相关论文: Information field dynamics for simulation scheme c…
Information Field Dynamics (IFD) by Torsten En{\ss}lin provides a tool to construct simulation schemes for data vectors $d(T)$ from measurements $d(0)$ which describe certain features of a physical process (signal), without any concrete…
We explore a new simulation scheme for partial differential equations (PDE's) called Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field inference,…
In this study we explore a new simulation scheme for partial differential equations known as Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field…
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data…
A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field…
Information field theory (IFT) is the application of probabilistic reasoning to fields. Physical fields are mathematical functions over continuous spaces that exhibit certain properties of regularity, such as limited variance and finite…
Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically driven, dynamically evolving field from finite…
A new class of functions, called the `Information sensitivity functions' (ISFs), which quantify the information gain about the parameters through the measurements/observables of a dynamical system are presented. These functions can be…
To characterize the complex higher-order interactions among variables within a system, this study introduces a novel framework, termed System Information Decomposition (SID), aimed at decomposing the information entropy of variables into…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…
Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most…
Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
A nonlinear-dynamical algorithm for city planning is proposed as an Impulse Pattern Formulation (IPF) for predicting relevant parameters like health, artistic freedom, or financial developments of different social or political stakeholders…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…