Georg Gottwald

Preprints

• P. Mandal and G.A. Gottwald
  UNO: Unlearning via orthogonalization in generative models
• G.A. Gottwald, S. Liu, Y. Marzouk, S. Reich and X.T. Tong
  Localized diffusion models for high dimensional distributions generation

Selected Review Articles

• G.A. Gottwald, D. Crommelin and C. Franzke
  Stochastic climate theory
  In Nonlinear and Stochastic Climate Dynamics, Cambridge University Press (C. Franzke and T. O'Kane, eds.) (2017) DOI
• G.A. Gottwald and I. Melbourne
  The 0-1 test for chaos: A review
  In Chaos Detection and Predictability, Springer Lecture Notes in Physics 915 (C. Skokos, G.A. Gottwald and J. Laskar, eds.) (2016) DOI

Peer-Reviewed Journal Articles

• G.A. Gottwald, E. Tziperman and A. Fedorov
  An improved noise model for representing westerly wind burst in the recharge oscillator model of ENSO Nonlinear Processes in Geophysics 33 (2026) 373-383. DOI
• O. Omel'chenko and G.A. Gottwald
  Mean-field approach to finite-size fluctuations in the Kuramoto-Sakaguchi model Physical Review Letters 136 (2026) 247201. DOI
• H. Irvine and G.A. Gottwald
  Finite-size induced random switching of chimeras in a deterministic two-population Kuramoto-Sakaguchi model Proc. Roy. Soc. A 482 (2026) 20250897. DOI
• G.A. Gottwald and S. Reich
  Localized Schrödinger bridge sampler Journal of Computational Physics 548 (2026) 114583. DOI
• P. Mandal and G.A. Gottwald
  On the choice of the non-trainable internal weights in random feature maps for forecasting chaotic dynamical systems Foundations of Data Science 8 (2026) 168-199. DOI

• J. Lohmann and G.A. Gottwald
  Choosing observables that capture critical slowing down before tipping points: a Fokker-Planck operator approach Physical Review E 112 (6) (2025) 064204. DOI
• Y. Xu, G.A. Gottwald and Z. Kuncic
  Learning chaotic dynamics with neuromorphic network dynamics APL Machine Learning 3 (4) (2025) 046104. DOI
• P. Mandal and G.A. Gottwald
  Learning dynamical systems with hit-and-run random feature maps Nature Communications 16 (2025) 5961. DOI
• Y. Xu, G.A. Gottwald and Z. Kuncic
  Dynamic reservoir computing with physical neuromorphic networks IEEE International Joint Conference on Neural Networks (IJCNN), Rome, Italy, (2025) 1-8. DOI
• L. Smith and G.A. Gottwald
  Data assimilation for networks of coupled oscillators: Inferring unknown model parameters from partial observations Proc. Roy. Soc. A 481 (2025) 20240813. DOI
• P. Cahill and G.A. Gottwald
  A modified Hegselmann-Krause model for interacting voters and political parties Physica A 665 (2025) 130490. DOI
• G.A. Gottwald, F. Li, Y. Marzouk and S. Reich
  Stable generative modelling using Schrödinger bridges Philosophical Transactions of the Royal Society A 383 (2025) 20240332. DOI

• W. Yue and G.A. Gottwald
  A stochastic approximation for the finite-size Kuramoto-Sakaguchi model Physica D 468 (2024) 134292. DOI
• G.A. Gottwald and I. Melbourne
  Time-reversibility and nonvanishing Lévy area Nonlinearity 37(7) (2024) 075018. DOI
• K. Riechers, N. Boers and G.A. Gottwald
  Glacial abrupt climate change as a multi-scale phenomenon resulting from monostable excitable dynamics Journal of Climate 37(8) (2024) 2741-2763. DOI
• M. Engel and G.A. Gottwald
  Canards in modified equations for Euler discretizations AMS Contemporary Mathematics 806 (2024) 15-28. DOI

• C. Jiao and G.A. Gottwald
  Lévy flights as an emergent phenomenon in a spatially extended system Proc. Roy. Soc. A 479 (2023) 20230349. DOI
• J. Fialkowski, S. Yanchuk, I. Sokolov, E. Schöll, G.A. Gottwald and R. Berner
  Heterogeneous nucleation in finite size adaptive dynamical networks Phys. Rev. Lett. 130 (2023) 067402. DOI
• A. Sandoz, V. Ducret, G.A. Gottwald, G. Vilmart and K. Perron
  SINDy for delay-differential equations: application to model bacterial zinc response Proc. Roy. Soc. A 479 (2023) 20220556. DOI A figure from this paper was chosen as the journal cover image.

