Related papers: Discrete Empirical Interpolation Method with Upper…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive to user-specified weights and can propagate errors into the…

Diffusion Probabilistic Models (DPMs) have been recently utilized to deal with various blind image restoration (IR) tasks, where they have demonstrated outstanding performance in terms of perceptual quality. However, the task-specific…

This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete…

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Exploration is a fundamental aspect of reinforcement learning (RL), and its effectiveness is a deciding factor in the performance of RL algorithms, especially when facing sparse extrinsic rewards. Recent studies have shown the effectiveness…

A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

We present a new method of DEEM, the direct energy encircling method, for characterising the performance of fibres in most astronomical spectroscopic applications. It's a versatile platform to measure focal ratio degradation (FRD),…

Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…

Optimization algorithms with momentum, e.g., (ADAM), have been widely used for building deep learning models due to the faster convergence rates compared with stochastic gradient descent (SGD). Momentum helps accelerate SGD in the relevant…

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

We describe a new algorithm for reconstruction of Differential Emission Measures (DEMs) in the solar corona. Although a number of such algorithms currently exist, they can have difficulty converging for some cases, and can be complex, slow,…

The introduction of Physics-informed Neural Networks (PINNs) has led to an increased interest in deep neural networks as universal approximators of PDEs in the solid mechanics community. Recently, the Deep Energy Method (DEM) has been…

Let $F$ be a compact set of a Banach space $\mathcal{X}$. This paper analyses the "Generalized Empirical Interpolation Method" (GEIM) which, given a function $f\in F$, builds an interpolant $\mathcal{J}_n[f]$ in an $n$-dimensional subspace…

In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep…