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Diffusion models (DMs) excel in unconditional generation, as well as on applications such as image editing and restoration. The success of DMs lies in the iterative nature of diffusion: diffusion breaks down the complex process of mapping…

Time-dependent density functional theory (TDDFT) is a standard approach for calculating optical excitations of molecules and solids, while ensemble DFT (EDFT) is a promising alternative under development. We introduce ensemble TDDFT…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

Celebrated fluctuation-dissipation theorem (FDT) linking the response function to time dependent correlations of observables measured in the reference unperturbed state is one of the central results in equilibrium statistical mechanics. In…

Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…

Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion…

This paper introduces a new generalization of the power generalized Weibull distribution called the generalized power generalized Weibull distribution. This distribution can also be considered as a generalization of Weibull distribution.…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

We present a framework based on the generalized lattice-Boltzmann equation using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows. Due to its flexibility in using disparate relaxation…

In this paper (Shivamoggi et al.), we explore a variant for the simple model based on a binomial multiplicative process of Meneveau and Sreenivasan that mimics the multi-fractal nature of the energy dissipation field in the inertial range…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot--dependence…

Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the…

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…

Deriving analytical expressions of dielectric permittivities is required for numerical and physical modeling of optical systems and the soar of non-hermitian photonics motivates their prolongation in the complex plane. Analytical models are…

Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…

We present technical results required for the description and understanding of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion…

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as L\'evy-Lorentz gas. To gain insight into…

In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…

We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be…