Roland Potthast
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Roland Potthast has a total of 82 co-authors. Here are the top co-authors by number of shared publications:
Gen Nakamura
4 shared publications- Gen Nakamura
Department of Mathematics Hokkaido University 060-0808 Sapporo Japan
4 shared publications Klaus Erhard
4 shared publications- Peter Beim Graben
School of Psychology and Clinical Language Sciences, University of Reading, Whiteknights, P.O. Box 217, Reading, RG6 6AH, UK,
4 shared publications D. Russell Luke
Department of Mathematical Sciences, University of Delaware, U.S.A.
3 shared publicationsEric Heinemeyer
3 shared publications
Latest Publications
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 17 (4) , 907
Corrigendum to "duality between range and no-response tests and its application for inverse problems"
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 17 (4) , 907
Corrigendum to "duality between range and no-response tests and its application for inverse problems"
- Open Access
Particle Filtering and Gaussian Mixtures -- On a Localized Mixture Coefficients Particle Filter (LMCPF) for global NWP
In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a Localized Mixture Coefficients Particle Filter (LMCPF). Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and $10^6$ model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework.Open AccessParticle Filtering and Gaussian Mixtures -- On a Localized Mixture Coefficients Particle Filter (LMCPF) for global NWP
In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a Localized Mixture Coefficients Particle Filter (LMCPF). Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and $10^6$ model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework. - 12 June 2022
- Published by Springer Nature
- p. 1734-1737
Inverse Problems in Neural Population Models
- 12 June 2022
- Published by Springer Nature
- p. 171-175
Amari Model
- Open Access
- 28 March 2022
- Published by Copernicus GmbH
EnVAR Quality Control and Observation Aggregation for ICON-LAM
The German Weather Service (DWD) operationally runs an LETKF (Localized Ensemble Kalman Filter) assimilation scheme for the regional weather forecasts with the ICON-LAM (ICON Limited Area Mode) Numerical Weather Prediction model. We investigate the potential of using an EnVAR (Ensemble Variational data assimilation) using the kilometre-scale Ensemble Data Assimilation (KENDA) ensemble. Quality Control (QC) and Observation Aggregation (OA) are essential parts of a data assimilation system. The former ensures that the assimilated observations are likely to be "acceptable", in the sense of technical, physical and statistical properties. The latter reduces the amount of data and computations under the aspect of efficiency, and helps handling redundant or correlated observations.We show results of assimilation experiments for KENDA and EnVAR using a similar selection of conventional observations after QC and OA, while using a fully dynamic B matrix and no variational QC. The difference of the results of the two algorithms does not only depend on the partially differing implementation of QC and OA, but also due to partially different implementations of the observation operators or even the supported observation types. Important differences to the operational global EnVAR code are e.g. the choice of suitable observation types and the interpolation specification of the first guess to the locations of the observations.As we use the same code for the EnVAR as in the DWD's global data assimilation scheme, we can potentially assimilate many other observations systems beyond conventional observations. This includes, after some adaptations, a wide range of spaceborne observations. Additionally, it is possible to run a regional EnVAR assimilation and a deterministic forecast with a coarse resolution first guess ensemble. Re-using existing ensembles for the ensemble B matrix might be a computationally efficient way to use a variational algorithm for deterministic forecasts.
