Related papers: Equation-Free Computations as DDDAS Protocols for …
Equation-free modeling aims at extracting low-dimensional macroscopic dynamics from complex high-dimensional systems that govern the evolution of microscopic states. This algorithm relies on lifting and restriction operators that map…
The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform…
Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…
We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…
Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…
Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal. Recent studies have shown that cells can extract multi-dimensional information from…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
Event-based vision represents a paradigm shift in how vision information is captured and processed. By only responding to dynamic intensity changes in the scene, event-based sensing produces far less data than conventional frame-based…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
The current National Airspace System (NAS) is reaching capacity due to increased air traffic, and is based on outdated pre-tactical planning. This study proposes a more dynamic airspace configuration (DAC) approach that could increase…
High fidelity design evaluation processes such as Computational Fluid Dynamics and Finite Element Analysis are often replaced with data driven surrogates to reduce computational cost in engineering design optimization. However, building…
Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
The article presents results of discrete thermodynamics (DTD) basic application to electrochemical systems. Consistent treatment of the electrochemical system as comprising two interacting subsystems - the chemical and the electrical…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Up to now, it is not possible to obtain analytical solutions for complex molecular association processes (e.g. Molecule recognition in Signaling or catalysis). Instead Brownian Dynamics (BD) simulations are commonly used to estimate the…