Related papers: An Introduction to MMPDElab
A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three aligned classes: MPOLY for CPU execution,…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
Active inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference. Active inference has seen growing applications in…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…
In this work, we present MOLPIPx, a versatile library designed to seamlessly integrate Permutationally Invariant Polynomials (PIPs) with modern machine learning frameworks, enabling the efficient development of linear models, neural…
The concept of dynamical movement primitives (DMPs) has become popular for modeling of motion, commonly applied to robots. This paper presents a framework that allows a robot operator to adjust DMPs in an intuitive way. Given a generated…
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as…
Mixture models are powerful statistical models used in many applications ranging from density estimation to clustering and classification. When dealing with mixture models, there are many issues that the experimenter should be aware of and…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
Molecular simulation is a scientific tool dealing with challenges in material science and biology. This is reflected in a permanent development and enhancement of algorithms within scientific simulation packages. Here, we present…
In recent years, machine learning potentials (MLPs) have become indispensable tools in physics, chemistry, and materials science, driving the development of software packages for molecular dynamics (MD) simulations and related applications.…
Point cloud video representation learning is challenging due to complex structures and unordered spatial arrangement. Traditional methods struggle with frame-to-frame correlations and point-wise correspondence tracking. Recently, partial…
Within the MNPBEM toolbox, developed for the simulation of plasmonic nanoparticles using a boundary element method approach, we show how to include substrate and layer structure effects. We develop the methodology for solving Maxwell's…
Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modifications for the nonlocal Helmholtz equation with general…