Related papers: Computing the quasipotential for highly dissipativ…

Nongradient SDEs with small white noise often arise when modeling biological and ecological time-irreversible processes. If the governing SDE were gradient, the maximum likelihood transition paths, transition rates, expected exit times, and…

The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition…

The quasi-potential is a key concept of the Large Deviation Theory for Stochastic Differential Equations (SDEs). Once the quasi-potential with respect to an attractor of the corresponding deterministic system is found, one can readily…

The quasipotential function allows for comprehension and prediction of the escape mechanisms from metastable states in nonlinear dynamical systems. This function acts as a natural extension of the potential function for non-gradient systems…

We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…

Nongradient stochastic differential equations (SDEs) with position-dependent and anisotropic diffusion are often used in biological modeling. The quasi-potential is a crucial function in the Large Deviation Theory that allows one to…

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of…

We present a new algorithm, the efficient jet marching method (EJM), for computing the quasipotential and its gradient for two-dimensional SDEs. The quasipotential is a potential-like function for nongradient SDEs that gives asymptotic…

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for…

Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…

In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational…

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…

Quasiparticles are an important decoherence mechanism in superconducting qubits, and can be described with a complex admittance that is a generalization of the Mattis-Bardeen theory. By injecting non-equilibrium quasiparticles with a tunnel…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the…

The hyperbolic tangent function is usually used as a reliable approximation of the equilibrium density distributions of a system with phase transitions. However, analyzing the accuracies of the numerical derivatives, we find that its…

In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our…