- 28 March 2022
- Published by Copernicus GmbH
Open AccessEnVAR Quality Control and Observation Aggregation for ICON-LAM
The German Weather Service (DWD) operationally runs an LETKF (Localized Ensemble Kalman Filter) assimilation scheme for the regional weather forecasts with the ICON-LAM (ICON Limited Area Mode) Numerical Weather Prediction model. We investigate the potential of using an EnVAR (Ensemble Variational data assimilation) using the kilometre-scale Ensemble Data Assimilation (KENDA) ensemble. Quality Control (QC) and Observation Aggregation (OA) are essential parts of a data assimilation system. The former ensures that the assimilated observations are likely to be "acceptable", in the sense of technical, physical and statistical properties. The latter reduces the amount of data and computations under the aspect of efficiency, and helps handling redundant or correlated observations.We show results of assimilation experiments for KENDA and EnVAR using a similar selection of conventional observations after QC and OA, while using a fully dynamic B matrix and no variational QC. The difference of the results of the two algorithms does not only depend on the partially differing implementation of QC and OA, but also due to partially different implementations of the observation operators or even the supported observation types. Important differences to the operational global EnVAR code are e.g. the choice of suitable observation types and the interpolation specification of the first guess to the locations of the observations.As we use the same code for the EnVAR as in the DWD's global data assimilation scheme, we can potentially assimilate many other observations systems beyond conventional observations. This includes, after some adaptations, a wide range of spaceborne observations. Additionally, it is possible to run a regional EnVAR assimilation and a deterministic forecast with a coarse resolution first guess ensemble. Re-using existing ensembles for the ensemble B matrix might be a computationally efficient way to use a variational algorithm for deterministic forecasts.
- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 15 (2) , 367-386
Duality between range and no-response tests and its application for inverse problems
In this paper we will show the duality between the range test (RT) and no-response test (NRT) for the inverse boundary value problem for the Laplace equation in $ \Omega\setminus\overline D $ with an unknown obstacle $ D\Subset\Omega $ whose boundary $ \partial D $ is visible from the boundary $ \partial\Omega $ of $ \Omega $ and a measurement is given as a set of Cauchy data on $ \partial\Omega $. Here the Cauchy data is given by a unique solution $ u $ of the boundary value problem for the Laplace equation in $ \Omega\setminus\overline D $ with homogeneous and inhomogeneous Dirichlet boundary condition on $ \partial D $ and $ \partial\Omega $, respectively. These testing methods are domain sampling methods to estimate the location of the obstacle using test domains and the associated indicator functions. Also both of these testing methods can test the analytic extension of $ u $ to the exterior of a test domain. Since these methods are defined via some operators which are dual to each other, we could expect that there is a duality between the two methods. We will give this duality in terms of the equivalence of the pre-indicator functions associated to their indicator functions. As an application of the duality, the reconstruction of $ D $ using the RT gives the reconstruction of $ D $ using the NRT and vice versa. We will also give each of these reconstructions without using the duality if the Dirichlet data of the Cauchy data on $ \partial\Omega $ is not identically zero and the solution to the associated forward problem does not have any analytic extension across $ \partial D $. Moreover, we will show that these methods can still give the reconstruction of $ D $ if we a priori knows that $ D $ is a convex polygon and it satisfies one of the following two properties: all of its corner angles are irrational and its diameter is less than its distance to $ \partial\Omega $.- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 15 (2) , 367-386
Duality between range and no-response tests and its application for inverse problems
In this paper we will show the duality between the range test (RT) and no-response test (NRT) for the inverse boundary value problem for the Laplace equation in $ \Omega\setminus\overline D $ with an unknown obstacle $ D\Subset\Omega $ whose boundary $ \partial D $ is visible from the boundary $ \partial\Omega $ of $ \Omega $ and a measurement is given as a set of Cauchy data on $ \partial\Omega $. Here the Cauchy data is given by a unique solution $ u $ of the boundary value problem for the Laplace equation in $ \Omega\setminus\overline D $ with homogeneous and inhomogeneous Dirichlet boundary condition on $ \partial D $ and $ \partial\Omega $, respectively. These testing methods are domain sampling methods to estimate the location of the obstacle using test domains and the associated indicator functions. Also both of these testing methods can test the analytic extension of $ u $ to the exterior of a test domain. Since these methods are defined via some operators which are dual to each other, we could expect that there is a duality between the two methods. We will give this duality in terms of the equivalence of the pre-indicator functions associated to their indicator functions. As an application of the duality, the reconstruction of $ D $ using the RT gives the reconstruction of $ D $ using the NRT and vice versa. We will also give each of these reconstructions without using the duality if the Dirichlet data of the Cauchy data on $ \partial\Omega $ is not identically zero and the solution to the associated forward problem does not have any analytic extension across $ \partial D $. Moreover, we will show that these methods can still give the reconstruction of $ D $ if we a priori knows that $ D $ is a convex polygon and it satisfies one of the following two properties: all of its corner angles are irrational and its diameter is less than its distance to $ \partial\Omega $.- Open Access
