Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/82020-07-09T18:49:16Z2020-07-09T18:49:16ZRobust risk aggregation with neural networksEckstein, Stephanpop233432Kupper, Michaelpop243845Pohl, Mathias123456789/500842020-07-01T11:25:38Z2020-06-13Robust risk aggregation with neural networks
Eckstein, Stephan; Kupper, Michael; Pohl, Mathias
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.
2020-06-13Eckstein, StephanKupper, MichaelPohl, Mathias510We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real‐world instance.WileyJOURNAL_ARTICLEeng10.1111/mafi.122800960-16271467-9965Mathematical Finance2020-07-01T13:25:38+02:00123456789/39Mathematical Finance ; 2020. - Wiley. - ISSN 0960-1627. - eISSN 1467-9965true2020-07-01T11:25:38ZtrueOptimal EPO dosing in hemodialysis patients using a non-linear model predictive control approachRogg, Sabrinapop210908Fuertinger, Doris H.Volkwein, Stefanpop214121Kappel, FranzKotanko, Peter123456789/41065.22020-06-25T01:02:43Z2019Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach
Rogg, Sabrina; Fuertinger, Doris H.; Volkwein, Stefan; Kappel, Franz; Kotanko, Peter
Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.
2019Rogg, SabrinaFuertinger, Doris H.Volkwein, StefanKappel, FranzKotanko, Peter510Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.SpringerJOURNAL_ARTICLEurn:nbn:de:bsz:352-2-1ghv42fqlclc0eng10.1007/s00285-019-01429-10303-68121432-141622812313796-7Journal of Mathematical Biology2020-06-24T15:11:53+02:00123456789/39Journal of Mathematical Biology ; 79 (2019), 6-7. - S. 2281-2313. - Springer. - ISSN 0303-6812. - eISSN 1432-1416true2020-06-24T13:11:53ZtrueEffects of history and heat models on the stability of thermoelastic Timoshenko systemsJorge Silva, Marcio A.Racke, Reinhardpop03677123456789/499702020-06-24T01:02:33Z2020Effects of history and heat models on the stability of thermoelastic Timoshenko systems
Jorge Silva, Marcio A.; Racke, Reinhard
We investigate different and new thermoelastic Timoshenko systems with or without history, and with Fourier or Cattaneo law for heat conduction, with respect to (non-)exponential stability. Results are obtained that shed a new light on the role of history terms and that of the heat conduction law. Improvements of previous results of earlier work [12] are presented, clarifying open questions, as well as results contrasting [14]. The sensitivity of the Timoshenko system with respect to heat conduction laws and history terms is illustrated.
2020Jorge Silva, Marcio A.Racke, Reinhard510We investigate different and new thermoelastic Timoshenko systems with or without history, and with Fourier or Cattaneo law for heat conduction, with respect to (non-)exponential stability. Results are obtained that shed a new light on the role of history terms and that of the heat conduction law. Improvements of previous results of earlier work [12] are presented, clarifying open questions, as well as results contrasting [14]. The sensitivity of the Timoshenko system with respect to heat conduction laws and history terms is illustrated.WORKINGPAPERurn:nbn:de:bsz:352-2-1tfhswxpw76d78engKonstanzer Schriften in Mathematik3912020-06-23T09:20:51+02:00123456789/392020-06-23T07:20:51ZNon-geometric convergence of the classical alternating Schwarz methodCiaramella, Gabrielepop513180Höfer, Richard123456789/499572020-06-23T01:02:35Z2020Non-geometric convergence of the classical alternating Schwarz method
Ciaramella, Gabriele; Höfer, Richard
2020Ciaramella, GabrieleHöfer, Richard510INPROCEEDINGSurn:nbn:de:bsz:352-2-15ntblpo8erd48eng25th International Domain Decomposition Conference2020-06-22T13:58:30+02:00123456789/3925th International Domain Decomposition ConferenceSt. John's, Newfoundland, Canada2018-06-23DD25 Conference : 25th International Domain Decomposition Conference2018-06-282020-06-22T11:58:30Z