Data analytics, forward and inverse modeling: geophysical and environmental fluid dynamics
A.A. 2023/2024
Obiettivi formativi
Provide the students with a basic knowledge of modelling techniques widely used in geophysics and for environmental studies. Specific focus will be given to applications of the theory of stochastic processes, also in the framework of data-mining techniques, to the numerical solution of partial derivative equations, to spectral analysis, to model calibration.
Risultati apprendimento attesi
1. Ability of critical comprehension of scientific papers and books for an enhanced knowledge of the topics presented during the lectures;
2. Ability of critical analysis of technical reports which include results of simulation models or of data analysis in environmental and geophysical field;
3. Skill in the set up of a deterministic or stochastic modeling workflow to simulate phenomena relevant in environmental and geophysical field.
2. Ability of critical analysis of technical reports which include results of simulation models or of data analysis in environmental and geophysical field;
3. Skill in the set up of a deterministic or stochastic modeling workflow to simulate phenomena relevant in environmental and geophysical field.
Periodo: Secondo semestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
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Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Secondo semestre
Programma
Development and application of a model.
Stochastic processes. Basic theory of stochastic processes; applications to geophysics and to environmental physics (Kalman filter; Markov chains; stochastic models of transport).
Machine learning methods. Regression methods; multivariate analysis (Principal Component Analysis & Factor analysis); clustering algorithms; artificial neural networks.
Numerical solution of flow and transport equations. Prototypical equations (equation of motion of geophysical fluids; advective-diffusive-dispersive transport equation with reactions); finite differences method (accuracy and convergence; Von Neumann stability analysis; Courant-Friedrichs-Lewy condition); finite volume method (or integrated finite differences) ; staggered grids; methods of solution of large linear systems (Gaussian elimination; successive over relaxation method; preconditioned conjugate gradient); explicit, implicit and Crank-Nicolson schemes for parabolic equations; basic properties of spectral methods (finite elements method; weighted residuals and variational approaches); analytical solutions of transport equation; particle tracking method for convective transport (Runge-Kutta method for ordinary differential equations); Monte Carlo methods for the advective-dispersive equation (Kolmogorov-Dmitriev theory of branching stochastic processes); nested models.
Spectral and wavelet analysis. Signals and systems; Fourier transform (representation of discrete-time signals and systems in the frequency domain; sampling); discrete Fourier transform (representation of periodic and finite-length discrete-time signals; power spectrum); wavelet analysis.
Model calibration by solution of inverse problems. General definition and properties of the discrete inverse problem; the null space; use of prior information and weighted least squares; Bayesian approach and maximum likelihood method; gradient-based optimization algorithms (Newton's method; Levenberg-Marquardt's algorithm); global optimization methods (genetic algorithms; differential evolution; simulated annealing); sensitivity analysis (one-at-a-time approach; adjoint-state equation; first-order sensitivity).
Students' project. The students will be asked to complete a project by developing original codes or by application of different codes (e.g., Princeton Ocean Model, CALMET/CALPUFF/CALGRID package).
Stochastic processes. Basic theory of stochastic processes; applications to geophysics and to environmental physics (Kalman filter; Markov chains; stochastic models of transport).
Machine learning methods. Regression methods; multivariate analysis (Principal Component Analysis & Factor analysis); clustering algorithms; artificial neural networks.
Numerical solution of flow and transport equations. Prototypical equations (equation of motion of geophysical fluids; advective-diffusive-dispersive transport equation with reactions); finite differences method (accuracy and convergence; Von Neumann stability analysis; Courant-Friedrichs-Lewy condition); finite volume method (or integrated finite differences) ; staggered grids; methods of solution of large linear systems (Gaussian elimination; successive over relaxation method; preconditioned conjugate gradient); explicit, implicit and Crank-Nicolson schemes for parabolic equations; basic properties of spectral methods (finite elements method; weighted residuals and variational approaches); analytical solutions of transport equation; particle tracking method for convective transport (Runge-Kutta method for ordinary differential equations); Monte Carlo methods for the advective-dispersive equation (Kolmogorov-Dmitriev theory of branching stochastic processes); nested models.
Spectral and wavelet analysis. Signals and systems; Fourier transform (representation of discrete-time signals and systems in the frequency domain; sampling); discrete Fourier transform (representation of periodic and finite-length discrete-time signals; power spectrum); wavelet analysis.
Model calibration by solution of inverse problems. General definition and properties of the discrete inverse problem; the null space; use of prior information and weighted least squares; Bayesian approach and maximum likelihood method; gradient-based optimization algorithms (Newton's method; Levenberg-Marquardt's algorithm); global optimization methods (genetic algorithms; differential evolution; simulated annealing); sensitivity analysis (one-at-a-time approach; adjoint-state equation; first-order sensitivity).
Students' project. The students will be asked to complete a project by developing original codes or by application of different codes (e.g., Princeton Ocean Model, CALMET/CALPUFF/CALGRID package).
Prerequisiti
Good knowledge of differential and integral calculus and basic knowledge of statistics. Good knowledge of classical physics. Basic computer skills and knowledge of a programming language (Python, Fortran, C++, Matlab,...).
Metodi didattici
Frontal lectures and guided exercises.
The students are required to develop an individual project.
The students are required to develop an individual project.
Materiale di riferimento
Lecture notes available on the course unit's Moodle site.
Further readings
1) C.C. Aggarwal (2018). Neural networks and deep learning. Springer.
2) J.L. Awange, B. Paláncz, R.H. Lewis & L. Völgyesi (2018). Mathematical Geosciences: Hybrid Symbolic-Numeric Methods. Springer.
3) J.C. Goswami & A.K. Chan (2011). Fundamentals of wavelets: theory, algorithms, and applications. John Wiley & Sons.
4) M.C. Hill & C.R. Tiedeman (2006). Effective groundwater model calibration: with analysis of data, sensitivities, predictions and uncertainty. J. Wiley & Sons.
5) N.T. Kottegoda & R. Rosso (1997). Statistics, probability and reliability for civil and environmental engineers. McGraw-Hill.
6) A.V. Oppenheim & R.W. Schafer (1989). Discrete-time signal processing. Prentice Hall.
7) W. Menke (2012). Geophysical data analysis: discrete inverse theory - 3rd edition. Academic Press.
8) A. Papoulis & S.U. Pillai (2015). Probability, random variables, and stochastic processes, 4th edition. McGraw-Hill.
9) W.H. Press, B.P. Flannery, S.A. Teukolsky & W.T. Vetterling (2007). Numerical Recipes - The art of scientific computing, 3rd edition. Cambridge University Press.
10) A. Saltelli, M. Ratto, T. Andres, F. Campolongo, et al. (2008). Global Sensitivity analysis - The Primer. J. Wiley & Sons.
11) A. Tarantola (2005). Inverse problem theory: methods for fitting and model parameter estimates. Society for Industrial and Applied Mathematics.
12) O.C. Zienkiewicz & R.L. Taylor (2000). The finite element method, Volume 1: the basis. Butterworth-Heineman.
Further readings
1) C.C. Aggarwal (2018). Neural networks and deep learning. Springer.
2) J.L. Awange, B. Paláncz, R.H. Lewis & L. Völgyesi (2018). Mathematical Geosciences: Hybrid Symbolic-Numeric Methods. Springer.
3) J.C. Goswami & A.K. Chan (2011). Fundamentals of wavelets: theory, algorithms, and applications. John Wiley & Sons.
4) M.C. Hill & C.R. Tiedeman (2006). Effective groundwater model calibration: with analysis of data, sensitivities, predictions and uncertainty. J. Wiley & Sons.
5) N.T. Kottegoda & R. Rosso (1997). Statistics, probability and reliability for civil and environmental engineers. McGraw-Hill.
6) A.V. Oppenheim & R.W. Schafer (1989). Discrete-time signal processing. Prentice Hall.
7) W. Menke (2012). Geophysical data analysis: discrete inverse theory - 3rd edition. Academic Press.
8) A. Papoulis & S.U. Pillai (2015). Probability, random variables, and stochastic processes, 4th edition. McGraw-Hill.
9) W.H. Press, B.P. Flannery, S.A. Teukolsky & W.T. Vetterling (2007). Numerical Recipes - The art of scientific computing, 3rd edition. Cambridge University Press.
10) A. Saltelli, M. Ratto, T. Andres, F. Campolongo, et al. (2008). Global Sensitivity analysis - The Primer. J. Wiley & Sons.
11) A. Tarantola (2005). Inverse problem theory: methods for fitting and model parameter estimates. Society for Industrial and Applied Mathematics.
12) O.C. Zienkiewicz & R.L. Taylor (2000). The finite element method, Volume 1: the basis. Butterworth-Heineman.
Modalità di verifica dell’apprendimento e criteri di valutazione
The assessment of students' preparation will be based on a written report and an oral exam. In particular:
a) Each student will write a report of his/her project;
b) Oral exam will include:
a. A discussion of the project report;
b. Questions on the topics taught during the lectures.
The final assessment will be based on the following criteria: quality of the student's project; strict application of the scientific method; critical reasoning; skill in the use of specialist lexicon.
The final score will be expressed in thirtieth.
a) Each student will write a report of his/her project;
b) Oral exam will include:
a. A discussion of the project report;
b. Questions on the topics taught during the lectures.
The final assessment will be based on the following criteria: quality of the student's project; strict application of the scientific method; critical reasoning; skill in the use of specialist lexicon.
The final score will be expressed in thirtieth.