Related papers: Solving Nonlinear PDEs with Sparse Radial Basis Fu…

Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function…

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

Diffusion probabilistic models (DPMs) are widely adopted for their outstanding generative fidelity, yet their sampling is computationally demanding. Polynomial-based multistep samplers mitigate this cost by accelerating inference; however,…

We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

For learning problem of Radial Basis Function Process Neural Network (RBF-PNN), an optimization training method based on GA combined with SA is proposed in this paper. Through building generalized Fr\'echet distance to measure similarity…

A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…

Radar-based perception has gained increasing attention in autonomous driving, yet the inherent sparsity of radars poses challenges. Radar raw data often contains excessive noise, whereas radar point clouds retain only limited information.…

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…

We introduce a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing…

In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…

We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…

We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this…

Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…

The analysis of neural network training beyond their linearization regime remains an outstanding open question, even in the simplest setup of a single hidden-layer. The limit of infinitely wide networks provides an appealing route forward…

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…