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Gas-particle flows are commonly simulated through two-fluid model at industrial-scale. However, these simulations need very fine grid to have accurate flow predictions, which is prohibitively demanding in terms of computational resources.…

In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive…

Quantum Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are scalable and robust, existing QGNNs often lack…

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal…

Link prediction is a fundamental problem in many graph based applications, such as protein-protein interaction prediction. Graph neural network (GNN) has recently been widely used for link prediction. However, existing GNN based link…

The prediction non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied…

Generative adversarial networks (GANs), modeled as a zero-sum game between a generator (G) and a discriminator (D), allow generating synthetic data with formal guarantees. Noting that D is a classifier, we begin by reformulating the GAN…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular,…

We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of the finite element method, we consider…

Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…

Multi-task learning through composite loss functions is fundamental to modern deep learning, yet optimizing competing objectives remains challenging. We present new theoretical and practical approaches for addressing directional conflicts…

Graph Neural Network (GNN) is an emerging technique for graph-based learning tasks such as node classification. In this work, we reveal the vulnerability of GNN to the imbalance of node labels. Traditional solutions for imbalanced…

Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…

This paper approaches the unsupervised learning problem by gradient descent in the space of probability density functions. A main result shows that along the gradient flow induced by a distribution-dependent ordinary differential equation…