INSTITUTION FÖR MATEMATISKA VETENSKAPER

 TILLÄMPAD MATEMATIK & STATISTIK

Annika Lang

Professor in Mathematics and Head of Unit in Applied Mathematics and Statistics

Postal address

Annika Lang Department of Mathematical Sciences Chalmers University of Technology SE-412 96 Göteborg Sweden Contact information Email: annika.lang@chalmers.se Phone: +46 31 772 5356 Room: L2086, Chalmers Tvärgata 3, Göteborg

Archives of the Mathematisches Forschungsinstitut Oberwolfach

Open projects

• If you are interested in a Bachelor and Master thesis, please contact me.
• Please see all our current open positions at the institute here.

Current postdocs and (main and co-)supervised PhD and master students

• Erik Jansson, PhD student (with Klas Modin)
• Kasper Bågmark, PhD student (with Adam Andersson and Stig Larsson)
• Oskar Eklund, PhD student (with Moritz Schauer)
• Johan Ulander, PhD student (with David Cohen)
• Malin Nilsson, PhD student (with Axel Målqvist)
• Ioanna Motschan-Armen, PhD student (with David Cohen)
• Sondre Wiersdalen, PhD student (with Balázs Kulcsár and Mike Pereira)

Former PhD students and postdocs

• Kristin Kirchner, currently at TU Delft
• Andreas Petersson, currently at University of Oslo
• Mike Pereira, currently at MINES Paris Tech

Preprints

• Galerkin-Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds, A. Lang, M. Pereira, arXiv:2107.02667, July 2021
• Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs, A. Andersson, A. Lang, A. Petersson, L. Schroer, arXiv:1910.05261, October 2019

Publications

• Numerical approximation and simulation of the stochastic wave equation on the sphere, D. Cohen, A. Lang, Calcolo, Vol. 59, No. 3, 32, September 2022
• Short-term traffic prediction using physics-aware neural networks, M. Pereira, A. Lang, B. Kulcsár, Transportation Research Part C: Emerging Technologies, Vol. 142, 103772, September 2022
• Approximation of SPDE covariance operators by finite elements: A semigroup approach, M. Kovács, A. Lang, A. Petersson, to appear in IMAJNA, arXiv:2107.10109, accepted April 2022
• Hilbert-Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations, M. Kovács, A. Lang, A. Petersson, to appear in Stochastic Analysis and Applications, April 2022, arXiv:2107.10104
• Connecting random fields on manifolds and stochastic partial differential equations in simulations, A. Lang, to appear in Oberwolfach Reports, 2022.
• Surface finite element approximation of spherical Whittle-Matérn Gaussian random fields, E. Jansson, M. Kovács, A. Lang, SIAM J. Sci. Comput., Vol. 44, No. 2, A825-A842, April 2022
• Parameter and density estimation from real-world traffic data: A kinetic compartmental approach, M. Pereira, P. Boyraz Baykas, B. Kulcsár, A. Lang, Transp. R. B, Vol. 155, 210-239, January 2022
• Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise, M. Kovács, A. Lang, A. Petersson, ESAIM:M2N, Vol. 54, No. 6, 2199-2227,  November-December 2020
• Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces, G. Cleanthous, A. Georgiadis, A. Lang, and E. Porcu, Stoch. Proc. Appl., Vol. 130, No. 8, 4873-4891, August 2020
• Drift-preserving numerical integrators for stochastic Hamiltonian systems, C. Chen, D. Cohen, R. D'Ambrosio, A. Lang,  Adv. Comput. Math., Vol. 46, No.2, 27, April 2020
• Random fields: How does regularity influence the resulting structures?, A. Lang. In Björn Engquist and Daniel Peterseim, editors, Computational Multiscale Methods, 35/2019 of Oberwolfach Reports. European Mathematical Society, 2019
• Drift-preserving numerical integrators for stochastic Hamiltonian systems, A.Lang. In Oliver Ernst, Fabio Nobile, Claudia Schillings and Tim Sullivan, editors, Uncertainty Quantification, 12/2019, Vol 16, No. 1 of Oberwolfach Reports, pp. 713-714. European Mathematical Society, 2019
• Fast generation of isotropic Gaussian random fields on the sphere, P.E. Creasey, A. Lang, Monte Carlo Meth. Appl., Vol. 24, No. 1, 1-11. (and code on github), March 2018
• Numerical analysis of lognormal diffusions on the sphere, L. Herrmann, A. Lang, Ch. Schwab, Stoch. PDE: Anal. Comp., Vol. 6, No. 1, 1-44, March 2018, (SAM report 2016-02)
• Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations, A. Lang, A. Petersson, Math. Comp. in Simulation, Vol. 143, pp. 99-113, January 2018
• Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions, A. Lang, A. Petersson, A. Thalhammer, BIT Num. Math., Vol. 57, No. 4, 963-990, December 2017
• Mean-square stability analysis of SPDE approximations, A. Lang. In L. Szpruch, M. Hutzenthaler, A. Lang, and L. Yaroslavtseva, editors, Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions, 9/2017, Vol. 14 of Oberwolfach Reports, pp. 476–479. European Mathematical Society, 2017
• Covariance structure of parabolic stochastic partial differential equations with multiplicative Lévy noise, K. Kirchner, A. Lang, S. Larsson, J. Diff. Equations, Vol. 262, No. 12, pp. 5896-5927, June 2017
• Continuity of random fields on Riemannian manifolds, A. Lang, J. Potthoff, M. Schlather, D. Schwab, Comm. Stoch. Anal., Vol. 10, No. 2, pp. 185-193, June 2016
  
