Related papers: Path integral methods for the dynamics of stochast…
We develop a machine learning algorithm to infer the emergent stochastic equation governing the evolution of an order parameter of a many-body system. We train our neural network to independently learn the directed force acting on the order…
This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid…
We study the dynamics involved in a sparse random network model. We extend the standard mean-field approximation for the dynamics of a random network by employing the path-integral approach. The result indicates that the distribution of the…
We present a general framework to study the metastability of random perturbations of dynamical systems. It integrates techniques from the theory of Markov processes, in particular the resolvent approach to metastability, with the spectral…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. Here, we describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium…
We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
Impulse methods are generalized to a family of integrators for Langevin systems with quadratic stiff potentials and arbitrary soft potentials. Uniform error bounds (independent from stiff parameters) are obtained on integrated positions…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
We construct path integrals for stochastic hybrid reaction-diffusion (RD) processes, in which the reaction terms depend on the discrete state of a randomly switching environment. We proceed by spatially discretizing a given RD system and…
We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate…
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…