Related papers: Solving Partial Differential Equations on Evolving…
In this paper we study the performance of the Projected Gradient Descent(PGD) algorithm for $\ell_{p}$-constrained least squares problems that arise in the framework of Compressed Sensing. Relying on the Restricted Isometry Property, we…
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…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
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…
Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime…
We propose Differentiable Surface Splatting (DSS), a high-fidelity differentiable renderer for point clouds. Gradients for point locations and normals are carefully designed to handle discontinuities of the rendering function.…
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
In this thesis a probabilistic framework is developed and proposed for Dynamic Object Recognition in 3D Environments. A software package is developed using C++ and Python in ROS that performs the detection and tracking task. Furthermore, a…
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…