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A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…
We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability…
We introduce an innovative approach for solving high-dimensional Fokker-Planck-L\'evy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology. We utilize a fractional score function and…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…
We present a new strategy to approximate the global solution of the Fokker-Planck equation efficiently in higher dimensions and show its convergence. The main ingredients are the Euler scheme to solve the associated stochastic differential…
This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is…
Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving forward and inverse problems involving partial differential equations (PDEs) by incorporating physical laws into the training process. However, the…
In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of…
We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
The Fokker-Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simulates FP equations through a mean field control (MFC)…
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Ito process. This work…
The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…