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Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. "Adaptive weak approximation of stochastic differential equations." Comm. Pure Appl. Math. 54 (2001), no. 10, 1169–1214. Keywords: Adaptive weak approximation of stochastic differential equations Read more | Website Refereed Journals Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios "Hyperbolic differential equations and adaptive numerics." Theory and numerics of differential equations (Durham, 2000), 231–280, Universitext, Springer, Berlin, 2001. Keywords: Hyperbolic differential equations and adaptive numerics Read
Babuška, Ivo; Liu, Kang-Man; Tempone, Raúl "Solving stochastic partial differential equations based on the experimental data." Dedicated to Jim Douglas, Jr. on the occasion of his 75th birthday. Math. Models Methods Appl. Sci. 13 (2003), no. 3, 415–444. Keywords: Covariance; Karhunen Loeve expansion; stationary random function; principle component analysis Read more | Website | Download Document Refereed Journals Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. "Convergence rates for adaptive approximation of ordinary differential equations." Numer. Math. 96 (2003)
Babuška, Ivo; Tempone, Raúl; Zouraris, Georgios E. "Galerkin finite element approximations of stochastic elliptic partial differential equations." SIAM J. Numer. Anal. 42 (2004), no. 2, 800–825. Keywords: stochastic elliptic equation, perturbation estimates, Karhunen–Lo`eve expansion, finite elements, Monte Carlo method, k × h-version, p × h-version, expected value, error estimates Read more | Website | Download Document Refereed Journals
I. Babuska, F. Nobile and R. Tempone. ”Worst-case scenario analysis for elliptic PDE’s with uncertainty”, Proceedings of the EURODYN conference, Paris, September 4-7, 2005. Keywords: Worst-case scenario analysis for elliptic PDE’s with uncertainty Read more | Website Conference Proceedings Oden, J. Tinsley; Babuška, Ivo; Nobile, Fabio; Feng, Yusheng; Tempone, Raul "Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty." Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 2-5, 195–204. Keywords: Modeling error estimation; Stochastic partial
I. Babuska, F. Nobile, J.T. Oden, R. Tempone. ”Reliability, Uncertainty Estimates, Validation and Verification”, ICES Report 04-05. 2006. Keywords: Reliability, Uncertainty Estimates, Validation, and Verification Read more Manuscripts I. Babuska, J.T. Oden, K. Liechti, J.C. Browne, L. Demkowicz, Y. Feng, F. Nobile, R. Tempone, and P. Hosatte. ”Reliability of Computer Predictions in Computational Solid Mechanics: Towards the Estimation and Control of Errors Due to Modeling, Discretization, and Uncertainty”. TICAM Report 03-44. 2006. Keywords: Reliability of Computer Predictions in Computational
Babuška, I.; Nobile, F.; Tempone, R "Reliability of computational science." Numer. Methods Partial Differential Equations 23 (2007), no. 4, 753–784. Keywords: model validation, uncertainty quantification, Bayesian update, failure probability Read more | Website Refereed Journals Babuška, Ivo; Nobile, Fabio; Tempone, Raúl "A stochastic collocation method for elliptic partial differential equations with random input data." SIAM J. Numer. Anal. 45 (2007), no. 3, 1005–1034. Keywords: collocation method, stochastic partial differential equations, finite elements, uncertainty quantification
I. Babuska, F. Nobile and R. Tempone. ”Formulation of the Static Frame Problem”, Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issues 29-32, pp. 2496-2499, (May 2008). Keywords: Model validation, Uncertainty quantification, Failure probability Read more Refereed Journals K. J. Dowding, J. Red-Horse, R. G. Hills, T. L. Paez, I. Babuska and R. Tempone.”Validation Challenge Workshop Summary”, Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issues 29-32, pp. 2381-2384, (May 2008). Keywords: Validation Challenge Workshop Summary Read more Refereed Journals I
Nobile, F., Tempone, Raul "Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients." Internat. J. Numer. Methods Engrg. 80 (2009), no. 6-7, 979–1006. Keywords: PDEs with random data, parabolic equations, multivariate polynomial approximation, Stochastic Galerkin methods, Stochastic Collocation methods, sparse grids, Smolyak approximation, Point Collocation, Monte Carlo sampling Read more | Website Refereed Journals
