Related papers: RelaxNet: A structure-preserving neural network to…

Federated Learning aims to train distributed deep models without sharing the raw data with the centralized server. Similarly, in distributed inference of neural networks, by partitioning the network and distributing it across several…

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…

In this paper we consider utilizing a residual neural network (ResNet) to solve ordinary differential equations. Stochastic gradient descent method is applied to obtain the optimal parameter set of weights and biases of the network. We…

The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…

Autoregressive learning of time-stepping operators provides an effective approach to data-driven partial differential equation (PDE) simulation, yet for conservation laws, they face a fundamental challenge: learned updates may violate…

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in…

This paper presents a novel framework of neural networks for isotropic hyperelasticity that enforces necessary physical and mathematical constraints while simultaneously satisfying the universal approximation theorem. The two key…

Electroencephalography (EEG) offers non-invasive, real-time mental workload assessment, which is crucial in high-stakes domains like aviation and medicine and for advancing brain-computer interface (BCI) technologies. This study introduces…

Optimizing deformation energies over a mesh, in two or three dimensions, is a common and critical problem in physical simulation and geometry processing. We present three new improvements to the state of the art: a barrier-aware line-search…

The ResNet and its variants have achieved remarkable successes in various computer vision tasks. Despite its success in making gradient flow through building blocks, the simple shortcut connection mechanism limits the ability of…

Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high…

We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to…

The approximation capabilities of Deep Q-Networks (DQNs) are commonly justified by general Universal Approximation Theorems (UATs) that do not leverage the intrinsic structural properties of the optimal Q-function, the solution to a Bellman…

We introduce a generalised relaxation-time-approximation form of the collision term in the Boltzmann kinetic equation that allows for using different relaxation times for elastic and inelastic collisions. The efficacy of the proposed…

We propose a structured prediction architecture, which exploits the local generic features extracted by Convolutional Neural Networks and the capacity of Recurrent Neural Networks (RNN) to retrieve distant dependencies. The proposed…

We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation…

We introduce BumpNet, a sparse multilayer perceptron (MLP) framework for PDE numerical solution and operator learning. BumpNet is based on basis function expansion, which makes them superficially similar to radial-basis function (RBF)…

Despite the rapid progress of neuromorphic computing, inadequate capacity and insufficient representation power of spiking neural networks (SNNs) severely restrict their application scope in practice. Residual learning and shortcuts have…

Robotic motion-planning problems, such as a UAV flying fast in a partially-known environment or a robot arm moving around cluttered objects, require finding collision-free paths quickly. Typically, this is solved by constructing a graph,…

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM…