相关论文: From Deterministic ODEs to Dynamic Structural Caus…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

The successful application of epidemic models hinges on our ability to estimate model parameters from limited observations reliably. An often-overlooked step before estimating model parameters consists of ensuring that the model parameters…

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the…

A new causal discovery method, Structural Agnostic Modeling (SAM), is presented in this paper. Leveraging both conditional independencies and distributional asymmetries, SAM aims to find the underlying causal structure from observational…

It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

The predominant method for evaluating the quality of causal models is to measure the graphical accuracy of the learned model structure. We present an alternative method for evaluating causal models that directly measures the accuracy of…

This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…

Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to…

Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems. Unfortunately, the underlying causal structure is often unknown, and estimating it from data…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…