C. Bayer, H. Hoel, P. Plechac, A. Szepessy, R. Tempone. ”How accurate is molecular dynamics?”, arXiv:1104.0953, 2011 Keywords: How accurate is molecular dynamics? Read more | Website Manuscripts M. Motamed and C. B. Macdonald and S. J. Ruuth. On the Linear Stability of the Fifth-Order WENO Discretization. Journal of Scientific Computing, vol. 47, no. 2, pp. 127-149, 2011. Keywords: Linear stability analysis, Method of lines, WENO, Multistep methods, Runge–Kutta methods, Hyperbolic conservation laws Read more | Website Refereed Journals J. Back, F. Nobile, L. Tamellini, and R. Tempone
Nadhir Ben Rached, "Adaptive Monte Carlo Euler Method For Options With Low Regularity Payoffs", Graduation Project Report, Tunisia Polytechnic School, Hosting Institution: KAUST, June 2012 Keywords: Adaptive Monte Carlo, Euler, low regularity, smoothing, low pass filter, Richardson extrapolation, single level, multilevel. Read more | Download Document Thesis A. Haji-Ali, “Pedestrian Flow in the Mean-field Limit”, Master Thesis, KAUST, November 2012. Keywords: Crowd modeling, Mean-Field, Helbing, Pedestrian, Particle MLMC Read more | Download Document Thesis H. Tembine, P. Vilanova, and M
Nowak, W., Litvinenko, A. Kriging and Spatial Design Accelerated by Orders of Magnitude: Combining Low-Rank Covariance Approximations with FFT-Techniques, Mathematical Geosciences, Vol. 45, Num. 4, pp 411--435, Springer 2013. Keywords: Low-rank tensor approximation, Spectral methods, Efficient geostatistical estimation, Geostatistical optimal design. Read more | Website Refereed Journals Chang Wang, K. J. H. Law, Panayotis. G. Kevrekidis, and Mason A. Porter, Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates. Physical Review A 87 023621 (2013). Keywords
Nadhir Ben Rached, Fatma Benkhelifa, Abla Kammoun, Mohamed-Slim Alouini, Raul Tempone, A Fast Simulation Method for the Sum of Subexponential Distributions, submitted to arXiv:1406.4689v4, Jun. 2014. Keywords: A Fast Simulation Method for the Sum of Subexponential Distributions. Read more | Website Manuscripts Kody J.H. Law, Hamidou Tembine, Raul Tempone, Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering, submitted to arXiv:1409.0628v2, Nov. 2014. Keywords: Deterministic Methods for Nonlinear Filtering, part I: Mean-field Ensemble Kalman Filtering
A. Iania, Basket option pricing for processes with jumps using sparse grids and Fourier transforms, Master Thesis, Politecnico di Torino - KAUST, 2015. Keywords: Basket option pricing for processes with jumps using sparse grids and Fourier transforms. Read more | Download Document Thesis N. Ben Rached, A. Kammoun, M. Alouini, R. Tempone, Unified Importance Sampling Schemes for Efficient Simulation of Outage Capacity over Generalized Fading Channels, Accepted for publication in IEEE Journal of Selected Topics in Signal Processing, 2015. Keywords: Outage capacity, naive Monte Carlo, hazard rate
E. Kalligiannaki, A. Chazirakis, A. Tsourtis, M.A. Katsoulakis, P. Plechac, and V. Harmandaris, Parametrizing coarse-grained models for molecular systems at equilibrium, EPJ ST, 225(8), 1347-1372, 2016, DOI: 10.1140/epjst/e2016-60145-x. Keywords: Parametrizing coarse-grained models for molecular systems at equilibrium Read more | Website Refereed Journals Soeren Wolfers, Fabio Nobile, Raul Tempone, Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. Submitted arXiv 1609.00246, Sept 2016 Keywords: Sparse approximation of multilinear problems with
Haji-Ali, Abdul-Lateef, and Raúl Tempone. " Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation." Statistics and Computing 28, no. 4 (2018): 923-935. Keywords: Multi-index Monte Carlo, Multilevel Monte Carlo, Monte Carlo Particle systems, McKean–Vlasov Mean-field, Stochastic differential equations, Weak approximation, Sparse approximation, Combination technique. Read more | Website | Download Document Refereed Journals Hoel, Hakon, Alexey Chernov, Kody Law, Fabio Nobile, and Raul Tempone. " Multilevel ensemble Kalman filtering for spatio-temporal processes." (2018)
Articles Rached, N. B., Botev, Z., Kammoun, A., Alouini, M.-S., & Tempone, R. (2018). On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances. IEEE Transactions on Wireless Communications, 17(11), 7801–7813. doi:10.1109/twc.2018.2871201 Keywords: Order statistics, outage probability, Generalized selection combining, Monte Carlo, Variance reduction techniques, Importance sampling, Conditional MC. Read more | Website | Download Document Bayer, C., Häppölä, J., & Tempone, R. (2018). Implied stopping rules for American basket options from Markovian projection
