Related papers: Discovering Asymptotic Expansions Using Symbolic R…
In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is…
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
The long-term dynamics of particles involved in an incompressible flow with a small viscosity ($\epsilon>0$) and slow chemical reactions, is depicted by a class of stochastic reaction-diffusion-advection (RDA) equations with a fast…
We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…
Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED),…
Symbolic Regression (SR) is a machine learning approach that explores the space of mathematical expressions to identify those that best fit a given dataset, balancing both accuracy and simplicity. We apply SR to the study of Gray-Body…
Understanding the complex interactions within the microbiome is crucial for developing effective diagnostic and therapeutic strategies. Traditional machine learning models often lack interpretability, which is essential for clinical and…
In recent years, symbolic regression has been of wide interest to provide an interpretable symbolic representation of potentially large data relationships. Initially circled to genetic algorithms, symbolic regression methods now include a…
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…
The typical methods for symbolic regression produce rather abrupt changes in solution candidates. In this work, we have tried to transform symbolic regression from an optimization problem, with a landscape that is so rugged that typical…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains…