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Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids at thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when…
Stochastic differential equations of Langevin-diffusion form have received significant attention, thanks to their foundational role in both Bayesian sampling algorithms and optimization in machine learning. In the latter, they serve as a…
Multiphase flow in parallel channels is often an efficient approach to manage heat and energy distribution in engineering systems. However, two-phase flow with heating in parallel channels is prone to maldistribution, resulting in…
The dissipation phenomena of relative entropy from an It\^o--Langevin dynamical system is a classic topic from stochastic analysis. Relying on the time-reversal of diffusions, a novel trajectorial approach investigates the pathwise behavior…
Sample-based trajectory optimisers are a promising tool for the control of robotics with non-differentiable dynamics and cost functions. Contemporary approaches derive from a restricted subclass of stochastic optimal control where the…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
We analyze a stochastic particle system of 5 neighbors. Considering eigenvalue problem of transition matrix, we propose a conjecture that asymptotic distribution of the system is determined by the number of specific local patterns in the…
A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a…
Consider a manifold $M$ endowed locally with a pair of complementary distributions $\Delta^H \oplus \Delta^V=TM$ and let $\text{Diff}(\Delta^H, M)$ and $\text{Diff}(\Delta^V, M)$ be the corresponding Lie subgroups generated by vector fields…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…