Related papers: Learning Symbolic Expressions: Mixed-Integer Formu…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Most computer algebra systems (CAS) support symbolic integration as core functionality. The majority of the integration packages use a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present…
We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…
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…
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
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,…
Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a…
Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Symbolic regression, a task discovering the formula best fitting the given data, is typically based on the heuristical search. These methods usually update candidate formulas to obtain new ones with lower prediction errors iteratively.…
In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of…
Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…
Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep…
[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…
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…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
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…
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
In this paper, we propose symbolic decision trees as surrogate models for approximating model predictive control laws. The proposed approach learns simultaneously the partition of the input domain (splitting logic) as well as local…