedings in Mathematics and Statistics, B 35 , 205-220, 2013 (pdf-file available here)

2012

• K. Bergemann and S. Reich, An ensemble Kalman-Bucy filter for continuous data assimilation. Meteorolog. Zeitschrift, 21 , 213-219, 2012 (pdf-file available here)

• S. Shin, S. Reich, and J. Frank, Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modeling. Quarterly Journal of the Royal Meteorological Society, 138 , 1388-1399, 2012 (pdf-file available here)

• S. Reich, A Gaussian mixture ensemble transform filters. Q.J.R. Meteorolog. Soc., 138 , 222-233, 2012 (pdf-file available here)

2011

• R.D. Skeel and S. Reich, Corrected potential energy functions for constrained molecular dynamics. European Physical Journal Special Topics, 200 , 55-72, 2011 (pdf-file available here)

• S. Reich and T. Hundertmark, On the use of constraints in molecular and geophysical fluid dynamics. European Physical Journal Special Topics, 200 , 259-270, 2011 (pdf-file available here)

• E. Akhmatskaya and S. Reich, New Hybrid Monte Carlo Methods for Efficient Sampling: from Physics to Biology and Statistics. Progress in Nuclear Science and Technology, 2, 447-462, 2011, (pdf-file available here)

• E. Akhmatskaya and S. Reich, Meso-GSHMC: A stochastic algorithm for meso-scale constant temperature simulations. Procedia Computer Science, 4 , 1353-1362, 2011, (pdf-file available here)

• G. Gottwald, L. Mitchell and S. Reich, Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter. Monthly Weather Review, 139 , 2650-2667, 2011, (pdf-file available here)

• S. Shin, G. Zoeller, M. Holschneider and S. Reich, A multigrid solver for modeling complex interseismic stress fields. Computers & Geosciences, 37 , 1075-1082, 2011, (pdf-file available here)

• S. Reich, A dynamical systems framework for intermittent data assimilation. BIT Numerical Analysis, 51 , 235-249, 2011, (pdf-file available here)

2010

• S. Reich, Ensemble Kalman and H_infty filters. AIP Conf. Proc., Volume 1281, 2010, pp. 19-22 (ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics), (pdf-file available here)

• K. Bergemann and S. Reich, A mollified ensemble Kalman filter. Q.J.R. Meteorolog. Soc. 136 , 1636-1643, 2010, (pdf-file available here)

• K. Bergemann and S. Reich, A localization technique for ensemble Kalman filters. Q.J.R. Meterolog. Soc. 136 , 701-707, 2010. (pdf-file of a slightly expanded version available here)

• S. Shin, M. Sommer, S. Reich and P. Nevir, Evaluation of three spatial discretization schemes with the Galewsky et al. test. Atmospheric Science Letters 11, 223-228, 2010 (pdf-file available here)

• M. Sommer and S. Reich, Phase space volume conservation under space and time discretization schemes for the shallow-water equations. Monthly Weather Review, 138, 4229-4236, 2010, (pdf-file available here)

• M. Laeuter et al, A 2D Unified (Non-) Hydrostatic Model of the Atmosphere with a discontinuous Galerkin Method. technical report, (pdf-file available here)

2009

• E. Akhmatskaya, N. Bour-Rabee and S. Reich, A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 228, 2256--2265, 2009 (pdf-file available here), an erratum is available here and has been published in J. Comput. Phys. 228, 7492--7496, 2009.

• S. Shin and S. Reich, Hamiltonian particle-mesh simulations for a non-hydrostatic vertical slice model. Atmospheric Science Letters 10 , 233-240, 2009 (pdf-file available here)

• B. Leimkuhler and S. Reich, A Metropolis adjusted Nose-Hoover thermostat. M2AN, 43, 74300756, 2009. (pdf-file available here)

• K. Bergemann, G. Gottwald, and S. Reich, Ensemble propagation and continuous matrix factorization algorithms. Q.J.R. Meteorolog. Soc., 135, 1560--1572, 2009. (pdf-file available here)

