arXiv subjects

Roland Potthast

Publications and source records attributed to Roland Potthast.

16 recordsLinked to original sources

arXiv2026

AICON: An operational global machine learning weather forecasting model

We introduce AICON, a global machine learning weather prediction (MLWP) model which generates forecasts at 13 km spatial resolution with a 3-hour time step, trained on the high-resolution, non-hydrostatic ICON-DREAM dataset. AICON is in full operational use at Deutscher Wetterdienst since 2nd of March 2026. The model employs a graph neural network (GNN) architecture with an encoder-processor-decoder structure, where node updates are performed using a graph attention mechanism. A key feature of AICON is its use of an icosahedral multi-mesh derived from the native grid of the ICON model, ensuring consistency with the training data. ICON's terrain-following vertical SLEVE coordinate is one of the major distinctions from existing emulators. AICON's training strategy prioritizes small-scale fidelity by avoiding autoregressive multi-step rollout and longer forecast horizons during training, a design choice motivated by the hypothesis that this approach preserves fine-scale features often damped in models optimized for longer-range forecasts. We describe the prognostic and diagnostic variables used for training, the transfer learning protocol employed to accelerate convergence, and the model's performance across a range of evaluation metrics. An extensive evaluation, including routine verification against observation, a tropical cyclone case and spectral analysis reveal the strengths and limitations in the representation of atmospheric variability across scales. Routine verification against observations demonstrates competitive skill relative to the operational ICON model, particularly for near-surface variables in the short to medium forecast range.

physics.ao-ph↗

arXiv2026

WP-MIP: An Artificial Intelligence, Hybrid, and Physically Based Model Intercomparison Project for Weather Prediction

Rapid progress in the field of machine-learning for weather prediction has led to the emergence of algorithms whose forecasting skill can exceed that of traditional physically based models. This development represents an opportunity to improve the quality of forecasting services provided by operational centers, particularly given the speed at which machine-learning based models generate predictions. Despite the clear promise of these systems, questions remain about the ability of the current generation of machine-learning models to generate physically consistent predictions of the full suite of required forecast fields under all conditions. Answering these questions will require careful comparisons between the well-understood physically based models, current state-of-the-art machine-learning models, and the hybrid models that combine elements of these two archetypes. The Weather Prediction Model Intercomparison Project (WP-MIP) is a World Meteorological Organization-supported initiative whose initial goal is to create a centralized database of physically based, machine-learning, and hybrid model forecasts to enable a distributed assessment and evaluation effort. The first instance of WP-MIP focuses on global deterministic predictions using both center-specific and common initializations to facilitate sensitivity studies. Forecasts contributed by institutions across six continents will be used to develop AI-ready verification techniques that highlight the strengths and weaknesses of each class of prediction system, with the goal of establishing best-practice guidance to model developers and national weather centers. The broad engagement of the operational and forecast-evaluation communities in WP-MIP will ensure that the project results are highly relevant to the development and deployment of next-generation weather prediction systems.

physics.ao-ph↗

arXiv2026

Learning Data-driven Surrogate and Correction Models for Satellite Observations in Numerical Weather Prediction

Satellite observations play a critical role in numerical weather prediction where they are assimilated through an observation operator that maps model states to radiances. In the traditional Ensemble Kalman Filter, these observations are used to update the state by weighting their associated errors against model uncertainties to produce an optimal estimate. This process requires radiative transfer simulations for passive, downward-viewing satellite radiometers operating in the visible, infrared, and microwave spectra. Typically, such simulations rely on numerically integrating physical laws via models like RTTOV. In this paper, we introduce two machine learning surrogate observation operators inspired by modern computer-vision architectures: First, a fully data-driven emulator of radiative transfer, and second, a hybrid incremental correction model that learns only the residual relative to RTTOV, thereby retaining established physics while enabling data-driven refinement in complex conditions such as cloud-affected situations. The residual formulation improves radiance accuracy (lower Root Mean Squared Error (RMSE) than the fully data-driven emulator and RTTOV) and adds only moderate computational costs to the assimilation step. Both models combine 3D convolutions for vertical profile encoding with a 2D U-Net operating on latitude-longitude grids, allowing joint learning of vertical structure, spatial correlations, and inter-channel dependencies. We further provide a theoretical justification for deploying the hybrid surrogate as an observation operator in data assimilation.

physics.ao-ph↗

arXiv2024

AI-based data assimilation: Learning the functional of analysis estimation

The integration of observational data into numerical models, known as data assimilation (DA), is fundamental for making Numerical Weather Prediction (NWP) possible, with breathtaking success over the past 60 years (Bauer et al. 2015). Traditional DA methods, such as variational techniques and ensemble Kalman filters, are basic pillars of current NWP by incorporating diverse observational data. However, the emergence of artificial intelligence (AI) presents new opportunities for further improvements. AI-based approaches can emulate the complex computations of traditional NWP models at a reduced computational cost, offering the potential to speed up and improve analyses and forecasts dramatically (e.g. Pathak et al., 2022; Bi et al., 2023; Lam et al., 2023; Bouallegue et al., 2023). AI itself plays a growing role in optimization (e.g. Fan et al., 2024), which offers new possibilities also beyond model emulation. In this paper, we introduce a novel AI-based variational DA approach designed to replace classical methods of DA by leveraging deep learning techniques. Unlike previous hybrid approaches, our method integrates the DA process directly into a neural network, utilizing the variational DA framework. This innovative AI-based system, termed AI-Var, employs a neural network trained to minimize the variational cost function, enabling it to perform DA without relying on pre-existing analysis datasets. We present a proof-of-concept implementation of this approach, demonstrating its feasibility through a series of idealized and real-world test cases. Our results indicate that the AI-Var system can efficiently assimilate observations and produce accurate initial conditions for NWP, highlighting its potential to carry out the DA process in weather forecasting. This advancement paves the way for fully data-driven NWP systems, offering a significant leap forward in computational efficiency.

physics.ao-ph↗

arXiv2023

Noise calibration for the stochastic rotating shallow water model

Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a judicious usage in modelling fluid evolution, one needs to calibrate the amplitude of the noise to data. In this paper we address this requirement for the stochastic rotating shallow water (SRSW) model. This work is a continuation of [LvLCP23], where a data assimilation methodology has been introduced for the SRSW model. The noise used in [LvLCP23] was introduced as an arbitrary random phase shift in the Fourier space. This is not necessarily consistent with the uncertainty induced by a model reduction procedure. In this paper, we introduce a new method of noise calibration of the SRSW model which is compatible with the model reduction technique. The method is generic and can be applied to arbitrary stochastic parametrizations. It is also agnostic as to the source of data (real or synthetic). It is based on a principal component analysis technique to generate the eigenvectors and the eigenvalues of the covariance matrix of the stochastic parametrization. For SRSW model covered in this paper, we calibrate the noise by using the elevation variable of the model, as this is an observable easily obtainable in practical application, and use synthetic data as input for the calibration procedure.

math.DS↗

arXiv2022

Inverse medium scattering problems with Kalman filter techniques

We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative optimization method is often adapted. A natural iterative approach to this problem is to place all available measurements and mappings into one long vector and mapping, respectively, and to iteratively solve the linearized large system equation using the Tikhonov regularization method, which is called the Levenberg-Marquardt scheme. However, this is computationally expensive because we must construct the larger system equations when the number of available measurements increases. In this paper, we propose two reconstruction algorithms based on the Kalman filter. One is the algorithm equivalent to the Levenberg-Marquardt scheme, and the other is inspired by the Extended Kalman Filter. For the algorithm derivation, we iteratively apply the Kalman filter to the linearized equation for our nonlinear equation. Our proposed algorithms sequentially update the state and the weight of the norm for the state space, which avoids the construction of a large system equation and retains the information of past updates. Finally, we provide numerical examples to demonstrate our proposed algorithms.

math.AP↗

arXiv2022

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.

stat.AP↗

arXiv2021

Bayesian Inference for Fluid Dynamics: A Case Study for the Stochastic Rotating Shallow Water Model

