Related papers: Leveraging Hamiltonian Structure for Accurate Unce…
We introduce a framework to prove propagation of chaos for interacting particle systems with singular, density-dependent interactions, a classical challenge in mean-field theory. Our approach is to define the dynamics implicitly via a…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure $\gamma$ with a unit diffusion operator and a drift of the form…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
In this work we show how the composition of maps allows us to multiply, enlarge and move stable domains in phase and parameter spaces of discrete nonlinear systems. Using H\'enon maps with distinct parameters we generate many identical…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…
We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic…
We investigate the feasibility of analyzing deep inelastic structure functions in Hamiltonian formalism by combining the light-front BJL limit of high energy amplitudes and the Fock space (multi-parton) description of hadrons. This study is…