Related papers: Equation Discovery for Nonlinear System Identifica…

Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space are usually used to study the solution structure such as…

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited…

Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in…

The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…

The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast…

This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…

We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for…

In this paper, we address the problem of identifying linear structural equation models. We first extend the edge set half-trek criterion to cover a broader class of models. We then show that any semi-Markovian linear model can be…

Process discovery is a family of techniques that helps to comprehend processes from their data footprints. Yet, as processes change over time so should their corresponding models, and failure to do so will lead to models that under- or…

The quality of a model resulting from (black-box) system identification is highly dependent on the quality of the data that is used during the identification procedure. Designing experiments for linear time-invariant systems is well…

A core task in process mining is process discovery which aims to learn an accurate process model from event log data. In this paper, we propose to use (block-) structured programs directly as target process models so as to establish…

A novel adaptive identifier is developed for nonlinear time-delay systems composed of linear, Lipschitz and non-Lipschitz components. To begin with, an identifier is designed for uncertain systems with a priori known delay values, and then…

Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…