1,721,001 research outputs found
Reduced Order Models and Data Assimilation for Hydrological Applications
Full text linkThe present thesis work concerns the study of Monte Carlo (MC)-based data assimilation methods applied to the numerical simulation of complex hydrological models with stochastic parameters. The ensemble Kalman filter (EnKF) and the sequential importance resampling (SIR) are implemented in the CATHY model, a solver that couples the subsurface water flow in porous media with the surface water dynamics. A detailed comparison of the results given by the two filters in a synthetic test case highlights the main benefits and drawbacks associated to these techniques. A modification of the SIR update is suggested to improve the performance of the filter in case of small ensemble sizes and small variances of the measurement errors. With this modification, both filters are able to assimilate pressure head and streamflow measurements and correct model errors, such as biased initial and boundary conditions. SIR technique seems to be better suited for the simulations at hand as they do not make use of the Gaussian approximation inherent the EnKF method. Further research is needed, however, to assess the robustness of the particle filters methods in particular to ensure accuracy of the results even when relatively small ensemble sizes are employed. In the second part of the thesis the focus is shifted to reducing the computational burden associated with the construction of the MC realizations (which constitutes the core of the EnKF and SIR). With this goal, we analyze the computational saving associated to the use of reduced order models (RM) for the generation of the ensemble of solutions. The proper orthogonal decomposition (POD) is applied to the linear equations of the groundwater flow in saturated porous media with a randomly distributed recharge and random heterogeneous hydraulic conductivity. Several test cases are used to assess the errors on the ensemble statistics caused by the RM approximation. Particular attention is given to the efficient computation of the principal components that are needed to project the model equations in the reduced space. The greedy algorithm selects the snapshots in the set of the MC realizations in such a way that the final principal components are parameter independent. An innovative residual-based estimation of the error associated to the RM solution is used to assess the precision of the RM and to stop the iterations of the greedy algorithm. By way of numerical applications in synthetic and real scenarios, we demonstrate that this modified greedy algorithm determines the minimum number of principal components to use in the reduction and, thus, leads to important computational savings
Calibration of Time-Dependent Parameters in Compartmental Epidemiological Models Using Physics-Informed Neural Networks: An Application to the Italian Covid-19 Pandemic
No full textWe propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. PINNs consider both the information from data (typically uncertain) and the governing equations of the system. We develop a reduced-split approach for the implementation of PINNs that:
• splits the training first on the epidemiological data, and then on the residual of the system equations; • reduces the number of functions that are approximated and eliminates any redundant term in the loss. Our results show that this implementation of PINNs outperforms the standard joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%)
A Physics-Informed Neural Network approach for compartmental epidemiological models
Full text linkCompartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic
Real-time projections of cholera outbreaks through data assimilation and rainfall forecasting
Full text linkAlthough treatment for cholera is well-known and cheap, outbreaks in epidemic regions still exact high death tolls mostly due to the unpreparedness of health care infrastructures to face unforeseen emergencies. In this context, mathematical models for the prediction of the evolution of an ongoing outbreak are of paramount importance. Here, we test a real-time forecasting framework that readily integrates new information as soon as available and periodically issues an updated forecast. The spread of cholera is modeled by a spatially-explicit scheme that accounts for the dynamics of susceptible, infected and recovered individuals hosted in different local communities connected through hydrologic and human mobility networks. The framework presents two major innovations for cholera modeling: the use of a data assimilation technique, specifically an ensemble Kalman filter, to update both state variables and parameters based on the observations, and the use of rainfall forecasts to force the model. The exercise of simulating the state of the system and the predictive capabilities of the novel tools, set at the initial phase of the 2010 Haitian cholera outbreak using only information that was available at that time, serves as a benchmark. Our results suggest that the assimilation procedure with the sequential update of the parameters outperforms calibration schemes based on Markov chain Monte Carlo. Moreover, in a forecasting mode the model usefully predicts the spatial incidence of cholera at least one month ahead. The performance decreases for longer time horizons yet allowing sufficient time to plan for deployment of medical supplies and staff, and to evaluate alternative strategies of emergency management
Improving Groundwater Modeling by Coupled HydroGeophysical Data Assimilation
No full textA sequential Bayesian approach for joint assimilation of hydrological and geophysical data in a variably saturated flow model is presented.
