Related papers: Critical Slowing Down in Bifurcating Stochastic Pa…

Complex systems, which consist of a large number of interacting constituents, often exhibit universal behavior near a phase transition. A slowdown of certain dynamical observables is one such recurring feature found in a vast array of…

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…

In this paper we consider a class of {\it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common noises, as well as the general version of the so-called…

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…

The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost…

Steady-state currents generically occur both in systems with continuous translation invariance and in nonequilibrium settings with particle drift. In either case, thermal fluctuations advected by the current act as a source of noise for…

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…

The main part of the thesis deals with continuously and discretely self-similar solutions and type II critical phenomena in a family of self-gravitating non-linear sigma-models. The phenomena strongly depend on the dimensionless coupling…

We present CS-SHRED, a novel deep learning architecture that integrates Compressed Sensing (CS) into a Shallow Recurrent Decoder (SHRED) to reconstruct spatiotemporal dynamics from incomplete, compressed, or corrupted data. Our approach…

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized PDE systems are expensive due to the high computational cost of high-fidelity simulations. Reduced/Latent state…

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…

This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…

A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…

We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can…

We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…

Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases.…

Semantic image synthesis (SIS) is a task to generate realistic images corresponding to semantic maps (labels). However, in real-world applications, SIS often encounters noisy user inputs. To address this, we propose Stochastic Conditional…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…