Related papers: Multi-resolution partial differential equations pr…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

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),…

Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…

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]…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…