• A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes, A. Lang. In Ronald Cools and Dirk Nuyens, editors, Monte Carlo and Quasi-Monte Carlo Methods, MCQMC, Leuven, Belgium, April 2014, pp. 489-505, Springer, June 2016
•  Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations, A. Lang, Ch. Schwab,  Ann. Appl. Prob., Vol. 25, No. 6, pp. 3047-3094, December 2015 (arXiv:1305.1170 [math.PR])
  
• Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds, R. Andreev, A. Lang, Potential Anal., Vol. 41, No. 3, pp. 761-769, October 2014 (arXiv:1307.4886 [math.PR])
• Stochastic partial differential equations, A. Lang. In Katsushi Ikeuchi, editor, Computer Vision: A Reference Guide, pp. 770–775, Springer, 2014
  
• Isotropic Gaussian random fields on the sphere, A. Lang, Oberwolfach Report 39/2013, pp. 38-41, August 2013
• Covariance structure of parabolic stochastic partial differential equations, A. Lang, S. Larsson, Ch. Schwab, Stoch. PDE: Anal. Comp., Vol. 1, No. 2, pp. 351-364, June 2013 (arXiv:1210.3447 [math.PR])
• L^p and almost sure convergence of a Milstein scheme for stochastic partial differential equations, A. Barth, A. Lang, Stoch. Proc. Appl., Vol. 123, No. 5, pp. 1563-1587, May 2013
• Multilevel Monte Carlo method for parabolic stochastic partial differential equations, A. Barth, A. Lang, Ch. Schwab, BIT Num. Math., Vol. 53, No. 1, pp. 3-27, March 2013
• Erratum: Fast simulation of Gaussian random fields, A. Lang, J. Potthoff, Monte Carlo Meth. Appl., Vol. 19, No. 1, pp. 73-75, March 2013
• Multilevel Monte Carlo method with applications to stochastic partial differential equations, A. Barth, A. Lang, J. Comp. Math., Vol. 89, No. 18, pp. 2479-2498, December 2012
• Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises, A. Barth, A. Lang, Appl. Math. Opt., Vol. 66, No. 3, pp. 387-413, December 2012
• A new similarity measure for nonlocal filtering in the presence of multiplicative noise, T. Teuber, A. Lang, Comp. Stat. Dat. Ana., Vol. 56, No. 12, pp. 3821-3842, December 2012
• Erratum: Almost Sure Convergence of a Semidiscrete Milstein Scheme for SPDEs of Zakai Type, A. Lang, P.-L. Chow, J. Potthoff, Stochastics, Vol. 84, No. 4, p. 561, August 2012
• Simulation of stochastic partial differential equations using finite element methods, A. Barth, A. Lang, Stochastics, Vol. 84, No. 2-3, pp. 217-231, April 2012
• Nonlocal filters for removing multiplicative noise, T. Teuber, A. Lang, in Scale Space and Variational Methods in Computer Vision, Springer Berlin / Heidelberg, 2012, LNCS 6667, pp. 50-61
• Almost sure convergence of a Galerkin approximation for SPDEs of Zakai type driven by square integrable martingales , A. Lang, J. Comp. Appl. Math., Vol. 236, No. 7, pp. 1724-1732, January 2012
• Fast simulation of Gaussian random fields, A. Lang, J. Potthoff, Monte Carlo Meth. Appl., Vol. 17, No. 3, pp. 195-214, September 2011
  Typo: In Algorithm 3.1, Remark d) it should read (k_i-N_i/2)/l_i instead of k_i/l_i. See also Monte Carlo Meth. Appl., Vol. 19, No. 1, pp. 73-75.
• A Lax equivalence theorem for stochastic differential equations, A. Lang, J. Comp. Appl. Math., Vol. 234, No. 12, pp. 3387-3396, October 2010
• Almost Sure Convergence of a Semidiscrete Milstein Scheme for SPDEs of Zakai Type, A. Lang, P.-L. Chow, J. Potthoff, Stochastics, Vol. 82, No. 3, pp. 315-326, June 2010
• Mean square convergence of a semidiscrete scheme for SPDEs of Zakai type driven by square integrable martingales, A. Lang, ICCS 2010 Proceedings, Procedia Computer Science, Vol. 1, No. 1, pp. 1609-1617, May 2010
• PhD thesis: Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours, A. Lang, December 2007
• Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound, A. Niehage, Quantum Information Processing, Vol. 6, No. 3, pp. 143-158, June 2007 and Mannheimer Manuskripte 279, May 2006
• Diploma thesis: Quantum Goppa Codes over Hyperelliptic Curves, arXiv.quant-ph/0501074, A. Niehage, November 2004

