Related papers: Genetic Programming Based Symbolic Regression for …
Learning symbolic expressions directly from experiment data is a vital step in AI-driven scientific discovery. Nevertheless, state-of-the-art approaches are limited to learning simple expressions. Regressing expressions involving many…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…
Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
Genetic Algorithms are a popular set of optimization algorithms often used to aid software testing. However, no work has been done to apply systematic software testing techniques to genetic algorithms because of the stochasticity and the…
We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
Symbolic regression, as one of the most crucial tasks in AI for science, discovers governing equations from experimental data. Popular approaches based on genetic programming, Monte Carlo tree search, or deep reinforcement learning learn…
Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular,…
In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled…
We introduce a composition-weighted symbolic regression framework for interpretable prediction of materials properties directly from chemical composition. The method jointly learns analytical functional forms and task-dependent elemental…
In this work, we show how a genetic algorithm (GA) can be used to find step-by-step solutions to introductory physics problems. Our perspective is that the underlying task for this is one of finding a sequence of equations that will lead to…
The research community continues to seek increasingly more advanced synthetic data generators to reliably evaluate the strengths and limitations of machine learning methods. This work aims to increase the availability of datasets…
We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally…
In this paper a data mining approach for variable selection and knowledge extraction from datasets is presented. The approach is based on unguided symbolic regression (every variable present in the dataset is treated as the target variable…
Artificial intelligence techniques are increasingly being applied to solve control problems, but often rely on black-box methods without transparent output generation. To improve the interpretability and transparency in control systems,…