相关论文: SciAI4Industry -- Solving PDEs for industry-scale …

Environmental science plays a pivotal role in safeguarding ecosystems, a domain driven by large-scale, heterogeneous data. In the big data era, artificial intelligence (AI) has emerged as a transformative tool for learning patterns and…

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based…

In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…

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…

Recently, deep learning techniques have enjoyed success in various multimedia applications, such as image classification and multi-modal data analysis. Large deep learning models are developed for learning rich representations of complex…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…

Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells…

Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…

We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…

Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and…

We propose a new deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and forward-backward stochastic differential equations with jumps (FBSDEJs). This novel algorithm can be viewed as an…

Training and deploying deep learning models in real-world applications require processing large amounts of data. This is a challenging task when the amount of data grows to a hundred terabytes, or even, petabyte-scale. We introduce a hybrid…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…

Scaling up model depth and size is now a common approach to raise accuracy in many deep learning (DL) applications, as evidenced by the widespread success of multi-billion or even trillion parameter models in natural language processing…

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…

Numerical modelling is an essential approach to understanding the behavior of thermal plasmas in various industrial applications. We propose a deep learning method for solving the partial differential equations in thermal plasma models. In…

In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…