| 1. |
- 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-
(författare)
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A Serendipitous Journey through Stochastic Processes
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this PhD thesis we 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.We then study the survival probability of an autonomous Ornstein-Uhlenbeck process using the asymptotic matching techniques developed in fluid dynamics. Here, we 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 Ni\~no and Southern Oscillation (ENSO), the largest inter-annual variability phenomenon in the tropical Pacific which has a global impact on climate.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.Finally, the Landauer principle is applied to investigate the thermodynamics of finite time information erasure, using a model of a Brownian particle in a symmetric double-well potential. Analytical tools are derived to calculate the distribution of the work required to erase information through an arbitrary continuous erasure protocol, and the theoretical findings are numerically validated.
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| 3. |
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| 4. |
- Giorgini, Ludovico Theo, et al.
(författare)
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Correlation functions of the anharmonic oscillator : Numerical verification of two-loop corrections to the large-order behavior
- 2022
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Ingår i: Physical Review D. - : American Physical Society (APS). - 2470-0010 .- 2470-0029. ; 105:10
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Tidskriftsartikel (refereegranskat)abstract
- Recently, the large-order behavior of correlation functions of the O(N)-anharmonic oscillator has been analyzed by us [L. T. Giorgini et al., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the O(1), O(2), and O(3) oscillators, and we demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior.
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| 5. |
- 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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| 6. |
- Giorgini, Ludovico Theo, et al.
(författare)
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Non-Gaussian stochastic dynamical model for the El Niño southern oscillation
- 2022
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:2
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Tidskriftsartikel (refereegranskat)abstract
- A nonautonomous stochastic dynamical model approach is developed to describe the seasonal to interannual variability of the El Niño southern oscillation (ENSO). We determine the model coefficients by systematic statistical estimations using partial observations involving only sea surface temperature data. Our approach reproduces the observed seasonal phase locking and its uncertainty, as well as the highly non-Gaussian statistics of ENSO. Finally, we recover the intermittent time series of the hidden processes, including the thermocline depth and the wind bursts.
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| 7. |
- Giorgini, Ludovico Theo, et al.
(författare)
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Thermodynamic cost of erasing information in finite time
- 2023
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Ingår i: Physical Review Research. - : American Physical Society. - 2643-1564. ; 5:2
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Tidskriftsartikel (refereegranskat)abstract
- The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasistatically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically.
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| 8. |
- Keyes, N. D. B., et al.
(författare)
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Stochastic paleoclimatology : Modeling the EPICA ice core climate records
- 2023
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 33:9
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Tidskriftsartikel (refereegranskat)abstract
- We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kiloyears of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the European Project for Ice Coring in Antarctica (EPICA) Dome-C ice core, which are characterized by 100 ky glacial cycles overlain by fluctuations across a wide range of timescales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near-red-noise and white-noise behavior below and above the 100 ky glacial cycle, respectively, in all records. This allows us to model each time series as a one-dimensional periodic nonautonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with intervariable coupling terms, which we interpret in terms of possible interrelationships among the four time series. Within the framework of our coupling coefficients, we find that carbon dioxide and temperature act to stabilize each other and methane and nitrous oxide, whereas the latter two destabilize each other and carbon dioxide and temperature. We also compute the response function for each pair of variables to assess the model performance by comparison to the data and confirm the model predictions regarding stability amongst variables. Taken together, our results are consistent with glacial pacing dominated by carbon dioxide and temperature that is modulated by terrestrial biosphere feedbacks associated with methane and nitrous oxide emissions.
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| 10. |
- Lim, Soon Hoe, et al.
(författare)
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Predicting critical transitions in multiscale dynamical systems using reservoir computing
- 2020
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 30:12
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Tidskriftsartikel (refereegranskat)abstract
- We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.
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