相关论文: Data-driven Progressive Discovery of Physical Laws
Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
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,…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…
This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on…
We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Symbolic regression (SR) is a data analysis problem where we search for the mathematical expression that best fits a numerical dataset. It is a global optimization problem. The most popular approach to SR is by genetic programming (SRGP).…
For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a…
Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities…
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…
We introduce 'Class Symbolic Regression' (Class SR) a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each realization being governed by its own (possibly) unique set of…