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Mr Philipp Wacker

Contact

Email: philipp.wacker@canterbury.ac.nz

Direct Dial: +64 3 3692359

Office: Jack Erskine 613

Languages: English, German

Strongly interested in good communication of math&stats, and in how we can improve learning and scientific collaboration. He/him.
About
Research / Creative works
Projects
Methods & Equipment

Fields of Research

  • Uncertainty Quantification
  • Particle-based methods for sampling, optimization, and filtering
  • Nested Sampling
  • Ensemble Kalman methods
  • Well-posedness of Bayesian Inversion for infinite-dimensional problems
  • Data Assimilation
  • Physical, geophysical, and biological applications
  • Gradient-free optimization
  • Stochastic/Partial/Ordinary Differential Equations

Researcher Summary

If you are a student interested in finding a project (Summer project, a thesis project, or a PhD project), or if you are a researcher interested in scientific collaboration, see my research webpage (link at the very end of this page). Feel free to write me an email or drop by my office if you'd like to discuss options!

I am interested in most mathematical aspects involving "getting information about hidden parameters via indirect and noisy observation". Different communities have different names for that, some of which are "(Nonparametric) Statistics", "Inverse Problems", "Bayesian statistics", "Inference", "Regression", "Data Assimilation", "(semi-)Supervised Learning".

These aspects include
• the question "can this work at all?" (i.e. well-posedness of the inversion process),
• Computational issues, algorithmic advances, and efficient implementation of inversion, which is often related to
• Useful mathematical/conceptual approximations (linearity/Gaussianity assumptions, e.g. within the Ensemble Kalman methodology; or the Laplace approximation as a surrogate measure for use in computational models) which make the problem computationally more feasible and raises the question of "how rough is this approximation?", which is a key question of
• Error analysis, convergence behaviour and stability of inversion schemes; as well as
• difficult mathematical questions related to probability theory, functional analysis (in particular for Banach-space-valued inverse problems)

Subject Area: Disciplines

  • Mathematics: Applied Mathematics
  • Statistics: Applied Statistics; Statistics

Resources

  • Reseach webpage and Student Supervision

Research/Scholarly/Creative Works

  • Bungert L. and Wacker P. (2023) Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion. SIAM-ASA Journal on Uncertainty Quantification 11(1): 320-357. http://dx.doi.org/10.1137/21M1429461. (Journal Articles)
  • Klebanov I. and Wacker P. (2023) Maximum a posteriori estimators in ℓ p are well-defined for diagonal Gaussian priors. Inverse Problems 39(6) http://dx.doi.org/10.1088/1361-6420/acce60. (Journal Articles)
  • Schillings C., Totzeck C. and Wacker P. (2023) Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling. Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling 11(3): 757-787. http://dx.doi.org/10.1137/22M1533281. (Journal Articles)
  • Ashton G., Bernstein N., Buchner J., Chen X., Csányi G., Fowlie A., Feroz F., Griffiths M., Handley W. and Habeck M. (2022) Nested sampling for physical scientists. Nature Reviews Methods Primers 2(1) http://dx.doi.org/10.1038/s43586-022-00121-x. (Journal Articles)
  • Blömker D., Schillings C., Wacker P. and Weissmann S. (2022) CONTINUOUS TIME LIMIT OF THE STOCHASTIC ENSEMBLE KALMAN INVERSION: STRONG CONVERGENCE ANALYSIS. SIAM Journal on Numerical Analysis 60(6): 3181-3215. http://dx.doi.org/10.1137/21M1437561. (Journal Articles)
  • Schillings C., Sprungk B. and Wacker P. (2020) On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems. Numerische Mathematik 145(4): 915-971. http://dx.doi.org/10.1007/s00211-020-01131-1. (Journal Articles)
  • Wacker P. and Knabner P. (2020) Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems. Methodology and Computing in Applied Probability 22(3): 853-879. http://dx.doi.org/10.1007/s11009-019-09736-2. (Journal Articles)
  • Blömker D., Schillings C., Wacker P. and Weissmann S. (2019) Well posedness and convergence analysis of the ensemble Kalman inversion. Inverse Problems 35(8) http://dx.doi.org/10.1088/1361-6420/ab149c. (Journal Articles)
  • Blömker D., Schillings C. and Wacker P. (2018) A strongly convergent numerical scheme from ensemble Kalman inversion. SIAM Journal on Numerical Analysis 56(4): 2537-2562. http://dx.doi.org/10.1137/17M1132367. (Journal Articles)
  • Bianchi LA., Blömker D. and Wacker P. (2017) Pattern size in Gaussian fields from spinodal decomposition. SIAM Journal on Applied Mathematics 77(4): 1292-1319. http://dx.doi.org/10.1137/15M1052081. (Journal Articles)
  • Blömker D., Wacker P. and Wanner T. (2017) Probabilistic estimates of the maximum norm of random Neumann Fourier series. Communications in Nonlinear Science and Numerical Simulation 47: 348-369. http://dx.doi.org/10.1016/j.cnsns.2016.11.023. (Journal Articles)

Future Research

  • Rare Event estimation
  • Design of experiments
  • Filtering and Inversion of nonlinear/non-Gaussian problems
  • Kernel methods

Key Methodologies

  • Sampling methods
  • Convergence Analysis, Stability, Well-posedness of dynamical systems
  • Numerical Simulation
  • Time-Intensive Debugging
  • Drinking Coffee
  • Stochastic/Partial/Ordinary Differential Equations
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