相关论文: The ideas behind the Self Consistent Expansion

Previous works have shown numerically that the response of a ``stochastic resonator'' is enhanced as a consequence of spatial coupling. Also, similar results have been obtained in a reaction-diffusion model by studying the phenomenon of…

Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…

Counterfactual explanations (CEs) offer interpretable insights into machine learning predictions by answering ``what if?" questions. However, in real-world settings where models are frequently updated, existing counterfactual explanations…

A nonlinearly coupled system of bouncing balls is shown to exhibit features like self-organised-criticality (SOC) and punctuated equilibrium (PE) in suitable parameter domains. The temporal evolution of the non-stationary amplitudes is…

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…

We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…

To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…

We analyze the phenomenon of system size stochastic resonance in a simple spatially extended system by exploiting the knowledge of the nonequilibrium potential. We show that through the analysis of that potential, and particularly its…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Contrastive learning has recently achieved compelling performance in unsupervised sentence representation. As an essential element, data augmentation protocols, however, have not been well explored. The pioneering work SimCSE resorting to a…

The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…

In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…

Counterfactual Explanation (CE) techniques have garnered attention as a means to provide insights to the users engaging with AI systems. While extensively researched in domains such as medical imaging and autonomous vehicles, Graph…

Continual Reinforcement Learning (CRL) is essential for developing agents that can learn, adapt, and accumulate knowledge over time. However, a fundamental challenge persists as agents must strike a delicate balance between plasticity,…

We study the dynamics of symmetric exclusion process (SEP) in the presence of stochastic resetting to two possible specific configurations -- with rate $r_1$ (respectively, $r_2$) the system is reset to a step-like configuration where all…

We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…

We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects. The aggregation term is assumed to be purely attractive, and…

The Quantum-Monte-Carlo technique known as the Stochastic Series Expansion (SSE) relies on a crucial no-branching condition: the SSE sampling is carried out in the computational basis, and the no-branching assumption ensures that…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…