@misc{WiljesTong2020,
  author    = {Wiljes, Jana de and Tong, Xin T.},
  title     = {Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  volume    = {33},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {9},
  publisher = {IOP Publ.},
  address   = {Bristol},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-54041},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-540417},
  pages     = {4752 -- 4782},
  year      = {2020},
  abstract  = {Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.},
  language  = {en}
}
@phdthesis{Maier2021,
  author    = {Maier, Corinna},
  title     = {Bayesian data assimilation and reinforcement learning for model-informed precision dosing in oncology},
  doi       = {10.25932/publishup-51587},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-515870},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 138},
  year      = {2021},
  abstract  = {While patients are known to respond differently to drug therapies, current clinical practice often still follows a standardized dosage regimen for all patients. For drugs with a narrow range of both effective and safe concentrations, this approach may lead to a high incidence of adverse events or subtherapeutic dosing in the presence of high patient variability. Model-informedprecision dosing (MIPD) is a quantitative approach towards dose individualization based on mathematical modeling of dose-response relationships integrating therapeutic drug/biomarker monitoring (TDM) data. MIPD may considerably improve the efficacy and safety of many drug therapies. Current MIPD approaches, however, rely either on pre-calculated dosing tables or on simple point predictions of the therapy outcome. These approaches lack a quantification of uncertainties and the ability to account for effects that are delayed. In addition, the underlying models are not improved while applied to patient data. Therefore, current approaches are not well suited for informed clinical decision-making based on a differentiated understanding of the individually predicted therapy outcome. The objective of this thesis is to develop mathematical approaches for MIPD, which (i) provide efficient fully Bayesian forecasting of the individual therapy outcome including associated uncertainties, (ii) integrate Markov decision processes via reinforcement learning (RL) for a comprehensive decision framework for dose individualization, (iii) allow for continuous learning across patients and hospitals. Cytotoxic anticancer chemotherapy with its major dose-limiting toxicity, neutropenia, serves as a therapeutically relevant application example. For more comprehensive therapy forecasting, we apply Bayesian data assimilation (DA) approaches, integrating patient-specific TDM data into mathematical models of chemotherapy-induced neutropenia that build on prior population analyses. The value of uncertainty quantification is demonstrated as it allows reliable computation of the patient-specific probabilities of relevant clinical quantities, e.g., the neutropenia grade. In view of novel home monitoring devices that increase the amount of TDM data available, the data processing of sequential DA methods proves to be more efficient and facilitates handling of the variability between dosing events. By transferring concepts from DA and RL we develop novel approaches for MIPD. While DA-guided dosing integrates individualized uncertainties into dose selection, RL-guided dosing provides a framework to consider delayed effects of dose selections. The combined DA-RL approach takes into account both aspects simultaneously and thus represents a holistic approach towards MIPD. Additionally, we show that RL can be used to gain insights into important patient characteristics for dose selection. The novel dosing strategies substantially reduce the occurrence of both subtherapeutic and life-threatening neutropenia grades in a simulation study based on a recent clinical study (CEPAC-TDM trial) compared to currently used MIPD approaches. If MIPD is to be implemented in routine clinical practice, a certain model bias with respect to the underlying model is inevitable, as the models are typically based on data from comparably small clinical trials that reflect only to a limited extent the diversity in real-world patient populations. We propose a sequential hierarchical Bayesian inference framework that enables continuous cross-patient learning to learn the underlying model parameters of the target patient population. It is important to note that the approach only requires summary information of the individual patient data to update the model. This separation of the individual inference from population inference enables implementation across different centers of care. The proposed approaches substantially improve current MIPD approaches, taking into account new trends in health care and aspects of practical applicability. They enable progress towards more informed clinical decision-making, ultimately increasing patient benefits beyond the current practice.},
  language  = {en}
}
@phdthesis{Schwetlick2023,
  author    = {Schwetlick, Lisa},
  title     = {Data assimilation for neurocognitive models of eye movement},
  doi       = {10.25932/publishup-59828},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-598280},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 209},
  year      = {2023},
  abstract  = {Visual perception is a complex and dynamic process that plays a crucial role in how we perceive and interact with the world. The eyes move in a sequence of saccades and fixations, actively modulating perception by moving different parts of the visual world into focus. Eye movement behavior can therefore offer rich insights into the underlying cognitive mechanisms and decision processes. Computational models in combination with a rigorous statistical framework are critical for advancing our understanding in this field, facilitating the testing of theory-driven predictions and accounting for observed data. In this thesis, I investigate eye movement behavior through the development of two mechanistic, generative, and theory-driven models. The first model is based on experimental research regarding the distribution of attention, particularly around the time of a saccade, and explains statistical characteristics of scan paths. The second model implements a self-avoiding random walk within a confining potential to represent the microscopic fixational drift, which is present even while the eye is at rest, and investigates the relationship to microsaccades. Both models are implemented in a likelihood-based framework, which supports the use of data assimilation methods to perform Bayesian parameter inference at the level of individual participants, analyses of the marginal posteriors of the interpretable parameters, model comparisons, and posterior predictive checks. The application of these methods enables a thorough investigation of individual variability in the space of parameters. Results show that dynamical modeling and the data assimilation framework are highly suitable for eye movement research and, more generally, for cognitive modeling.},
  language  = {en}
}
@phdthesis{Aseev2020,
  author    = {Aseev, Nikita},
  title     = {Modeling and understanding dynamics of charged particles in the Earth's inner magnetosphere},
  doi       = {10.25932/publishup-47921},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-479211},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xxii, 154},
  year      = {2020},
  abstract  = {The Earth's inner magnetosphere is a very dynamic system, mostly driven by the external solar wind forcing exerted upon the magnetic field of our planet. Disturbances in the solar wind, such as coronal mass ejections and co-rotating interaction regions, cause geomagnetic storms, which lead to prominent changes in charged particle populations of the inner magnetosphere - the plasmasphere, ring current, and radiation belts. Satellites operating in the regions of elevated energetic and relativistic electron fluxes can be damaged by deep dielectric or surface charging during severe space weather events. Predicting the dynamics of the charged particles and mitigating their effects on the infrastructure is of particular importance, due to our increasing reliance on space technologies. The dynamics of particles in the plasmasphere, ring current, and radiation belts are strongly coupled by means of collisions and collisionless interactions with electromagnetic fields induced by the motion of charged particles. Multidimensional numerical models simplify the treatment of transport, acceleration, and loss processes of these particles, and allow us to predict how the near-Earth space environment responds to solar storms. The models inevitably rely on a number of simplifications and assumptions that affect model accuracy and complicate the interpretation of the results. In this dissertation, we quantify the processes that control electron dynamics in the inner magnetosphere, paying particular attention to the uncertainties of the employed numerical codes and tools. We use a set of convenient analytical solutions for advection and diffusion equations to test the accuracy and stability of the four-dimensional Versatile Electron Radiation Belt (VERB-4D) code. We show that numerical schemes implemented in the code converge to the analytical solutions and that the VERB-4D code demonstrates stable behavior independent of the assumed time step. The order of the numerical scheme for the convection equation is demonstrated to affect results of ring current and radiation belt simulations, and it is crucially important to use high-order numerical schemes to decrease numerical errors in the model. Using the thoroughly tested VERB-4D code, we model the dynamics of the ring current electrons during the 17 March 2013 storm. The discrepancies between the model and observations above 4.5 Earth's radii can be explained by uncertainties in the outer boundary conditions. Simulation results indicate that the electrons were transported from the geostationary orbit towards the Earth by the global-scale electric and magnetic fields. We investigate how simulation results depend on the input models and parameters. The model is shown to be particularly sensitive to the global electric field and electron lifetimes below 4.5 Earth's radii. The effects of radial diffusion and subauroral polarization streams are also quantified. We developed a data-assimilative code that blends together a convection model of energetic electron transport and loss and Van Allen Probes satellite data by means of the Kalman filter. We show that the Kalman filter can correct model uncertainties in the convection electric field, electron lifetimes, and boundary conditions. It is also demonstrated how the innovation vector - the difference between observations and model prediction - can be used to identify physical processes missing in the model of energetic electron dynamics. We computed radial profiles of phase space density of ultrarelativistic electrons, using Van Allen Probes measurements. We analyze the shape of the profiles during geomagnetically quiet and disturbed times and show that the formation of new local minimums in the radial profiles coincides with the ground observations of electromagnetic ion-cyclotron (EMIC) waves. This correlation indicates that EMIC waves are responsible for the loss of ultrarelativistic electrons from the heart of the outer radiation belt into the Earth's atmosphere.},
  language  = {en}
}
@misc{AcevedoReichCubasch2015,
