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Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural…

In this study, a deep-learning-based multi-stage network architecture called Multi-Stage Depth Prediction Network (MSDPN) is proposed to predict a dense depth map using a 2D LiDAR and a monocular camera. Our proposed network consists of a…

In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo EM stochastic algorithms were recently proposed to estimate all…

We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…

We propose a deep learning-based surrogate model for stochastic simulators. The basic idea is to use generative neural network to approximate the stochastic response. The challenge with such a framework resides in designing the network…

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…

Depth prediction is a critical problem in robotics applications especially autonomous driving. Generally, depth prediction based on binocular stereo matching and fusion of monocular image and laser point cloud are two mainstream methods.…

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

Successful machine learning on graphs or networks requires embeddings that not only represent nodes and edges as low-dimensional vectors but also preserve the graph structure. Established methods for generating embeddings require flexible…

Many scientific and engineering systems exhibit intrinsically multimodal behavior arising from latent regime switching and non-unique physical mechanisms. In such settings, learning the full conditional distribution of admissible outcomes…

Research in the past years introduced Steered Mixture-of-Experts (SMoE) as a framework to form sparse, edge-aware models for 2D- and higher dimensional pixel data, applicable to compression, denoising, and beyond, and capable to compete…

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical…

We propose a new deep learning method for tumour segmentation when dealing with missing imaging modalities. Instead of producing one network for each possible subset of observed modalities or using arithmetic operations to combine feature…

This paper presents a class of efficient manifold optimization algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational functional. Variational arguments show…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Real-world machine learning applications often face simultaneous covariate and semantic shifts, challenging traditional domain generalization and out-of-distribution (OOD) detection methods. We introduce Meta-learned Across Domain…

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and…

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced…

In this paper, we study an application of deep learning to uplink multiuser detection (MUD) for non-orthogonal multiple access (NOMA) scheme based on Welch bound equality spread multiple access (WSMA). Several non-cooperating users, each…