Related papers: PIETOOLS 2022: User Manual
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and…
While traditional machine learning can effectively tackle a wide range of problems, it primarily operates within a closed-world setting, which presents limitations when dealing with streaming data. As a solution, incremental learning…
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…
Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering…
Executing a control sequence requires computation. While this is a simple observation, developing a framework that relates a controller's required computation to its ability to successfully control a system (e.g. lower control cost) is…
This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
MLOps tools enable continuous development of machine learning, following the DevOps process. Different MLOps tools have been presented on the market, however, such a number of tools often create confusion on the most appropriate tool to be…
Summary: ipd is an open-source R software package for the downstream modeling of an outcome and its associated features where a potentially sizable portion of the outcome data has been imputed by an artificial intelligence or machine…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
In practical applications of machine learning, it is necessary to look beyond standard metrics such as test accuracy in order to validate various qualitative properties of a model. Partial dependence plots (PDP), including instance-specific…
Machine learning is a general-purpose technology holding promises for many interdisciplinary research problems. However, significant barriers exist in crossing disciplinary boundaries when most machine learning tools are developed in…
This paper introduces PROOFTOOL, the graphical user interface for the General Architecture for Proof Theory (GAPT) framework. Its features are described with a focus not only on the visualization but also on the analysis and transformation…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
Multi-objective evolutionary algorithms (MOEAs) have emerged as powerful tools for solving complex optimization problems characterized by multiple, often conflicting, objectives. While advancements have been made in computational efficiency…
High-quality ordinary differential equation (ODE) solver libraries have a long history, going back to the 1970s. Over the past several years we have implemented, on top of the PETSc linear and nonlinear solver package, a new…
SModelS is an automatised tool enabling the fast interpretation of simplified model results from the LHC within any model of new physics respecting a $\mathbb{Z}_2$ symmetry. With the version 1.2 we announce several new features. First,…
A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE)…
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…