  author    = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  volume    = {46},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {892},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43636},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436363},
  pages     = {1909 -- 1920},
  year      = {2015},
  abstract  = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.},
  language  = {en}
}
@phdthesis{CervantesVilla2021,
  author    = {Cervantes Villa, Juan Sebastian},
  title     = {Understanding the dynamics of radiation belt electrons by means of data assimilation},
  doi       = {10.25932/publishup-51982},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-519827},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xxv, 116},
  year      = {2021},
  abstract  = {The Earth's electron radiation belts exhibit a two-zone structure, with the outer belt being highly dynamic due to the constant competition between a number of physical processes, including acceleration, loss, and transport. The flux of electrons in the outer belt can vary over several orders of magnitude, reaching levels that may disrupt satellite operations. Therefore, understanding the mechanisms that drive these variations is of high interest to the scientific community. In particular, the important role played by loss mechanisms in controlling relativistic electron dynamics has become increasingly clear in recent years. It is now widely accepted that radiation belt electrons can be lost either by precipitation into the atmosphere or by transport across the magnetopause, called magnetopause shadowing. Precipitation of electrons occurs due to pitch-angle scattering by resonant interaction with various types of waves, including whistler mode chorus, plasmaspheric hiss, and electromagnetic ion cyclotron waves. In addition, the compression of the magnetopause due to increases in solar wind dynamic pressure can substantially deplete electrons at high L shells where they find themselves in open drift paths, whereas electrons at low L shells can be lost through outward radial diffusion. Nevertheless, the role played by each physical process during electron flux dropouts still remains a fundamental puzzle. Differentiation between these processes and quantification of their relative contributions to the evolution of radiation belt electrons requires high-resolution profiles of phase space density (PSD). However, such profiles of PSD are difficult to obtain due to restrictions of spacecraft observations to a single measurement in space and time, which is also compounded by the inaccuracy of instruments. Data assimilation techniques aim to blend incomplete and inaccurate spaceborne data with physics-based models in an optimal way. In the Earth's radiation belts, it is used to reconstruct the entire radial profile of electron PSD, and it has become an increasingly important tool in validating our current understanding of radiation belt dynamics, identifying new physical processes, and predicting the near-Earth hazardous radiation environment. In this study, sparse measurements from Van Allen Probes A and B and Geostationary Operational Environmental Satellites (GOES) 13 and 15 are assimilated into the three-dimensional Versatile Electron Radiation Belt (VERB-3D) diffusion model, by means of a split-operator Kalman filter over a four-year period from 01 October 2012 to 01 October 2016. In comparison to previous works, the 3D model accounts for more physical processes, namely mixed pitch angle-energy diffusion, scattering by EMIC waves, and magnetopause shadowing. It is shown how data assimilation, by means of the innovation vector (the residual between observations and model forecast), can be used to account for missing physics in the model. This method is used to identify the radial distances from the Earth and the geomagnetic conditions where the model is inconsistent with the measured PSD for different values of the adiabatic invariants mu and K. As a result, the Kalman filter adjusts the predictions in order to match the observations, and this is interpreted as evidence of where and when additional source or loss processes are active. Furthermore, two distinct loss mechanisms responsible for the rapid dropouts of radiation belt electrons are investigated: EMIC wave-induced scattering and magnetopause shadowing. The innovation vector is inspected for values of the invariant mu ranging from 300 to 3000 MeV/G, and a statistical analysis is performed to quantitatively assess the effect of both processes as a function of various geomagnetic indices, solar wind parameters, and radial distance from the Earth. The results of this work are in agreement with previous studies that demonstrated the energy dependence of these two mechanisms. EMIC wave scattering dominates loss at lower L shells and it may amount to between 10\%/hr to 30\%/hr of the maximum value of PSD over all L shells for fixed first and second adiabatic invariants. On the other hand, magnetopause shadowing is found to deplete electrons across all energies, mostly at higher L shells, resulting in loss from 50\%/hr to 70\%/hr of the maximum PSD. Nevertheless, during times of enhanced geomagnetic activity, both processes can operate beyond such location and encompass the entire outer radiation belt. The results of this study are two-fold. Firstly, it demonstrates that the 3D data assimilative code provides a comprehensive picture of the radiation belts and is an important step toward performing reanalysis using observations from current and future missions. Secondly, it achieves a better understanding and provides critical clues of the dominant loss mechanisms responsible for the rapid dropouts of electrons at different locations over the outer radiation belt.},
  language  = {en}
}