• Marco Giorgetta, Tobias Hundertmark, Peter Korn, Sebastian Reich, Marco Restelli, Conservative space and time regularizations for the ICON model. Berichte zur Erdsystemforschung, Report 67, MPI for Meteorology, Hamburg. (pdf-file available here)

• E. Akhmatskaya and S. Reich, Stochastic algorithms for meso-scale constant temperature simulations. technical report. (pdf-file available here)

• C.J. Cotter, D.A. Ham, Ch.C. Pain and S. Reich, LBB stability of a mixed Galerkin finite element pair for fluid flow simulations.J. Comput. Phys. 228, 336-348, 2009. (pdf-file available here)

2008

• E. Akhmatskaya and S. Reich, GSHMC: An efficient method for molecular simulation. J. Comp. Phys. 227, 4934-4954, 2008. (pdf-file available here)

2007

• C.J. Cotter, J. Frank, and S. Reich, The remapped particle-mesh semi-Lagrangian advection scheme. Q.J.R. Meteorolog. Soc. 133, 251-260, 2007. (pdf-file available here)

• S. Reich, N. Wood, and A. Staniforth, Semi-implicit methods, nonlinear balance, and regularized equations. Atmospheric Science Letters 8, 1-6, 2007. (pdf-file available here)

• T. Hundertmark and S. Reich, A regularization approach for a vertical slice model and semi-Lagrangian Stormer-Verlet time-stepping. Q.J.R. Meteorolog. Soc. 133, 1575-1587, 2007. (pdf-file available here)

• S. Reich, An explicit and conservative remapping strategy for semi-Lagrangian advection. Atmospheric Science Letters 8, 58-63, 2007. (pdf-file available here)

2006

• J. Frank, B. Moore, and S. Reich, Linear PDEs and numerical methods that preserve a multi-symplectic conservation law. SIAM J Scientific Computing 28, 260-277, 2006. (pdf-file available here)

• E. Akhmatskaya and S. Reich, The targetted shadowing hybrid Monte Carlo (TSHMC) method. New Algorithms for Macromolecular Simulation, Lecture Notes in Computational Science and Engineering 49, editors: B. Leimkuhler C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schuette, R. Skeel, 145-158, 2006. (pdf-file available here)

• N. Wood, A. Staniforth, and S. Reich, Improved regularization for time-staggered discretization and its link to the semi-implicit method. Atmospheric Science Letters 7, 21-25, 2006. (pdf-file available here)

• C.J. Cotter and S. Reich, Semi-geostrophic particle motion and exponentially accurate normal forms. SIAM Multiscale Modelling 5, 476-496, 2006. (pdf-file available here)

• S. Reich, Linearly implicit time stepping methods for numerical weather prediction. BIT 46, 607-616, 2006. (pdf-file available here)

• T.J. Bridges and S. Reich, Numerical methods for Hamiltonian PDEs. J. Phys. A: Math. Gen. 39, 5287-5320, 2006. (pdf-file available here)

• A. Staniforth, N. Wood, and S. Reich, A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations. Q.J.R. Meteorolog. Soc. 132, 3107-3116, 2006. (pdf-file available here)

• M. Dubal, A. Staniforth, N. Wood, and S. Reich, Analysis of a regularized, time-staggered discretization applied to a vertical slice model. Atmospheric Science Letters 7, 86-92, 2006. (pdf-file available here)

2005

• J. Frank, S. Reich, A. Staniforth, A. White, and N. Wood, Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method. Atmospheric Science Letters 6, 97-104, 2005. (pdf-file available here)

• T. Bridges, P. Hydon and S. Reich, Vorticity and symplecticity in Lagrangian fluid dynamics. J. Phys. A: Math. Gen. 38, 1403-1418, 2005. (pdf-file available here)

2004

• C.J. Cotter and S. Reich, Adiabatic invariance and applications: From MD to NWP. BIT, 44, 439-455, 2004. (pdf-file available here)

• J. Frank and S. Reich, The Hamiltonian Particle Mesh method for the spherical shallow-water equations. Atmospheric Science Letters 5, 89-95, 2004. (pdf-file available here)

• C.J. Cotter and S. Reich, Time Stepping Algorithms for Classical Molecular Dynamics. Computational Nanotechnology (eds. M. Rieth and W. Schommers), to appear. (pdf-file available here -- version 27/03/2004)

• M. Dixon and S. Reich, Symplectic Time-Stepping for Particle Methods. GAMM Mitteilungen 27, 9-24, 2004. (pdf-file available here)

• J. Frank and S. Reich, Energy-conserving semi-discretizations and spurious numerical reflections. technical report (pdf-file available here)

• C.J. Cotter, J. Frank and S. Reich, Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation. SIAM J Applied Dynamical Systems 3, 69-83, 2004. (pdf-file available here)

• C.J. Cotter and S. Reich, Geometric Integration of a Wave-Vortex Model. APNUM 48, 293-305, 2004. (ps.gz-file available here)

2003

• C.J. Cotter and S. Reich, An Extended Dissipative Particle Dynamics Model. Europhys. Lett. 64, 723-729, 2003. (pdf-file available here)

• B. Moore and S. Reich, Multi-symplectic Integration Methods for Hamiltonian PDEs. Future Generation Computer Systems 19, 395-402, 2003. (ps.gz-file available here)

• B. Moore and S. Reich, Backward error analysis for multi-symplectic integration methods. Numerische Mathematik 95, 625-652, 2003. (pdf-file available here)

• J. Frank and S. Reich, Conservation Properties of Smoothed Particle Hydrodynamics Applied to the Shallow Water Equations. BIT 43, 40-54, 2003. (ps.gz-file available here)

2002

• J. Frank, G. Gottwald, and S. Reich, A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations. Lecture Notes in Computational Science and Engineering, Vol. 26, 131-142, 2002. (ps.gz-file available here)

• E. Barth, B. Leimkuhler and S. Reich, A test set for molecular dynamics. Lecture Notes in Computational Science and Engineering, Vol. 24, 73-103, 2002. (ps.gz-file available here)

• J. Frank and S. Reich, A Particle-Mesh Method for the Shallow Water Equations near Geostrophic Balance. J. Comput. Phys. 180, 407-426, 2002. (ps.gz-file available here)

2001

• Th.J. Bridges and S. Reich, Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations. Physica D 152 , 491-504, 2001. (ps.gz-file available here)

• Th.J. Bridges and S. Reich, Computing Lyapunov exponents on a Stiefel manifold. Physica D, 156, 219-238, 2001. (ps.gz-file available here)

• B. Leimkuhler and S. Reich, A reversible averaging integrator for multiple time-scale dynamics. J. Comput. Physics 171 , 95-114, 2001. (ps.gz-file available here)

• Th.J. Bridges and S. Reich, Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Physics Letters A 284 , 184-193, 2001. (ps.gz-file available here)

• Th. Holder, B. Leimkuhler, and S. Reich, Explicit variable step-size and time-reversible integration. APNUM 39, 367-377, 2001. (ps.gz-file available here)

2000

• J. Zhou, S. Reich and B.R Brooks, Elastic molecular dynamics with self-consistent flexible constraints. J. Chem. Phys. 112 , 7919--7929, 2000. (ps.gz-file available here)

• S. Reich, Finite volume methods for multi-symplectic PDEs. BIT 40 , 559--582, 2000. (ps.gz-file available here)

• S. Reich, The repulsive-particle method and the symplectic integration of the shallow-water equations. technical report. (ps.gz-file available here)

• S. Reich, Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations. J. Comput. Phys. 157 , 473--499, 2000. (ps.gz-file available here)

• S. Reich, Smoothed Langevin dynamics of highly oscillatory systems. Physica D 138, 210-224, 2000. (ps.gz-file available here)

1999

• J. Izaguirre, S. Reich, and R.D. Skeel, Longer time steps for molecular dynamics. J. Chem. Phys. 110 , 9853-9864, 1999. (ps.gz-file available here)

• S. Reich, Backward error analysis for numerical integrators. SIAM J. Numer. Anal. 36 , 1549-1570, 1999. (ps.gz-file available here)

• S. Reich, Multiple time-scales in classical and quantum-classical molecular dynamics. J. Comput. Phys. 151 , 49-73, 1999. (ps.gz-file available here)

