相关论文: Prediction of Dynamical Systems by Symbolic Regres…

Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…

This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…

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…

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…

A data-driven computational method is introduced to extract chemical reaction mechanisms from time series chemical concentration data. It is realized through the use of dynamic symbolic regression in which a sparse analytical form for a…

Computational fluid dynamics (CFD) analysis is widely used in engineering. Although CFD calculations are accurate, the computational cost associated with complex systems makes it difficult to obtain empirical equations between system…

The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…

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…

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…

General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input…

Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets…

Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions,…

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…

Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…

Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…

Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…

Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…