The Fokker--Planck (FP) equation governing the evolution of probability density function (PDF) is applicable to many disciplines, but it requires specification coefficients for each case, which can be functions space-time and not just constants hence require development a data-driven modeling approach. When data available directly on PDF, there exist methods inverse problems that employed infer thus determine FP subsequently obtain its solution. Herein, we address more realistic scenario,...

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A network (NN) represents the solution, while a PDE-induced NN is coupled solution NN, and all operators are treated using automatic differentiation. Here, we first employ standard PINN stochastic version, sPINN, forward inverse problems governed by non-linear advection–diffusion–reaction (ADR) equation, assuming have some sparse measurements of...

Abstract As train speeds increase, aerodynamic drag becomes a significant factor in resistance. The geometric profile of the train’s end connection changes abruptly, enhancing this Implementing an external windshield effectively mitigates resistance, particularly for middle- and rear-train cars. This study utilizes three-dimensional, steady Navier–Stokes (N-S) equations open line conditions unsteady N-S tunnel environments to analyze reduction effects trains with without windshields both...

Pancreatic cancer (PC) is a highly invasive tumor with early metastasis and poor prognosis, yet the mechanisms for progression have not been fully elucidated. Emerging evidence indicates that microRNA-331-3p (miR-331-3p) plays an important role in of diverse human cancers. Here, we found miR-331-3p was significantly upregulated specimens PC patients cell lines. Functional studies showed downregulation inhibited proliferation epithelial–mesenchymal transition (EMT)-mediated vitro....

This paper considers the dynamics of escape in stochastic FitzHugh–Nagumo (FHN) neuronal model driven by symmetric α-stable Lévy noise. External or internal stimulation may make excitable system produce a pulse not, which can be interpreted as an problem. A new method to analyse state transition from rest excitatory is presented. approach consists two deterministic indices: first probability (FEP) and mean exit time (MFET). We find that higher FEP (equilibrium) promotes such MFET reflects...

We investigate a quantitative bistable two-dimensional model (MeKS network) of gene expression dynamics describing the competence development in Bacillus subtilis under influence Lévy as well Brownian motions. To analyze transitions between vegetative and regions therein, two dimensionless deterministic quantities, mean first exit time (MFET) escape probability, are determined from microscopic perspective, their averaged versions macroscopic perspective. The relative contribution factor λ,...

We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes equilibrium states with its most probable phase portraits. have found some peculiar phenomena in contrast to deterministic counterpart: (i) When non-Gaussianity parameter varies, there is either one, two or no backward pitchfork type bifurcations; (ii) vector field are three forward (iii) The clearly leads fundamentally more...

Many complex real world phenomena exhibit abrupt, intermittent, or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian Lévy noise. Among these phenomena, the most likely transition paths between metastable states important since rare events may have a high impact in certain scenarios. Based on large deviation principle, path could treated as minimizer of rate function upon that connect two points. One challenges calculate for...

This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian stable Levy noise via stochastic averaging. When the observations are only available slow components, we show that averaged, filter approximates original filter, by examining corresponding Zakai partial differential equations. Furthermore, demonstrate dynamics of system, parameter estimation and most probable paths.

Abstract One of the most exciting applications artificial intelligence is automated scientific discovery based on previously amassed data, coupled with restrictions provided by known physical principles, including symmetries and conservation laws. Such hypothesis creation verification can assist scientists in studying complex phenomena, where traditional intuition may fail. Here we develop a platform generalized Onsager principle to learn macroscopic dynamical descriptions arbitrary...

A fully discrete scheme is proposed for numerically solving the strongly nonlinear time-fractional parabolic problems. Time discretization achieved by using Grünwald–Letnikov (G–L) method and some linearized techniques, spatial standard second-order central difference scheme. Through a Grönwall-type inequality complementary kernels, optimal time-stepping error estimates of are obtained. Finally, several numerical examples given to confirm theoretical results.

Abstract The bogie is a critical component of high-velocity trains. As train velocity rises, the operational quality increasingly influenced by aerodynamic forces. characteristics bogies significantly impact safety operations. This article examines real model, constructing 3-group and developing mathematical model operation on open lines. Using three-dimensional steady-state Navier–Stokes equations, flow field characteristics, pressure spread, forces, torque body locomotives operating at...

In this article, a Newton linearized compact finite difference scheme is proposed to numerically solve class of Sobolev equations. The unique solvability, convergence, and stability the are proved. It shown that method order 2 in temporal direction 4 spatial direction. Moreover, compare classical extrapolated Crank‐Nicolson or second‐order multistep implicit–explicit methods, easier be implemented as it only requires one starting value. Finally, numerical experiments on two‐dimensional...

Extracting the governing stochastic differential equation model from elusive data is crucial to understand and forecast dynamics for various systems. We devise a method extract drift term estimate diffusion coefficient of dynamical system, its time-series most probable transition trajectory. By Onsager–Machlup theory, trajectory satisfies corresponding Euler–Lagrange equation, which second-order deterministic ordinary (ODE) involving coefficient. first coefficients based on trajectory, then...

In this paper, we present a class of finite difference methods for numerically solving fractional differential equations. Such numerical schemes are developed based on the change in variable and piecewise interpolations. Error analysis is obtained by using Grönwall-type inequality. Numerical examples given to confirm theoretical results.

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A network (NN) represents the solution while a PDE-induced NN is coupled NN, and all operators are treated using automatic differentiation. Here, we first employ standard PINN stochastic version, sPINN, forward inverse problems governed by nonlinear advection-diffusion-reaction (ADR) equation, assuming have some sparse measurements of concentration...

Hardware design methods for impulse ground penetrating radar (GPR) are presented. The designed GPR system mainly consists of ultra wideband (UWB) transmitting and receiving antennas, generator, sampling down converter, time varying gain amplifier, timing synchronization controller, high accuracy digitizer, so on. All these modules were realized. can operate from 100 to 1000 MHz obtain different detecting depth precision. An experimental had been completed field test proved this was successful