• N. James, M. Menzies and G.A. Gottwald
  On financial market correlation structures and diversification benefits across and within equity sectors Physica A 604 (2022) 127682. DOI

• G.A. Gottwald and S. Reich
  Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations Chaos 31 (2021) 101103. DOI This paper was selected as Featured and as a Scilight
• M. Cartwright and G.A. Gottwald
  A collective coordinate framework to study solitary waves in stochastically perturbed Korteweg-de Vries equations Phys. Rev. E 104 (2021) 024201. DOI
• L. Smith and G.A. Gottwald
  Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks Chaos 31 (2021) 073116. DOI
• G.A. Gottwald and S. Reich
  Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation Physica D 423 (2021) 132911. DOI
• G.A. Gottwald and I. Melbourne
  Simulation of non-Lipschitz stochastic differential equations driven by α-stable noise: a method based on deterministic homogenisation SIAM MMS 19 (2021) 665-687. DOI
• G.A. Gottwald
  A model for Dansgaard-Oeschger events and millennial-scale abrupt climate change without external forcing Climate Dynamics 56 (2021) 227-243. DOI

• L. Smith and G.A. Gottwald
  Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit Chaos 30 (2020) 093107. DOI
• B. Giggins and G.A. Gottwald
  Stochastically perturbed bred vectors in single-scale systems Q.J.R. Meteorolog. Soc. 146(733) (2020) 4038-4054. DOI
• W. Yue, L. Smith and G.A. Gottwald
  Model reduction for the Kuramoto-Sakaguchi model: The importance of non-entrained rogue oscillators Phys. Rev. E 101 (2020) 062213. DOI
• G.A. Gottwald and F. Gugole
  Detecting regime transitions using dynamic mode decomposition J. Stat. Phys. 179 (2020) 1028-1045. DOI

• C. Wormell and G.A. Gottwald
  Linear response for macroscopic observables in high-dimensional systems Chaos 29 (2019) 113127. This paper was chosen as an Editor's pick. DOI
• I. Wohltmann, R. Lehmann, G.A. Gottwald, K. Peters, A. Protat, V. Louf, C. Williams, W. Feng and M. Rex
  A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts Geoscientific Model Development 12 (2019) 4387-4407. DOI
• J. Wouters and G.A. Gottwald
  Stochastic model reduction for slow-fast systems with moderate time-scale separation SIAM MMS 17(4) (2019) 1172-1188. DOI
• L. Smith and G.A. Gottwald
  Chaos in networks of coupled oscillators with multimodal frequency distributions Chaos 29 (2019) 093127. DOI
• M. Cartwright and G.A. Gottwald
  A collective coordinate framework to study the dynamics of travelling waves in stochastic partial differential equations Physica D 397 (2019) 54-64. DOI
• J. Wouters and G.A. Gottwald
  Edgeworth expansions for slow-fast systems with finite time scale separation Proc. Roy. Soc. A 475 (2019) 20180358. DOI
• B. Giggins and G.A. Gottwald
  Stochastically perturbed bred vectors in multi-scale systems Q.J.R. Meteorolog. Soc. 145(719) (2019) 642-658. DOI

• G.A. Gottwald and D.E. Pelinovsky
  On the impossibility of solitary Rossby waves in meridionally unbounded domains Physics of Fluids 30 (2018) 116601. DOI
• S. Balasuriya and G.A. Gottwald
  On estimating stochastic stable and unstable sets and their role as transport barriers in stochastic flows Phys. Rev. E 98 (2018) 013106. DOI
• E.J. Hancock and G.A. Gottwald
  Model reduction for Kuramoto models with complex topologies Phys. Rev. E 98 (2018) 012307. DOI
• C. Wormell and G.A. Gottwald
  On the validity of linear response theory in high-dimensional deterministic dynamical systems J. Stat. Phys. 172 (2018) 1479-1498. DOI
• J. Frank and G.A. Gottwald
  A note on statistical consistency of numerical integrators for multi-scale dynamics SIAM MMS 16(2) (2018) 1017-1033. DOI

