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- Giorgini, Ludovico Theo
(författare)
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A Serendipitous Journey through Stochastic Processes
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this licentiate thesis I will present some new insights in different problems in the field of stochastic processes. A stochastic resonance system is studied using path integral techniques, originally developed in quantum field theory, to recover the optimal means through which noise self-organises before a rare transition from one potential well to the other. These results allow one to determine precursors to a rare events in such system.I then study the survival probability of an autonomous Ornstein-Uhlenbeck process using the asymptotic matching techniques developed in fluid dynamics. Here, I obtain a simple analytical expression for this quantity that exhibits a good agreement with numerical determination.Next, rare events in similar systems are studied using a recurrent neural network to model the noisy part of the signal. The neural network facilitates the prediction of future noise realisations and hence rare transitions.Using a combination of analytical and numerical techniques a low-dimensional model is constructed and it is able to predict and to reproduce the main dynamical and equilibrium features of the El Niño and Southern Oscillation (ENSO), the largest inter-annual variability phenomenon in the tropical Pacific which has a global impact on climate.Finally, using the results obtained for the survival probability of the Ornstein-Uhlenbeck process, an approximate analytical solution for the probability density function and the response is derived for a stochastic resonance system in the non-adiabatic limit.
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| 2. |
- Giorgini, Ludovico Theo, 1994-, et al.
(författare)
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Modeling the El Niño Southern Oscillation with Neural Differential Equations
- 2021
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Konferensbidrag (refereegranskat)abstract
- We use a Neural Ordinary Differential Equation to model and predict the seasonal to interannual variability of El Niño Southern Oscillation (ENSO). We train our neural network model using partial observations involving only sea surface temperature data. Our approach is computationally inexpensive, it reproduces the main seasonal features of ENSO, and exhibits robust predictions skills.
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| 3. |
- Moon, Woosok, et al.
(författare)
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Analytical solution of stochastic resonance in the nonadiabatic regime
- 2021
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Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 104:4
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Tidskriftsartikel (refereegranskat)abstract
- We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.
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