Popular science publications

• Sampling of random fields on manifolds, E. Jansson, A. Lang, M. Pereira, ECMI blog, May 2021

Organized Workshops/Seminars

• 4th Workshop on Scientific Computing in Sweden (SwedComp22), Gothenburg, October 26-27, 2022
• Theory and Computational Methods for SPDEs, BIRS Oaxaca (CMO), September 11-16, 2022
• Mini-Symposium on "Numerical methods for stochastic (partial) differential equations" at SciCADE 2021, Reykjavík, MOVED TO July 25-29, 2022
• canceled and to be rescheduled: Theory and Computational Methods for SPDEs, BIRS Oaxaca (CMO), September 6-11, 2020
• Mini-Symposium on "Numerical methods for stochastic (partial) differential equations" at SciCADE 2019, Insbruck, July 22-26, 2019
• Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Institut Mittag-Leffler, May 20-24, 2019
• CAM seminar at Chalmers & University of Gothenburg (weekly seminar in Computational and Applied Mathematics organized by Klas Modin and Annika Lang)
• SPA 2018 - The 40th Conference on Stochastic Processes and Their Applications, Chalmers & University of Gothenburg, June 11-15, 2018
• SPDEs: From Theory to Simulation, Special Session at the Meeting of the Catalan, Spanish, Swedish Math Societies, Umeå, June 2017
• Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions, Mathematisches Forschungsinstitut Oberwolfach, February 5-11, 2017
• NASPDE 2016, Chalmers & University of Gothenburg, September 6-7, 2016
  
• Advances in Numerical Methods for SPDEs, Institut Mittag-Leffler, June 16-18, 2015
  

Talks and Posters

• Talk: Stochastic partial differential equations and random fields on Riemannian manifolds, Numerical analysis and applications of SDEs, Banach Centre, Bedlewo, September 2022
• Talk: Simulation of random fields on Riemannian manifolds, DMV Annual Meeting, Berlin, September 2022
• Talk: Short-term traffic prediction using physics-aware neural networks, Statistics for Stochastic Processes: SDEs, SPDEs and concentration of measure, Luxembourg, September 2022
• Talk: The stochastic wave equation on the sphere: properties and simulation, SciCADE 2021, Reykjavík, July 2022
• Summer school: Introduction to stochastic partial differential equations and their approximation, Summer School on Computational Mathematics, Gdańsk, July 2022
• Talk: Simulation of random fields on Riemannian manifolds, 30th Birthday of Acta Numerica, Banach Centre, Bedlewo, June 2022
• Talk: Short-term traffic prediction using physics-aware neural networks, Thematic Program Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data, ESI Wien, May/June 2022
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, KTH Seminar on Numerical Analysis, Stockholm, April 2022
  
