相关论文: Inferring the Structure of Ordinary Differential E…

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…

Explaining and reasoning about processes which underlie observed black-box phenomena enables the discovery of causal mechanisms, derivation of suitable abstract representations and the formulation of more robust predictions. We propose to…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

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 propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…

We propose SYRAN, an unsupervised anomaly detection method based on symbolic regression. Instead of encoding normal patterns in an opaque, high-dimensional model, our method learns an ensemble of human-readable equations that describe…

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…

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve…

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…

Explaining and reasoning about processes which underlie observed black-box phenomena enables the discovery of causal mechanisms, derivation of suitable abstract representations and the formulation of more robust predictions. We propose to…

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which…

A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in…

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…

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…

Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…