Search

For a wide range of applications the structure of systems like Neural Networks or complex simulations, is unknown and approximation is costly or even impossible. Black-box optimization seeks to find optimal (hyper-) parameters for these systems such that a pre-defined objective function is minimized. Polynomial-Model-Based Optimization (PMBO) is a novel blackbox optimizer that finds the minimum by fitting a polynomial surrogate to the objective function. Motivated by Bayesian optimization the model is iteratively updated according to the acquisition function Expected Improvement, thus balancing the exploitation and exploration rate and providing an uncertainty estimate of the model. PMBO is benchmarked against other state-of-the-art algorithms for a given set of artificial, analytical functions. PMBO competes successfully with those algorithms and even outperforms all of them in some cases. As the results suggest, we believe PMBO is the pivotal choice for solving blackbox optimization tasks occurring in a wide range of disciplines.

Researchers are continuously developing novel methods and algorithms in the field of applied uncertainty quantification (UQ). During the development phase of a novel method or algorithm, researchers and developers often rely on test functions taken from the literature for validation purposes. Afterward, they employ these test functions as a fair means to compare the performance of the novel method against that of the state-of-the-art methods in terms of accuracy and efficiency measures. UQTestFuns is an open-source Python3 library of test functions commonly used within the applied UQ community. Specifically, the package provides: - an implementation with minimal dependencies (i.e., NumPy and SciPy) and a common interface of many test functions available in the UQ literature - a single entry point collecting test functions and their probabilistic input specifications in a single Python package - an opportunity for an open-source contribution, supporting the implementation of new test functions and posting reference results. UQTestFuns aims to save the researchers' and developers' time from having to reimplement many of the commonly used test functions themselves.

minterpy is an open-source Python package for a multivariate generalization of the classical Newton and Lagrange interpolation schemes as well as related tasks. It is based on an optimized re-implementation of the multivariate interpolation prototype algorithm (MIP) by Hecht et al.1 and thereby provides software solutions that lift the curse of dimensionality from interpolation tasks. While interpolation occurs as the bottleneck of most computational challenges, minterpy aims to free empirical sciences from their computational limitations.

Many solutions to the computational challenges arising in the fields of computational science and engineering rely on solving interpolation tasks of highly-varying sparse and scattered data. The tasks include surrogate modeling, sparse data regression, global black-box optimization, model inference, as well as solutions for partial differential equations (PDE) on complex geometries. Interpolation tasks in multi-dimensional space typically suffer from the curse of dimensionality in which the computational cost of interpolation scales exponentially with the number of dimensions. The open-source Python package minterpy developed and maintained by the Hecht-Lab, CASUS, aims to lift the curse of dimensionality from a brand field of interpolation tasks arising across scientific disciplines.