Related papers: Hypothesis-driven construction of mesoscopic dynam…

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this…

Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO)…

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…

The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

This paper extends Bayesian probability theory by developing a multidimensional space of events (MDSE) theory that accounts for mutual influences between events and hypotheses sets. While traditional Bayesian approaches assume conditional…

We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training…

We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

Accurate estimation of long-term risk is essential for the design and analysis of stochastic dynamical systems. Existing risk quantification methods typically rely on extensive datasets involving risk events observed over extended time…

The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…

Discrete mesoscale network models, in which explicitly modeled polymer chains are replaced by implicit pairwise potentials, are capable of predicting the macroscale mechanical response of polymeric materials such as elastomers and gels,…

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…

Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…

A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium…

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where…