• E. Barth, B. Leimkuhler, S. Reich, A time-reversible variable stepsize integrator for constrained dynamics. SIAM J. Sci. Comput. 21, 1027-1044, 1999. (ps.gz-file available here)

• U. Ascher, S. Reich, The midpoint scheme and variants for Hamiltonian systems: advantages and pitfalls. SIAM J. Sci. Comput. 21, 1045-1065, 1999. (ps.gz-file available here)

• S. Reich, Preservation of adiabatic invariants under symplectic discretization. Applied Numerical Mathematics 29, 45-56, 1999. (ps.gz-file available here)

1998

• U. Ascher, S. Reich, On some difficulties in integrating highly oscillatory Hamiltonian systems. Lecture Notes in Computational Science and Engineering, Vol. 4, 281-296, 1998. (ps.gz-file available here)

• S. Reich, Modified potential energy functions for constrained molecular dynamics. Numerical Algorithms 19, 213-221, 1998. (ps.gz-file available here)

• P. Nettesheim and S. Reich, Symplectic multiple-time-stepping integrators for quantum-classical molecular dynamics. Lecture Notes in Computational Science and Engineering, Vol. 4, 412-420, 1998. (ps.gz-file available here)

prehistoric stuff

• S. Reich, Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten. Wissenschaftliche Zeitschrift der TU Dresden 38, 217-220, 1989.

• S. Reich, On a geometric interpretation of DAEs. Circ. Syst., Sig. Processing 9, 367-382, 1990.

• S. Reich, On a geometric characterization of DAEs. Mathematical Research Vol. 59, Akademie-Verlag, 105-113, 1990.

• S. Reich, New results on the numerical and analytical treatment of DAEs. in: Tagungsbericht des ITG-Seminars: Neue Anwendungen theoretischer Konzepten in der Elektrotechnik, Hannover, 79-90, 1990.

• E. Eich, C. Fuhrer, B. Leimkuhler, S. Reich, Stabilization and projection methods for multibody dynamics Report A281, Helsinki Univ. of Technology, 1990.

• S. Reich, On an existence and uniqueness theory for nonlinear DAEs. Circ. Syst., Sig. Processing 10, 344-359, 1991.

• S. Reich, DAEs and applications in circuit theory. Archiv für Elektronik and Übertragungstechnik (AEÜ)46, 298-304, 1992.

• U. Ascher, H. Chin, S. Reich, Stabilization of DAEs and invariant manifolds. Numerische Mathematik 67, 131-149, 1994. (ps.gz-file available here)

• B. Leimkuhler, S. Reich, Symplectic integration of constrained Hamiltonian systems. Math. Comp. 63, 598-605, 1994. (ps.gz-file available here)

• S. Reich, Momentum conserving symplectic integrators. Physica D 76, 375-383, 1994.

• S. Reich, On the local qualitative behavior of DAEs. Circ. Syst., Sig. Processing 14, 427-443, 1994.

• U. Ascher, H. Chin, L. Petzold, S. Reich, Stabilization of constrained mechanical systems with DAEs and invariant manifolds. Mech. Struct. & Mach. 23, 135-157, 1995. (ps.gz-file available here)

• S. Reich, Smoothed dynamics of highly oscillatory Hamiltonian systems. Physica D 89, 28-42, 1995. (ps.gz-file available here)

• S. Reich, Enhanced energy conserving methods. BIT 36, 122-134, 1996. (ps.gz-file available here)

• S. Reich, Symplectic integration of conservative multibody systems. Fields Institute Communications 10, 181-191, 1996. (ps.gz-file available here)

• B. Leimkuhler, S. Reich, R.D. Skeel, Integration methods for molecular dynamics. IMA Volumes in Mathematics and its Applications Vol. 82, Springer Verlag, 161-186, 1996. (ps.gz-file available here)

• S. Reich, Torsion dynamics of molecular systems. Phys. Rev. E 53, 4176-4181, 1996. (ps.gz-file available here and Fig. 1 , Fig. 2, Fig. 3)

• S. Reich, Symplectic integration of constrained Hamiltonian systems by composition methods. SIAM J. Numer. Anal. 33, 475-491, 1996.