Articles Litvinenko, A., Logashenko, D., Tempone, R., Wittum, G., & Keyes, D. (2019). Efficient Simulations for Contamination of Groundwater Aquifers under Uncertainties. PAMM, 19(1). doi:10.1002/pamm.201900023 Read more | Website | Download Document Ballesio, M., Beck, J., Pandey, A., Parisi, L., von Schwerin, E., & Tempone, R. (2019). Multilevel Monte Carlo acceleration of seismic wave propagation under uncertainty. GEM - International Journal on Geomathematics, 10(1). doi:10.1007/s13137-019-0135-5 Keywords: Multilevel Monte Carlo, Propagation of Uncertainty, Seismic Wave Propagation
Articles Chernov, A., Hoel, H., Law, K. J. H., Nobile, F., & Tempone, R. (2020). Multilevel ensemble Kalman filtering for spatio-temporal processes. Numerische Mathematik. doi:10.1007/s00211-020-01159-3 Read more | Website | Download Document Piazzola, C., Tamellini, L., & Tempone, R. (2020). A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology. Mathematical Biosciences, 108514. doi:10.1016/j.mbs.2020.108514 Keywords: Dynamical Systems, Mathematical Epidemiology, Uncertainty Quantification, Model Identifiability, Bayesian Inversion
Articles Kabanov, D. I., Espath, L., Kiessling, J., & Tempone, R. F. (2021). Estimating divergence-free flows via neural networks. PAMM, 21(1). doi:10.1002/pamm.202100173 Read more | Website | Download Document Kiessling, J., Ström, E., & Tempone, R. (2021). Wind field reconstruction with adaptive random Fourier features. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2255). doi:10.1098/rspa.2021.0236 Keywords: Random Fourier features, Metropolis algorithm, spatial interpolation, machine learning, wind field reconstruction, flow field estimation Read
Bibliography: Renzo Caballero, Ahmed Kebaier, Marco Scavino, and Raúl Tempone, "A Derivative Tracking Model for Wind Power Forecast Error", arXiv, 2006.15907, 2020 Authors: Renzo Caballero, Ahmed Kebaier, Marco Scavino, Raúl Tempone Keywords: Wind power, probabilistic forecasting, stochastic differential equations, Lamperti transform, numerical optimization, model selection, time-inhomogeneous Jacobi diffusion Year: 2020 Abstract: Reliable wind power generation forecasting is crucial for applications such as the allocation of energy reserves, optimization for electricity price, and
Bibliography: A.-L Haji-Ali, H. Hoel, and R. Tempone. "A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean--Vlasov equations", arXiv preprint arXiv:2101.00886, 2021 Authors: A.-L Haji-Ali, H. Hoel, And R. Tempone Keywords: Interacting stochastic particle systems, Stochastic mean-field limit, Weak and strong convergence rates. Year: 2021 Website | Download Document
Bibliography: Ben Rached, Nadhir, Daniel MacKinlay, Zdravko Botev, Raúl Tempone, and Mohamed-Slim Alouini, "A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems", IEEE Transactions on Wireless Communications, 2020 Authors: Nadhir Ben Rached, Daniel MacKinlay, Zdravko Botev, Raul Tempone, Mohamed-Slim Alouini Keywords: Rare event, performance evaluation, multilevel splitting algorithm, variance reduction Year: 2020 Abstract: We propose a unified rare-event estimator for the performance evaluation of wireless communication systems. The estimator is
Bibliography: Ballesio, Marco, Ajay Jasra, Erik von Schwerin, and Raúl Tempone; "A Wasserstein Coupled Particle Filter for Multilevel Estimation", arXiv, 2004.03981, 2020. Authors: Marco Ballesio, Ajay Jasra, Erik Von Schwerin, Raúl Tempone Keywords: Filtering, Diffusions, Multilevel Monte Carlo, Particle Filters Year: 2020 Abstract: In this paper, we consider the filtering problem for partially observed diffusions, which are regularly observed at discrete times. We are concerned with the case when one must resort to time-discretization of the diffusion process if the transition density is not
Bibliography: Ben Rached, Nadhir, Abla Kammoun, Mohamed-Slim Alouini, and Raúl Tempone, "An Accurate Sample Rejection Estimator of the Outage Probability With Equal Gain Combining", IEEE Open Journal of the Communications Society, Volume 1 (2020), Pages 1022-1034. Authors: Nadhir Ben Rached, Abla Kammoun, Mohamed-Slim Alouini, Raúl Tempone Keywords: Outage probability, equal gain combining, importance sampling, sample rejection, generalised selection combining, bounded relative error. Year: 2020 Abstract: We evaluate the outage probability (OP) for L-branch equal gain combining (EGC)
List of completed Graduation Project Reports Nadhir Ben Rached, "Adaptive Monte Carlo Euler Method For Options With Low Regularity Payoffs", Graduation Project Report, Tunisia Polytechnic School, Hosting Institution: KAUST, June 2012. Chaouki Ben Said, "Uncertainty quantification in European type contingent claims", Graduation Project Report, Tunisia Polytechnic School, Hosting Institution: KAUST, June 2013. Chiheb Ben Hammouda, "Numerical Methods For Uncertainty Quantification In Option Pricing", Graduation Project Report, Tunisia Polytechnic School, Hosting Institution: KAUST, June 2013
