Related papers: Solving Inverse Stochastic Problems from Discrete …

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

In this study, we propose a new method that is useful for estimating unknown parameter values of stochastic differential equation (SDE) models, based on probability density function (PDF) data measured from random dynamical systems. As our…

A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes.…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular,…

Sampling invariant distributions from an It\^o diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy…

Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often…

Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical…

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output…

One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…

Efficiently solving the Fokker-Planck equation (FPE) is crucial for understanding the probabilistic evolution of stochastic particles in dynamical systems, however, analytical solutions or density functions are only attainable in specific…

Classical nonlinear dynamical systems are often characterized by their steady-state probability distribution functions (PDFs). Typically, PDFs are accumulated from numerical simulations that involve solving the underlying dynamical…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

Scientific machine learning (SciML) methods such as physics-informed neural networks (PINNs) are used to estimate parameters of interest from governing equations and small quantities of data. However, there has been little work in assessing…

We present a Parametrization of the Physics Informed Neural Network (P-PINN) approach to tackle the problem of uncertainty quantification in reservoir engineering problems. We demonstrate the approach with the immiscible two phase flow…