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Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
The Free Energy Principle (FEP) is a leading framework for mathematically modeling self-organization and learning, while Integrated Information Theory (IIT) is a computational ontology of consciousness oriented around irreducible cause and…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
An important issue during an engineering design process is to develop an understanding which design parameters have the most influence on the performance. Especially in the context of optimization approaches this knowledge is crucial in…
Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and…
A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this…
This presentation's Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational…
We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extraction of coarse-grained, macroscopic information from…
In the context of the energy transition, with increasing integration of renewable sources and cross-border electricity exchanges, power grids are encountering greater uncertainty and operational risk. Maintaining grid stability under…
We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is…
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states.…
This study employed an artificial intelligence-enhanced molecular simulation framework to enable efficient Path Integral Molecular Dynamics (PIMD) simulations. Owing to its modular architecture and high-throughput capabilities, the…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Large eddy simulation has been widely used to simulate turbulence at balanced computational cost and accuracy. Many Subgrid-Scale (SGS) models have been proposed over the years, where data-driven and machine learning-aided approaches set…
This paper reviews Irradiation Driven Molecular Dynamics (IDMD) - a novel computational methodology for atomistic simulations of the irradiation driven transformations of complex molecular systems implemented in the MBN Explorer software…
In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data,…
There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere…