相关论文: Enhancing Symbolic Regression and Universal Physic…

This work explores using the physics-inspired AI Feynman symbolic regression algorithm to automatically rediscover a fundamental equation in astronomy -- the Equation of the Centre. Through the introduction of observational and inductive…

Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…

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 is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression…

This paper introduces Deep Policy Iteration (DPI), a novel approach that integrates the strengths of Neural Networks with the stability and convergence advantages of Policy Iteration (PI) to address high-dimensional stochastic Mean Field…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…

The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…

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 quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…

In this paper we introduce an active learning method for symbolic regression using StackGP. The approach begins with a small number of data points for StackGP to model. To improve the model the system incrementally adds a data point such…

Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…

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…

Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to…

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built $\Phi$-SO, a Physical Symbolic…

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…