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, Workshop on Space-Time Methods for Time-Dependent Partial Differential Equations, MF Oberwolfach, February 2022
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, Mathematics & Statistics Colloquium, Maynooth University, Ireland, February 2022
• Talk: STOchastic traffic NEtworks, AI research sample, Chalmers AI Research Center - Zooming out!, Göteborg, December 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, Workshop "Junior Female Researchers in Probability", Berlin, October 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, XII Forum of PDEs, Banach Center in Będlewo, September 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, NUMDIFF-16,  Martin Luther University Halle-Wittenberg, September 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, MCM 2021, Universität Mannheim, August 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, One world SNIP seminar, ICMS, June 2021
• Talk: Connecting random fields on manifolds and stochastic partial differential equations in simulations, YRbGSA2021 summer school, June 2021
• Talk: The stochastic wave equation on the sphere: properties and simulation, stochastic analysis seminar, UNICAMP, Brazil, June 2021
• Talk: The stochastic heat and wave equation on the sphere, matstat seminar, Stockholms universitet, May 2021
• Talk: The stochastic wave equation on the sphere: properties and simulation, STAR seminar, University of Oslo, March 2021
• Talk: A finite element approximation of Gaussian random fields on the sphere, CRC1114 Conference 2021, Berlin, March 2021
• Talk: Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs, Young researchers between geometry and stochastic analysis, University of Bergen, February 2020
• Talk: Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs, Workshop on multiscale methods for deterministic and stochastic dynamics, Université de Genève, January 2020
• Talk: Random fields: Regularity and simulation, Ecole des Mines, Fontainebleau, November 2019
• Talk: Quadratic functionals of SPDE solutions: Efficient computation via Lyapunov equations, Statistical Inference for Stochastic PDEs, September 2019
• Talk: Random fields: How does regularity influence the resulting structures?, MFO, July 2019
• Talk: Deep learning and stochastic partial differential equations: a possible connection, Workshop on Mathematics for Complex Data, June 2019
• Talk: Drift-preserving numerical integrators for stochastic Hamiltonian systems, MFO March 2019
• Talk: SPDE simulation on spheres,  Nonlinear Stochastic Evolution Equations: Analysis, Numerics and Applications, TU Berlin, December 2018
• Talk: SPDE simulation on spheres, Forum on Numerical Methods for SPDEs, Chinese Academy of Sciences, Beijing, China, October 2018
• Talk: SPDE simulation on spheres, NUMDIFF-15, Martin Luther Universität Halle-Wittenberg, September 2018
• Talk: Simulation of random models: where stochastic analysis meets high performance computing, MV colloquium, Chalmers & GU, September 2018
• Talk: The stochastic heat equation: A short review on 15 years of simulation, Universität Mannheim, June 2018
• Talk: Random field simulation: bridging stochastic processes and their applications, Seminar in Mathematical Statistics, KTH, November 2017
• Talk: Random field simulation: bridging stochastic processes and their applications, FINEWSTOCH Networkshop II, University of Oslo, November 2017
• Talk: Simulating weak convergence rates for SPDE approximations, Meeting of the Catalan, Spanish, Swedish Math Societies, Umeå, June 2017
• Talk: Simulating weak convergence rates for SPDE approximations, Recent Developments in Numerical Methods with Applications in Statistics and Finance, Universität Mannheim, June 2017
• Talk: Mean-square stability analysis of SPDE approximations, Oberwolfach Mini-Workshop "Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions", MFO, February 2017
• Talk: Mean-square stability analysis of SPDE approximations, Multiscale Methods for Stochastic Dynamics, University of Geneva, February 2017
• Talk: Simulating weak convergence rates for SPDE approximations, Nonlinear Stochastic Evolution Equations: Analysis and Numerics, TU Berlin, November 2016
  
• Talk: Weak error simulation for stochastic partial differential equations, Scientific Computing in Sweden, Uppsala Universitet, October 2016
• Talk: Stochastic simulation: How do we generate pictures and what do they show?, docentföreläsning, Chalmers, September 2016
  
• Poster: Stochastic Simulation and SPDEs, Inauguration Cluster Computer Hebbe, Chalmers, May 2016
  
• Talk: (Multilevel) Monte Carlo in error computation, Uncertainty Quantification, Institut Mittag-Leffler, May 2016
  
• Talk: Multilevel Monte Carlo with applications to stochastic partial differential equations, Uppsala Universitet, December 2015
  
• Talk: Stochastic and random partial differential equations: a shared simulation problem, NASPDE 2015, Sophia Antipolis, September 2015
  
• Talk: What is the importance of strong vs. weak error analysis when computing stochastic partial differential equations?, SciCADE 2015, Potsdam, September 2015
  
• Talk: How can SPDE simulations become more efficient?, SciCADE 2015, Potsdam, September 2015
  
• Talk: PDE simulation: How does "P" increase the complexity?, MCM 2015, Linz, July 2015
  
• Talk: Computing stochastic partial differential equations: a variety of challenges, MCM 2015, Linz, July 2015
  
• Talk: Gaussian random fields in the plane and on spheres: regularity and approximation, Big New Researchers Get-Together, Göteborg, October 2014
  
• Talk: How can solutions of SPDEs be simulated on a computer?, RDSN14, Mannheim, June 2014
  
• Talk: Gaussian random fields on the sphere: one class of random fields on manifolds, Spatial Statistics and UQ, Bath, May 2014
  
• Talk: Multilevel Monte Carlo method with applications to stochastic partial differential equations, MCQMC 2014, Leuven, April 2014
  
• Talk: Hilbertraumwertige Zufallsvariablen: Was ist das und welche Methoden nutzen bei der Charakterisierung?, Universität Köln, January 2014
  
• Talk: Simulation von Zufallsfeldern & stochastischen partiellen Differentialgleichungen: Was verbindet sie?, Goethe-Universität Frankfurt, January 2014
  
• Talk: Zufallsfelder: Approximation, Regularität und Anwendungen. Universität Mannheim, December 2013
  
• Talk: How does one computationally solve a stochastic partial differential equation?, Chalmers University of Technology, Göteborg, November 2013
  
• Talk: Isotropic Gaussian random fields on the sphere, Sixth Workshop on Random Dynamical Systems, Universität Bielefeld, October 2013
  
• Talk: Covariance structure of parabolic stochastic partial differential equations, Dirichlet Forms and Applications: German-Japanese Open Meeting on Stochastic Analysis, Universität Leipzig, September 2013
• Talk: Simulating the driving noise of a stochastic partial differential equation, Summer School on "Numerical Methods for Stochastic Differential Equations", TU Wien, September 2013
• Talk: Isotropic Gaussian random fields on the sphere, Oberwolfach Workshop on "Multiscale and High-Dimensional Problems", MFO, July 2013
• Talk: Wie löst man eine stochastische partielle Differentialgleichung mit dem Computer?, Universität Frankfurt, July 2013
• Talk: Zufallsfelder zwischen Approximation, Regularität und Anwendungen, WWU Münster, May 2013
• Talk: Model versus reality in my research, Chalmers University, Göteborg, April 2013
• Talk: Was ist die vom Computer simulierte Lösung einer stochastischen partiellen Differentialgleichung?, Universität Paderborn, March 2013
• Talk: Von stochastischen Prozessen zu Zufallszahlen, Universität Stuttgart, November 2012
• Talk: Von stochastischen Prozessen zu Zufallszahlen, TU Darmstadt, November 2012
• Talk: Simulation of stochastic processes, Oberseminar Numerik, Universität Bielefeld, January 2012
• Talk: Multilevel Monte Carlo Methode für stochastische partielle Differentialgleichungen, TU Darmstadt, December 2011
• Talk: Multi-level Monte Carlo Finite Element method for parabolic stochastic partial differential equations, Chalmers University, Göteborg, October 2011
• Talk: Multi-level Monte Carlo Finite Element method for parabolic stochastic partial differential equations, Universität Basel, October 2011
• Talk: Multi-level Monte Carlo Finite Element method for parabolic stochastic partial differential equations, Workshop on High-Dimensional Aspects of Stochastic PDEs, HIM, Bonn, August 2011
• Talk: Lax's Equivalence Theorem for Stochastic Differential Equations, 24th NACONF, Glasgow, June 2011
• Talk: Stochastische partielle Differentialgleichungen - Numerik und Simulation, TU Kaiserslautern, June 2010
• Talk: Mean square convergence of a semidiscrete scheme for SPDEs of Zakai type driven by square integrable martingales, ICCS 2010, Amsterdam, May/June 2010
• Talk: Stochastische partielle Differentialgleichungen - Numerik und Simulation, WWU Münster, May 2010
• Talk: Lax's Equivalence Theorem for Stochastic Differential Equations, SAM, ETH Zürich, February 2010
• Talk: Lax's Equivalence Theorem for Stochastic Differential Equations, CMA Oslo, December 2009
• Talk: Stochastische partielle Differentialgleichungen - Numerik und Simulation, Universität Leipzig, August 2009
• Talk: A Milstein Scheme for Zakai's Equation, SPA 2009, Berlin, July 2009
• Talk: Almost Sure Convergence of Discrete-Time Solutions to Some Stochastic PDEs, Wayne State University, Detroit, May 2009
• Talk: Simulation of Stochastic Partial Differential Equations, TU Darmstadt, February 2009
• Talk: Simulation of Stochastic PDE's and Segmentation Problem, Wayne State University, Detroit, July 2008
• Talk: Gaussian Random Fields, Wayne State University, Detroit, July 2008
• Talk: Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours, Rhein-Main Workshop "Mathematics of Computation", June 2008
• Talk: Gaussian Random Fields, CMA Oslo, January 2007
• Talk: Gaussian Random Fields and Segmentation, Summerschool on Stochastic Differential Equations, Copenhagen, May 2006
• Talk: Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound, AGCT 10, CIRM Luminy, September 2005
• Poster: Quantum AG Codes over Non-Binary Fields, Summer School on Quantum Information, Waterloo, June 2004

Teaching