Duality between range and no-response tests and its application for inverse problems
In this paper we will show the duality between the range test (RT) and no-response test (NRT) for the inverse boundary value problem for the Laplace equation in $\Omega\setminus\overline D$ with an obstacle $D\Subset\Omega$ whose boundary $\partial D$ is visible from the boundary $\partial\Omega$ of $\Omega$ and a measurement is given as a set of Cauchy data on $\partial\Omega$. Here the Cauchy data is given by a unique solution $u$ of the boundary value problem for the Laplace equation in $\Omega\setminus\overline D$ with homogeneous and inhomogeneous Dirichlet boundary condition on $\partial D$ and $\partial\Omega$, respectively. These testing methods are domain sampling method to estimate the location of the obstacle using test domains and the associated indicator functions. Also both of these testing methods can test the analytic extension of $u$ to the exterior of a test domain. Since these methods are defined via some operators which are dual to each other, we could expect that there is a duality between the two methods. We will give this duality in terms of the equivalence of the pre-indicator functions associated to their indicator functions. As an application of the duality, the reconstruction of $D$ using the RT gives the reconstruction of $D$ using the NRT and vice versa. We will also give each of these reconstructions without using the duality if the Dirichlet data of the Cauchy data on $\partial\Omega$ is not identically zero and the solution to the associated forward problem does not have any analytic extension across $\partial D$. Moreover, we will show that these methods can still give the reconstruction of $D$ if $D$ is a convex polygon and it satisfies one of the following two properties: all of its corner angles are irrational and its diameter is less than its distance to $\partial\Omega$.Open AccessDuality between range and no-response tests and its application for inverse problems
In this paper we will show the duality between the range test (RT) and no-response test (NRT) for the inverse boundary value problem for the Laplace equation in $\Omega\setminus\overline D$ with an obstacle $D\Subset\Omega$ whose boundary $\partial D$ is visible from the boundary $\partial\Omega$ of $\Omega$ and a measurement is given as a set of Cauchy data on $\partial\Omega$. Here the Cauchy data is given by a unique solution $u$ of the boundary value problem for the Laplace equation in $\Omega\setminus\overline D$ with homogeneous and inhomogeneous Dirichlet boundary condition on $\partial D$ and $\partial\Omega$, respectively. These testing methods are domain sampling method to estimate the location of the obstacle using test domains and the associated indicator functions. Also both of these testing methods can test the analytic extension of $u$ to the exterior of a test domain. Since these methods are defined via some operators which are dual to each other, we could expect that there is a duality between the two methods. We will give this duality in terms of the equivalence of the pre-indicator functions associated to their indicator functions. As an application of the duality, the reconstruction of $D$ using the RT gives the reconstruction of $D$ using the NRT and vice versa. We will also give each of these reconstructions without using the duality if the Dirichlet data of the Cauchy data on $\partial\Omega$ is not identically zero and the solution to the associated forward problem does not have any analytic extension across $\partial D$. Moreover, we will show that these methods can still give the reconstruction of $D$ if $D$ is a convex polygon and it satisfies one of the following two properties: all of its corner angles are irrational and its diameter is less than its distance to $\partial\Omega$. - 1 July 2018
- Published by Elsevier in Journal of Computational and Applied Mathematics
- Vol. 336, 338-352
On sequential multiscale inversion and data assimilation
- 1 July 2018
- Published by Elsevier in Journal of Computational and Applied Mathematics
- Vol. 336, 338-352
On sequential multiscale inversion and data assimilation
- Open Access
- 5 February 2018
- Published by Springer Nature in The Journal of Mathematical Neuroscience
- Vol. 8 (1) , 3
Kernel Reconstruction for Delayed Neural Field Equations
Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.
- 5 February 2018
- Published by Springer Nature in The Journal of Mathematical Neuroscience
- Vol. 8 (1) , 3
Open AccessKernel Reconstruction for Delayed Neural Field Equations
Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.