The study aims to improve simulation results and system understanding by assimilation of multiple type data using a Monte Carlo approach and avoiding the inversion of the geophysical measurements.
A SIR based particle filter data assimilation is implemented in a 3D variably saturated flow model.
Point measurements are directly assimilated in time while spatial information are blended in the simulation by assimilating Electrical Resistivity Tomography (ERT) measurements. To avoid the inversion of the latter, a forward 3D model of electrical current distribution is implemented as the
measurements model in the data assimilation algorithm. The connection with the hydrological parameters occurs via the Archie's law.
A synthetic test case is used to test the assimilation of pressure data, ERT data and the joint assimilation of pressure and ERT data. Performance of the proposed modelling approach are evaluated in terms of predicton efficiency and parameter estimation. Perspectives and limitations of
coupled hydrogeophysical data assimilation are discussed
A reduced order model-based preconditioner for the efficient solution of transient diffusion equations
No full textThis paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive-definite linear systems arising from the numerical discretization of transient parabolic and self-adjoint partial differential equations. The preconditioners are obtained by nesting appropriate projections of reduced-order models into the classical iteration of the preconditioned conjugate gradient (PCG). The main idea is to employ the reduced-order solver to project the residual associated with the conjugate gradient iterations onto the space spanned by the reduced bases. This approach is particularly appealing for transient systems where the full-model solution has to be computed at each time step. In these cases, the natural reduced space is the one generated by full-model solutions at previous time steps. When increasing the size of the projection space, the proposed methodology highly reduces the system conditioning number and the number of PCG iterations at every time step. The cost of the application of the preconditioner linearly increases with the size of the projection basis, and a trade-off must be found to effectively reduce the PCG computational cost. The quality and efficiency of the proposed approach is finally tested in the solution of groundwater flow models
Hydro-geophysical monitoring and stochastic inverse modeling of a controlled irrigation experiment
No full textEnsemble Kalman filter versus particle filter for a physically-based coupled surface–subsurface model
No full textThe ensemble Kalman filter (EnKF) and sequential importance resampling (SIR) are two Monte Carlo-based sequential data assimilation (DA) methods developed to solve the filtering problem in nonlinear systems. Both methods present drawbacks when applied to physically-based nonlinear models: the EnKF update is affected by the inherent Gaussian approximation, while SIR may require a large number of Monte Carlo realizations to ensure consistent updates. In this work we implemented EnKF and SIR into a physically-based coupled surface-subsurface flow model and applied it to a synthetic test case that considers a uniform soil v-shaped catchment subject to rainfall and evaporation events. After a sensitivity analysis on the number of Monte Carlo realizations and the correlation time of the atmospheric forcing, the comparison between the two filters is done on the basis of different simulation scenarios varying observations (outlet streamflow and/or pressure head), assimilation frequency, and type of bias (atmospheric forcing or initial conditions). The results demonstrate that both EnKF and SIR are suitable DA methods for detailed physically-based hydrological modeling using the same, relatively small, ensemble size. We highlight that the Gaussian approximation in the EnKF updates leads to a state estimation that can be not consistent with the physics of the model, resulting in a slowdown of the numerical solver. SIR instead duplicates physically consistent realizations, but can display difficulties in updates when the realizations are far from the true state. We propose and test a modification of the SIR algorithm to overcome this issue and preserve assimilation efficiency
Time lapse Electrical Resistivity Tomography and Distributed Temperature Measurements in the hyporheic zone of an alpine river
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