| مجال التميز | تميز دراسي وبحثي + جائزة تفوقية |
البحوث المنشورة |
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| البحث (1): | |
| عنوان البحث: |
Instantons for rare events in heavy-tailed distributions |
| رابط إلى البحث: |
https://iopscience.iop.org/article/10.1088/1751-8121/abe67b/pdf |
| تاريخ النشر: | 06/04/2021 |
| موجز عن البحث: |
Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution and probability of rare events. At its core lies the fact that rare events are, under the right circumstances, dominated by their least unlikely realization. Their computation through a saddle-point approximation of the path integral for the corresponding stochastic field theory then reduces an inefficient stochastic sampling problem into a deterministic optimization problem: finding the path of smallest action, the instanton. In the presence of heavy tails, though, standard algorithms to compute the instanton critically fail to converge. The reason for this failure is the divergence of the scaled cumulant generating function (CGF) due to a non-convex large deviation rate function. We propose a solution to this problem by ‘convexifying’ the rate function through a nonlinear reparametrization of the observable, which allows us to compute instantons even in the presence of super-exponential or algebraic tail decay. The approach is generalizable to other situations where the existence of the CGF is required, such as exponential tilting in importance sampling for Monte-Carlo algorithms. We demonstrate the proposed formalism by applying it to rare events in several stochastic systems with heavy tails, including extreme power spikes in fiber optics induced by soliton formation. |
المؤتمرات العلمية |
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| المؤتمر (1): | |
| عنوان المؤتمر: |
Bernoulli-IMS One World Symposium 2020 |
| تاريخ الإنعقاد: |
24/08/2020 |
| مكان الإنعقاد: | |
| طبيعة المشاركة: |
Poster presentation |
| عنوان المشاركة: |
Computation of rare events with non-convex rate functions |
| ملخص المشاركة: |
The importance of rare events studies comes from their devastating effects, such as economic crises, natural disasters and epidemics,…etc. In rare events simulations, change of probability measure is preferably used and worked effectively with tail events where a scaled Cumulant generating function (CGF) is well-defined and differentiable. In this poster, a generalisation to this approach is proposed when the general method fails. More precisely, numerical computation over a set of rare or extreme events is unsuccessful when it is associated with a heavy-tailed distribution which has a non-convex rate function, corresponding to a non-differentiable CGF. The modification is by rescaling the map between the rare event itself and the tilting variable (Lagrange multiplier) via a suitable nonlinear function (or functional). |
| الرابط: | |
| المؤتمر (2): | |
| عنوان المؤتمر: |
BMC-BAMC Glasgow 2021 |
| تاريخ الإنعقاد: |
06/04/2021 |
| مكان الإنعقاد: |
Glasgow.UK |
| طبيعة المشاركة: |
Poster presentation |
| عنوان المشاركة: |
Extreme events of Lagrangian model of passive scalar turbulence via large deviation theory |
| ملخص المشاركة: |
Large deviation theory is the theory behind quantifying the probability of rare and extreme events. These are of interest to physicists, actuaries, biologists, etc., depending on the underlying system. If a large deviation principle (LDP) holds, then the probability of these tail events decays exponentially, but the dominating contribution can be estimated from the minima of the rate function. This poster presents a difficulty of probing these unlikely events in a stochastic differential equation, when the quantity of interest has a heavy-tailed distribution, meaning its rate function is nonconvex. In this case, the standard procedure, which is exponential tilting, fails. We offer a solution, which is a nonlinear reparameterization, justified by convex analysis and the Gärtner-Ellis theorem, including the duality between the cumulant generating function (CGF) and the rate function. We demonstrate the applicability of our method by considering a Lagrangian model of passive scalar turbulence, which exhibits heavy-tailed distribution. |
| الرابط: | |
جوائز التكريم |
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| مسمى الجائزة: |
BMC-BAMC 2021 POSTER PRIZE |
| الجهة المانحة: |
BMC BAMC 2021 Management Committee |
| تاريخ الجائزة: |
09/04/2021 |
| مجال التكريم: |
The student won the BMC-BAMC 2021 Poster Prize for the poster ‘Extreme events of Lagrangian model of passive scalar turbulence via large deviation theory’ presented at “BMC-BAMC 2021” |
| الرابط: | |