In this work, we use a tempering-based adaptive particle filter to infer from a partially observed stochastic rotating shallow water (SRSW) model which has been derived using the Stochastic Advection by Lie Transport (SALT) approach. The methodology we present here validates the applicability of tempering and sample regeneration via a Metropolis-Hastings algorithm to high-dimensional models used in stochastic fluid dynamics. The methodology is first tested on the Lorenz '63 model with both full and partial observations. Then we discuss the efficiency of the particle filter the SALT-SRSW model.

math.NA↗

arXiv2021

Inverse medium scattering problems with Kalman filter techniques I. Linear case

In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which becomes possible to sequentially estimate the inhomogeneous medium. We also show that in the linear inverse problem, the estimation for the Kalman filter is equivalent to that for the Tikhonov regularization. Finally, we give numerical examples to demonstrate our proposed method.

math.AP↗

arXiv2021

Inverse medium scattering problems with Kalman filter techniques II. Nonlinear case

In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while in the second part, we deal with the nonlinear problem. The main idea is to apply the linear Kalman filter to the linearized problem. There are several ways to linearize, which introduce two reconstruction algorithms. Finally, we give numerical examples to demonstrate our proposed method.

math.AP↗

arXiv2021

Regularising linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements

We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary distribution. The measuring process can be repeated, which allows to reduce and estimate the measurement error through averaging. We show convergence against the true solution of the infinite-dimensional problem for a priori and a posteriori regularisation schemes as the number of measurements and the dimension of the discretisation tend to infinity under natural and easily verifiable conditions for the discretisation.

math.NA↗

arXiv2020

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 $Ω\setminus\overline D$ with an obstacle $D\SubsetΩ$ whose boundary $\partial D$ is visible from the boundary $\partialΩ$ of $Ω$ and a measurement is given as a set of Cauchy data on $\partialΩ$. Here the Cauchy data is given by a unique solution $u$ of the boundary value problem for the Laplace equation in $Ω\setminus\overline D$ with homogeneous and inhomogeneous Dirichlet boundary condition on $\partial D$ and $\partialΩ$, 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 $\partialΩ$ 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 $\partialΩ$.

math.AP↗

arXiv2020

Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution

This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinskii veto tells us, that we are not able to solve the equation if we do not know the noise level. But in applications it is ad hoc unrealistic to know the error of a measurement. In practice, the error of a measurement may often be estimated through averaging of multiple measurements. We integrated that in our anlaysis and obtained convergence to the true solution, with the only assumption that the measurements are unbiased, independent and identically distributed according to an unknown distribution.

math.NA↗

arXiv2019

Particle filters for high-dimensional geoscience applications: a review

Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localisation and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state of the art discussion of present efforts of developing particle filters for highly nonlinear geoscience state-estimation problems with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations, and unifications, highlighting hidden connections, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction suggesting that they will become mainstream soon.

stat.AP↗

arXiv2013

Universal neural field computation

Turing machines and Gödel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a Gödel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.

cs.FL↗

arXiv2012

Implementing Turing Machines in Dynamic Field Architectures

Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent Gödel encoding of the symbolic repertoire. The resulting nonlinear dynamical automata (NDA) are piecewise affine-linear maps acting on the unit square that is partitioned into rectangular domains. Iterating a single point, i.e. a microstate, by the dynamics yields a trajectory of, in principle, infinitely many points scattered through phase space. Therefore, the NDAs microstate dynamics does not necessarily terminate in contrast to its counterpart, the symbolic dynamics obtained from the rectangular partition. In order to regain the proper symbolic interpretation, one has to prepare ensembles of randomly distributed microstates with rectangular supports. Only the resulting macrostate evolution corresponds then to the original Turing machine computation. However, the introduction of random initial conditions into a deterministic dynamics is not really satisfactory. As a possible solution for this problem we suggest a change of perspective. Instead of looking at point dynamics in phase space, we consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation, yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. Thus, the symbolically meaningful NDA macrostate dynamics becomes represented by iterated function dynamics in DFT; hence we call the resulting representation dynamic field automata.

cs.FL↗