Related papers: Partition Function Expansion on Region-Graphs and …
Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions,…
Radio maps provide radio frequency metrics, such as the received signal strength, at every location of a geographic area. These maps, which are estimated using a set of measurements collected at multiple positions, find a wide range of…
We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…
To make a statement about the nature and mechanism of fragmentation, it is necessary to probe directly any competition, or lack thereof, between the emission of various particle species as a function of excitation energy. The task is then…
With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by…
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…
For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a…
In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by…
We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights. Our results reveal an order-to-chaos expressivity phase…
Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three…
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…