• G.A. Gottwald
  Finite-size effects in a stochastic Kuramoto model Chaos 27 (2017) 101103. DOI
• C.J. Cotter, G.A. Gottwald and D.D. Holm
  Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics Proc. Roy. Soc. A 473 (2017) 20170388. DOI
• G.A. Gottwald, H. Mohamad and M. Oliver
  Optimal balance via adiabatic invariance of approximate slow manifolds SIAM MMS 15(4) (2017) 1404-1422. DOI
• D. Dritschel, G.A. Gottwald and M. Oliver
  Comparison of variational balance models for the rotating shallow water equations Journal of Fluid Mechanics 822 (2017) 689-716. DOI

• G.A. Gottwald and I. Melbourne
  On the detection of superdiffusive behaviour in time series J. Stat. Mech. 2016 (12) (2016) 123205. DOI
• G.A. Gottwald and I. Melbourne
  Central limit theorems and suppression of anomalous diffusion for systems with symmetry Nonlinearity 29 (2016) 2941-2960. DOI
• G.A. Gottwald, J.P. Wormell and J. Wouters
  On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series Physica D 331 (2016) 89-101. DOI
• G. Froyland, G.A. Gottwald and A. Hammerlindl
  A trajectory-free framework for analysing multiscale systems Physica D 328-329 (2016) 34-43. DOI
• G.A. Gottwald and I. Melbourne
  Broadband nature of power spectra for intermittent maps with summable and nonsummable decay of correlations Journal of Physics A 49 (2016) 174003. This paper was chosen as a 2016 Highlight article. DOI
• G.A. Gottwald, K. Peters and L. Davies
  A data-driven method for the stochastic parametrisation of subgrid-scale tropical convective area fraction
  Q.J.R. Meteorolog. Soc. 142 (2016) 349-359. DOI

• G.A. Gottwald
  Model reduction for networks of coupled oscillators
  Chaos 25 (2015) 053111. DOI
• J. Maclean and G.A. Gottwald
  On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations
  Journal of Computational and Applied Mathematics 288 (2015) 44-69. DOI

• G. Froyland, G.A. Gottwald and A. Hammerlindl
  A computational method to extract macroscopic variables and their dynamics in multi-scale systems
  SIAM Journal on Applied Dynamical Systems 13(4) (2014) 1816-1846. DOI
• G.A. Gottwald and M. Oliver
  Slow dynamics via degenerate variational asymptotics
  Proc. Roy. Soc. A 470 (2014) 20140460. DOI
• G.A. Gottwald and I. Melbourne
  A test for a conjecture on the nature of attractors for smooth dynamical systems
  Chaos 24 (2014) 024403. DOI
• G.A. Gottwald
  Controlling balance in an Ensemble Kalman filter
  Nonlin. Processes Geophys. 21 (2014) 417-426. DOI
• J. Maclean and G.A. Gottwald
  On convergence of the projective integration method for stiff ordinary differential equations
  Comm. Math. Sci. 12(2) (2014) 235-255. DOI

• G.A. Gottwald and A.J. Majda
  A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks
  Nonlin. Processes Geophys. 20 (2013) 705-712. DOI
• G.A. Gottwald and I. Melbourne
  Homogenization for deterministic maps and multiplicative noise
  Proc. Roy. Soc. A 469 (2013) 20130201. DOI
  corrected version, April 2015
• G.A. Gottwald and I. Melbourne
  A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
  Proc. Natl. Acad. Sci. USA
• G.A. Gottwald and J. Harlim
  The role of additive and multiplicative noise in filtering complex dynamical systems
  (with Appendix)
  Proc. Roy. Soc. A 469 (2013) 20130096. DOI
• J. Frank and G.A. Gottwald
  Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere
  Physica D 254 (2013) 45-65. DOI
• L. Mitchell and G.A. Gottwald
  Controlling model error of underdamped forecast models in sparse observational networks using a variance limiting Kalman filter
  Q.J.R. Meteorolog. Soc. 139 (2013) 212-225. DOI

• L. Mitchell and G.A. Gottwald
  On finite size Lyapunov exponents in multiscale systems
  Chaos 22 (2012) 023115. DOI
• L. Mitchell and G.A. Gottwald
  Data assimilation in slow-fast systems using homogenized climate models
  J. Atmos. Sci. 69 (2012) 1359-1377. DOI

• J. Frank and G.A. Gottwald
  The Langevin equation limit of the Nosé-Hoover-Langevin thermostat
  J. Stat. Phys. 143 (2011) 715-724. DOI
• D. Kelly and G.A. Gottwald
  On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators
  Chaos 21 (2011) 025110. DOI
• G.A. 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 (2011) 2650-2667. DOI

• S. Hermann and G.A. Gottwald
  The large core limit of spiral waves in excitable media: A numerical approach
  SIAM Journal on Applied Dynamical Systems 9 (2010) 536-567. DOI
• S. Balasuriya and G.A. Gottwald
  Wavespeed in reaction-diffusion systems, with applications to chemotaxis and population pressure
  J. Math. Biolog. 61 (2010) 377-399. DOI

• D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
  Late time evolution of unforced inviscid two-dimensional turbulence
  Journal of Fluid Mechanics 640 (2009) 217-235. DOI
• K. Bergemann, G.A. Gottwald and S. Reich
  Ensemble propagation and continuous matrix factorization algorithms
  Q.J.R. Meteorolog. Soc. 135 (2009) 1560-1572. DOI
• G.A. Gottwald and I. Melbourne
  On the validity of the 0-1 test for chaos
  Nonlinearity 22 (2009) 1367-1382. DOI
• G.A. Gottwald and M. Oliver
  Boltzmann's dilemma - an introduction to statistical mechanics via the Kac ring
  SIAM Review 51 (2009) 613-635. DOI
• S. Menon and G.A. Gottwald
  On bifurcations in a chaotically stirred excitable medium
  Physica D 238 (2009) 461-475. DOI
• G.A. Gottwald and I. Melbourne
  On the implementation of the 0-1 test for chaos
  SIAM Journal on Applied Dynamical Systems 8 (2009) 129-145. DOI

• D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
  Unifying scaling theory for vortex dynamics in two-dimensional turbulence
  Phys. Rev. Lett. 101 (2008) 094501. This paper was chosen as an Editor's Suggestion. DOI
• G.A. Gottwald
  Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
  Chaos 18 (2008) 013129. DOI
• G.A. Gottwald and I. Melbourne
  Comment on "Reliability of the 0-1 test for chaos"
  Phys. Rev. E 77 (2008) 028201. DOI
• G.A. Gottwald and I. Melbourne
  Power spectra for deterministic chaotic dynamical systems
  Nonlinearity 21 (2008) 179-189. This paper was chosen as a 2008 High-Profile article. DOI

• G.A. Gottwald
  Dispersive regularizations and numerical discretizations for the inviscid Burgers equation
  J. Phys. A 40 (2007) 14745-14758. DOI
• S. Menon and G.A. Gottwald
  Bifurcations of flame filaments in chaotically mixed combustion reactions
  Phys. Rev. E 75 (2007) 016209. DOI
• S. Balasuriya, G.A. Gottwald, J. Hornibrook and S. Lafortune
  High Lewis number combustion wavefronts: A perturbative Melnikov analysis
  SIAM J. Applied Math. 67 (2007) 464-486. DOI
• G.A. Gottwald, M. Oliver and N. Tecu
  Long-time accuracy for approximate slow manifolds in a finite dimensional model of balance
  Journal of Nonlinear Science 17 (2007) 383-307. DOI
• I. Falconer, G.A. Gottwald, I. Melbourne and K. Wormnes
  Application of the 0-1 test for chaos to experimental data
  SIAM Journal on Applied Dynamical Systems 6 (2007) 395-402. DOI

• G.A. Gottwald and L. Kramer
  A normalform for excitable media
  Chaos 16 (2006) 013122. DOI
• S. Cox and G.A. Gottwald
  A bistable reaction-diffusion system in a stretching flow
  Physica D 216 (2006) 307-318. DOI
• R.A. Thuraisingham and G.A. Gottwald
  On multiscale entropy analysis for physiological data
  Physica A 366 (2006) 323-332. DOI

• S. Menon and G.A. Gottwald
  Bifurcations in reaction-diffusion systems in chaotic flows
  Phys. Rev. E 71 (2005) 066201. DOI
• G.A. Gottwald and I. Melbourne
  Testing for chaos in deterministic systems with noise
  Physica D 212 (2005) 100-110. DOI
• G. Derks and G.A. Gottwald
  A robust numerical method to study oscillatory instability of gap solitary waves
  SIAM Journal on Applied Dynamical Systems 4 (2005) 140-158. DOI

• H.R. Dullin, G.A. Gottwald and D.D. Holm
  On asymptotically equivalent shallow water wave equations
  Physica D 190 (2004) 1-14. DOI
• G.A. Gottwald and L. Kramer
  Propagation failure in one- and two-dimensional excitable media
  Chaos 14 (2004) 855-863. DOI
• G.A. Gottwald and I. Melbourne
  A new test for chaos in deterministic systems
  Proc. Roy. Soc. Lond. A 460 (2004) 603-611. DOI

• H.R. Dullin, G.A. Gottwald and D.D. Holm
  Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves
  Fluid Dynamics Research 33 (2003) 73-95. DOI

• J. Frank, G.A. Gottwald and S. Reich
  A Hamiltonian particle-mesh method for the rotating shallow-water equations
  Meshless Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering ( M. Griebel and M.A. Schweitzer, eds.), Springer, 26 (2002) 131-142.
• R.H.J. Grimshaw, B. Malomed and G.A. Gottwald
  Singular and regular gap solitons between three dispersion curves
  Phys. Rev. E 65 (2002) 066606. DOI
• G.A. Gottwald and M. Nicol
  On the nature of Benford's Law
  Physica A 303 (2002) 387-396. DOI
• T. Bridges, G. Derks, G.A. Gottwald
  Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
  Physica D 172 (2002) 190-216. DOI

• H.R. Dullin, G.A. Gottwald and D.D. Holm
  An integrable shallow water system with linear and nonlinear dispersion
  Phys. Rev. Lett. 87 (2001) 194501. DOI
• G.A. Gottwald, A. Pumir and V. Krinsky
  Spiral wave drift induced by stimulating wave trains
  Chaos 11 (2001) 487-494. DOI

• G.A. Gottwald, L. Kramer, V. Krinsky, A. Pumir and V. Barelko
  Persistence of zero velocity fronts in reaction diffusion systems
  Chaos 10 (2000) 731-737. DOI

• G.A. Gottwald and R.H.J. Grimshaw
  The effect of topography on the dynamics of interacting solitary waves as an example for atmospheric blocking
  J. Atmos. Sci. 56 (1999) 3663-3678. DOI
• G.A. Gottwald and R.H.J. Grimshaw
  The formation of coherent structures in the context of blocking
  J. Atmos. Sci. 56 (1999) 3640-3662. DOI

• G.A. Gottwald, R.H.J. Grimshaw and B. Malomed
  Stable two-dimensional parametric solitons in hydrodynamic models
  Phys. Lett. A 248 (1998) 208-218. DOI

• G.A. Gottwald, R.H.J. Grimshaw and B. Malomed
  Parametric envelope solitons in coupled Korteweg-de Vries equations
  Phys. Lett. A 227 (1997) 47-54. DOI

Conference Proceedings and Other Publications

• G.A. Gottwald
  Introduction to Focus Issue: Linear response theory: Potentials and limits
  Chaos 30 (2020) 020401. DOI
• G.A. Gottwald and C. Skokos
  Preface to the Focus Issue: Chaos Detection Methods and Predictability
  Chaos 24 (2014) 024201. DOI
• G.A. Gottwald, A. Majda, L. Mitchell and S. Reich
  Constraining overestimation of error covariances in ensemble Kalman filters
  In: Oberwolfach Reports, Volume 9, Issue 4, (2012). DOI
• G.A. Gottwald
  On recent trends in climate dynamics
  Gazette of the Australian Mathematical Society 37 (5) (2010) 319-326.
• D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
  Vortex self-similarity and the evolution of unforced inviscid two-dimensional turbulence
  Advances in Turbulence XII, Springer Proceedings in Physics 132 (2009) 461-464. DOI
• G.A. Gottwald and L. Kramer
  On a normalform for excitable media
  In: Oberwolfach Reports, Volume 2, Issue 3, (2005) 1941-1942. DOI
• R.H.J. Grimshaw, B. Malomed and G.A. Gottwald
  Cuspons and peakons vis-a-vis regular solitons and collapse in a three-wave system
  In: Proceedings of the AMS-IMS-SIAM Conference "The Legacy of Inverse Scattering Theory in Nonlinear Wave Propagation" (J. Bona, R. Choudhury and D. Kaup, eds.). CONM (Contemporary Math) AMS series (2002). DOI
• R.H.J. Grimshaw and G.A. Gottwald
  Models for instability in geophysical flows
  In: Proceedings of IUTAM Symposium on Advances in Mathematical Modelling of Atmosphere and Ocean Dynamics, (P.F. Hodnett, ed.), Kluwer Academic Publishers (2001) 153-161.
• G.A. Gottwald, L. Kramer, V. Krinsky, A. Pumir and V. Barelko
  Co-existence of stable states in reaction diffusion systems
  In: Proceedings of "La 3ème Rencontre du Non-linéaire 2000", (Y. Pomeau and R. Ribotta, eds.), Orsay (2001) 154-158.