Related papers: Pathwise estimates for effective dynamics: the cas…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in…
Reaction coordinates (RCs) are low-dimensional representations of complex dynamical systems that capture their long-term dynamics. In this work, we focus on the criteria of lumpability and decomposability, previously established for…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical…
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Complex microscopic many-body processes are often interpreted in terms of so-called `reaction coordinates', i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of…
The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in…
The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
The equations for effective action for nonlinear $\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these…