Related papers: Encoder-decoder neural network for solving the non…

We investigate the physics-constrained training of an encoder-decoder neural network for approximating the Fokker-Planck-Landau collision operator in the 5-dimensional kinetic fusion simulation in XGC. To train this network, we propose a…

The recursive intra-frame block partitioning decision process, a crucial component of the next-generation video coding standards, exerts significant influence over the encoding time. In this paper, we propose an encoder-decoder neural…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Collisional processes are critical in the understanding of non-Maxwellian plasmas. The Landau form of the Fokker-Planck equation is the gold standard for modeling collisions in most plasmas, however O(N^2) work complexity inhibits its…

Encoder--decoder neural networks (EDNN) condense information most relevant to the output of the feedforward network to activation values at a bottleneck layer. We study the use of this architecture in emulation and interpretation of…

Materials data, especially those related to high-temperature properties, pose significant challenges for machine learning models due to extreme skewness, wide feature ranges, modality, and complex relationships. While traditional models…

The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…

Nonlinear time-dependent partial differential equations are essential in modeling complex phenomena across diverse fields, yet they pose significant challenges due to their computational complexity, especially in higher dimensions. This…

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

We propose a new encoder-decoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a…

Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, we apply discretization-invariant neural operators to learn…

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…

Integrating machine learning techniques in established numerical solvers represents a modern approach to enhancing computational fluid dynamics simulations. Within the lattice Boltzmann method (LBM), the collision operator serves as an…

A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…

Neural networks (NNs) have proven to be a viable alternative to traditional direct numerical algorithms, with the potential to accelerate computational time by several orders of magnitude. In the present paper we study the use of…

Experimental particle physics demands a sophisticated trigger and acquisition system capable to efficiently retain the collisions of interest for further investigation. Heterogeneous computing with the employment of FPGA cards may emerge as…