Valeur temps de l'argent | EPFL Graph Search

La valeur temps de l'argent ou valeur temporelle de l'argent est un concept en finance qui veut qu'un montant d'argent reçu ou émis plus tôt vaut davantage qu'un même montant reçu ou émis plus tard. C'est sur la valeur temps de l'argent que s’appuient plusieurs concepts fondamentaux de la finance, notamment l'actualisation et l'intérêt. La valeur temps de l'argent est l'un des facteurs considérés dans le calcul du coût d'opportunité à savoir s'il est préférable de dépenser, d'épargner ou d'investir un montant. Le concept est également présenté comme l'une des justifications de la perception de l'intérêt comme compensation au prêteur pour la perte de leur usage de leur argent. Calcul de l'intérêt Un euro aujourd'hui peut être placé à un certain taux d'intérêt, et il deviendra donc plus qu'un euro demain.

Si cet euro est placé à intérêt simple, il accumulera le même intérêt à chaque période. Par exemple, placé à un intérêt simple de 5 % annuel générera 5 centimes d'i

Fast prediction and evaluation of gravitational waveforms using surrogate models

Jan Sickmann Hesthaven

We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the generation of waveforms using standard methods can be prohibitively expensive. Our approach is based on three offline steps resulting in an accurate reduced-order model in both parameter and physical dimensions that can be used as a surrogate for the true/fiducial waveform family. First, a set of m parameter values is determined using a greedy algorithm from which a reduced basis representation is constructed. Second, these m parameters induce the selection of m time values for interpolating a waveform time series using an empirical interpolant that is built for the fiducial waveform family. Third, a fit in the parameter dimension is performed for the waveform’s value at each of these m times. The cost of predicting L waveform time samples for a generic parameter choice is of order O (mL + mc) online operations where c denotes the fitting function operation count and, typically, m ≪ L. The result is a compact, computationally efficient, and accurate surrogate model that retains the original physics of the fiducial waveform family while also being fast to evaluate. We generate accurate surrogate models for Effective One Body (EOB) waveforms of non-spinning binary black hole coalescences with durations as long as 105M, mass ratios from 1 to 10, and for multiple spherical harmonic modes. We find that these surrogates are more than three orders of magnitude faster to evaluate as compared to the cost of generating EOB waveforms in standard ways. Surrogate model building for other waveform families and models follow the same steps and have the same low computational online scaling cost. For expensive numerical simulations of binary black hole coalescences we thus anticipate extremely large speedups in generating new waveforms with a surrogate. As waveform generation is one of the dominant costs in parameter estimation algorithms and parameter space exploration, surrogate models offer a new and practical way to dramatically accelerate such studies without impacting accuracy.

American Physical Society2014

Fast prediction and evaluation of gravitational waveforms using surrogate models

Jan Sickmann Hesthaven

American Physical Society2014