Related papers: Discovering Asymptotic Expansions Using Symbolic R…
In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features…
Rejective sampling improves design and estimation efficiency of single-phase sampling when auxiliary information in a finite population is available. When such auxiliary information is unavailable, we propose to use two-phase rejective…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…
Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this…
Symbolic regression (SR) seeks to recover closed-form mathematical expressions that describe observed data. While existing methods have advanced the discovery of either explicit mappings (i.e., $y = f(\mathbf{x})$) or discovering implicit…
We showcase the potential of symbolic regression as an analytic method for use in materials research. First, we briefly describe the current state-of-the-art method, genetic programming-based symbolic regression (GPSR), and recent advances…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
We consider the Helmholtz equation in an angular sector partially covered by a homogeneous layer of small thickness, denoted $\varepsilon$. We propose in this work an asymptotic expansion of the solution with respect to $\varepsilon$ at any…
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.…
Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and…
Extracting interpretable equations from observational datasets to describe complex natural phenomena is one of the core goals of artificial intelligence. This field is known as symbolic regression (SR). In recent years, Transformer-based…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…
In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value…