Related papers: Physics-Informed Neural PDE Solvers via Spatio-Tem…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer…

Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, standard…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1]…

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…

Physics-informed neural networks (PINNs) have gained prominence for their capability to tackle supervised learning tasks that conform to physical laws, notably nonlinear partial differential equations (PDEs). This paper presents…

A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…

The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…