Related papers: Can Physics Informed Neural Operators Self Improve…

The demand for high-performance materials, along with advanced synthesis technologies such as additive manufacturing and 3D printing, has spurred the development of hierarchical composites with superior properties. However, computational…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

This study investigates the use of an unsupervised, physics-informed deep learning framework to model a one-degree-of-freedom mass-spring system subjected to a nonlinear friction bow force and governed by a set of ordinary differential…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of…

Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…

Physics informed neural networks (PINNs) have recently been proposed as surrogate models for solving process optimization problems. However, in an active learning setting collecting enough data for reliably training PINNs poses a challenge.…

Self-training is one of the earliest and simplest semi-supervised methods. The key idea is to augment the original labeled dataset with unlabeled data paired with the model's prediction (i.e. the pseudo-parallel data). While self-training…

We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…

Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs. We propose a modularized approach and study the choices of…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Flexible and accurate interpolation schemes using machine learning could be of great benefit for many use-cases in numerical simulations and post-processing, such as temporal upsampling or storage reduction. In this work, we adapt the…