Bridging the gap: Connecting math and AI for discovery

Some, however, find that bridging fields opens new realms of possibility. Henry Kvinge, who trained as a mathematician but ...
New Scientist

The sneaky maths trick for solving problems without answering them

How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...
GitHub

delay-differential-equations

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...
GitHub

A Linear Operator Library for Python

PyLops is an open-source Python library focused on providing a backend-agnostic, idiomatic, matrix-free library of linear operators and related computations. It is inspired by the iconic MATLAB Spot – ...
Monash University

Solving exponential and logarithmic equations

Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...
IEEE

Zhang Approximation Inverse (ZAI), Basis Matrix, and Simple Optimal ZAI Alternative Used for Solving Linear Matrix-Vector Equation (LMVE)

Abstract: In this paper, a new iterative algorithm for linear matrix-vector equation (LMVE) solving on the basis of Zhang approximation inverse (ZAI) is proposed. The optimal Zhang approximation ...
IEEE

A Zeroing Neural Network Approach for Calculating Time-Varying G-Outer Inverse of Arbitrary Matrix

Abstract: Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to ...
PNAS

In-context operator learning with data prompts for differential equation problems

This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.
Frontiers

A more basic modeling framework for life cycle methods to cover non-linear, dynamic, and integrated effects–looking beyond linear inverse modeling

Social life cycle assessment is used to evaluate social impact (UNEP, 2020). Life cycle costing and related methods are used to estimate the financial/economic impact (Rödger et al., 2018). Life cycle ...