Related papers: Bridging Traditional and Machine Learning-based Al…

In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\mathbb{R}^d$. Our method…

Ensemble learning methods are designed to benefit from multiple learning algorithms for better predictive performance. The tradeoff of this improved performance is slower speed and larger size of ensemble learning systems compared to single…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on $[-R_m,R_m]$ and fixed,…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Probabilistic Face Embeddings (PFE) can improve face recognition performance in unconstrained scenarios by integrating data uncertainty into the feature representation. However, existing PFE methods tend to be over-confident in estimating…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…

In recent years, researchers pay growing attention to the few-shot learning (FSL) task to address the data-scarce problem. A standard FSL framework is composed of two components: i) Pre-train. Employ the base data to generate a CNN-based…

The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…

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…

Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…