Bibliography: Bayer, Christian, Chiheb Ben Hammouda, and Raul Tempone. "Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model." Quantitative Finance (2020), DOI: 10.1080/14697688.2020.1744700. Authors: Christian Bayer, Chiheb Ben Hammouda, And Raul Tempone Keywords: Rough volatility, Monte Carlo, Adaptive sparse grids, Quasi-Monte Carlo, Brownian bridge construction, Richardson extrapolation. Year: 2020 Abstract: The rough Bergomi (rBergomi) model, introduced recently in (Bayer, Friz, Gatheral, 2016), is a promising rough volatility
List of completed Master Thesis Eliza Rezvanova, “Optimal policies for battery operation and design via stochastic optimal control of jump diffusions”, MS-Thesis, KAUST, April 2021. Renzo Caballero, “Stochastic Optimal Control of Renewable Energy”, MS-Thesis, KAUST, June 2019. Soumaya Elkantassi, "Probabilistic Forecast of Wind Power Generation by Stochastic Differential Equation Models", MS-Thesis, KAUST, April 2017. Marco Ballesio, "Indirect Inference for Scalar Time-homogeneous Stochastic Differential Equations Based on Moment Expansions", Master Thesis, Politecnico of Torino and Real
Bibliography: Beck, Joakim, Ben Mansour Dia, Luis Espath, Raúl Tempone. "Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design". Int J Numer Methods Eng. (2020); 121: 3482– 3503 Authors: Joakim Beck, Ben Mansour Dia, Luis Espath, Raúl Tempone Keywords: Electrical impedance tomography, Expected information gain, Importance sampling, Multilevel, Stochastic collocation Year: 2020 Abstract: An optimal experimental set‐up maximizes the value of data for statistical inferences. The efficiency of strategies for
Bibliography: Chernov, Alexey, Haakon Hoel, Kody Law, Fabio Nobile, and Raúl Tempone, "Multilevel Ensemble Kalman filtering for spatially extended models", arXiv preprint 1608.08558. To appear in Numerische Mathematik, 2020. Authors : Alexey Chernov, Haakon Hoel, Kody Law, Fabio Nobile, Raúl Tempone Keywords: Monte Carlo, multilevel, filtering, Kalman filter, ensemble Kalman filter Year: 2020 Abstract: This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF), thereby yielding a multilevel ensemble Kalman filter (MLEnKF)
Bibliography: Haji-Ali, Abdul-Lateef, Fabio Nobile, Raúl Tempone, and Sören Wolfers, "Multilevel weighted least-squares polynomial approximation", ESAIM: M2AN, Volume 54, no. 2, (2020): 649–677 Authors: Abdul-Lateef Haji-Ali, Fabio Nobile, Raúl Tempone, Sören Wolfers Keywords: Multilevel methods, least-squares approximation, multivariate approximation, polynomial approximation, convergence rates, error analysis Year: 2020 Abstract: Weighted least-squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using
Bibliography: Carlon, André Gustavo, Ben Mansour Dia, Luis Espath, Rafael Holdorf Lopez, Raúl Tempone, "Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization", Computer Methods in Applied Mechanics and Engineering, Volume 363, (2020). Authors: André Gustavo Carlon, Ben Mansour Dia, Luis Espath, Rafael Holdorf Lopez, Raúl Tempone Keywords: Optimal experimental design, Bayesian inference, Laplace approximation, Stochastic optimization, Accelerated gradient descent, Importance sampling Year: 2020 Abstract: Finding the best setup for experiments
List of Completed PhD Thesis Chiheb Ben Hammouda, "Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks", Ph.D. thesis, KAUST July 2020. Sören Wolfers, "Efficient Numerical Methods for High-Dimensional Approximation Problems", Ph.D. thesis, KAUST February 2019. Nadhir Ben Rached, "Rare Events Simulations with Applications to the Performance Evaluation of Wireless Communication Systems", Ph.D. thesis, KAUST October 2018. Zaid Sawlan, "Statistical analysis and Bayesian methods for fatigue life prediction and inverse problems in linear time dependent PDEs with
Bibliography: Bayer, Christian, Raúl Tempone, and Sören Wolfers, "Pricing American Options by Exercise Rate Optimization", Quantitative Finance, (2020). Authors: Christian Bayer, Raúl Tempone, Sören Wolfers Keywords: Computational finance, American option pricing, stochastic optimization problem, Monte Carlo, multivariate approximation, rough volatility Year: 2020 Abstract: A new method for the numerical pricing of American options We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous
