Related papers: Computing Singularly Perturbed Differential Equati…
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
We consider the problem of using experimental time-series data for parameter estimation in nonlinear ordinary differential equations, focusing on the case where the data is noisy, sparse, irregularly sampled, includes multiple experiments,…
We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…
Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This…
We study a variance reduction strategy based on control variables for simulating the averaged macroscopic behavior of a stochastic slow-fast system. We assume that this averaged behavior can be written in terms of a few slow degrees of…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
We propose a semiparametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear semiparametric mixed…
Open quantum systems host a wide range of intriguing phenomena, yet their simulation on well-controlled quantum devices is challenging, owing to the exponential growth of the Hilbert space and the inherently non-unitary nature of the…
We study coarse-graining methods for stochastic differential equations. In particular we consider averaging and a type of projection operator method, sometimes referred to as effective dynamic via conditional expectations. The projection…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…