相关论文: Parsimonious Physics-Informed Random Projection Ne…

We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) with a focus on stiff problems. We address an Extreme…

We present a linear stability analysis of physics-informed random projection neural networks (PI-RPNNs), for the numerical solution of {the initial value problem (IVP)} of (stiff) ODEs. We begin by proving that PI-RPNNs are uniform…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks…

Many-query problems, arising from uncertainty quantification, Bayesian inversion, Bayesian optimal experimental design, and optimization under uncertainty-require numerous evaluations of a parameter-to-output map. These evaluations become…

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical…

Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

We propose a novel machine learning framework for solving optimization problems governed by large-scale partial differential equations (PDEs) with high-dimensional random parameters. Such optimization under uncertainty (OUU) problems may be…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…