Related papers: Adaptive deep density approximation for Fokker-Pla…
Compressing a set of unordered points is far more challenging than compressing images/videos of regular sample grids, because of the difficulties in characterizing neighboring relations in an irregular layout of points. Many researchers…
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…
We propose a dimensionality reduction method for infinite-dimensional measure-valued evolution equations such as the Fokker-Planck partial differential equation or the Kushner-Stratonovich resp. Duncan-Mortensen-Zakai stochastic partial…
An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used…
We introduce a camera relocalization pipeline that combines absolute pose regression (APR) and direct feature matching. By incorporating exposure-adaptive novel view synthesis, our method successfully addresses photometric distortions in…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows and columns of the solution matrix and updates them using a…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) calculations and an extension to it we called "corrected" HF DFT (C(HF)-DFT). In this work, we take a further…
Accurate and efficient positioning in complex environments is critical for applications where traditional satellite-based systems face limitations, such as indoors or urban canyons. This paper introduces WK-Pnet, an FM-based indoor…
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and…
Nowadays, the rapid growth of Deep Neural Network (DNN) architectures has established them as the defacto approach for providing advanced Machine Learning tasks with excellent accuracy. Targeting low-power DNN computing, this paper examines…
The dynamical evolution of a neural network during training has been an incredibly fascinating subject of study. First principal derivation of generic evolution of variables in statistical physics systems has proved useful when used to…
In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation…
A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system…
Developing models capable of complex, multi-step reasoning is a central goal in artificial intelligence. While representing problems as graphs is a powerful approach, Graph Neural Networks (GNNs) are fundamentally constrained by their…
Unsupervised domain adaptation (UDA) aims at exploiting related but different data sources to tackle a common task in a target domain. UDA remains a central yet challenging problem in machine learning. In this paper, we present an approach…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical systems. Its non-local structure requires taking into account the whole evolution history during the time integration, which then possibly causes…
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…