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The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…

In order to find a fast and reliable method for selecting metal poor galaxies (MPGs), especially in large surveys and huge database, an Artificial Neural Network (ANN) method is applied to a sample of star-forming galaxies from the Sloan…

Disorder is often considered detrimental to coherence. However, under specific conditions, it can enhance synchronization. We develop a machine-learning framework to design optimal disorder configurations that maximize phase…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in…

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring…

Artificial neural networks (ANNs) perform extraordinarily on numerous tasks including classification or prediction, e.g., speech processing and image classification. These new functions are based on a computational model that is enabled to…

Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…

Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

Parameter-efficient tuning (PET) methods fit pre-trained language models (PLMs) to downstream tasks by either computing a small compressed update for a subset of model parameters, or appending and fine-tuning a small number of new model…

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…