相关论文: Kolmogorov n-Widths for Multitask Physics-Informed…

The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new machine learning-based method is obtained by solving a…

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…

Physics-informed neural networks have proven to be a powerful tool for solving differential equations, leveraging the principles of physics to inform the learning process. However, traditional deep neural networks often face challenges in…

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatio-temporal scales have enabled the rapid advancement of data-driven and especially deep learning…

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional…

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

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.…

Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function.…

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular 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…

Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in…

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 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…

The recent development of machine learning (ML) and Deep Learning (DL) increases the opportunities in all the sectors. ML is a significant tool that can be applied across many disciplines, but its direct application to civil engineering…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

Understanding the grain morphology, orientation distribution, and crystal structure of nanocrystals is essential for optimizing the mechanical and physical properties of functional materials. Synchrotron X-ray Laue microdiffraction is a…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…