Related papers: Model Selection for Ordinary Differential Equation…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these…
Detection of out-of-distribution (OoD) samples in the context of image classification has recently become an area of interest and active study, along with the topic of uncertainty estimation, to which it is closely related. In this paper we…
Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles, limit cycle bifurcations and multistability. The results…
Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO)…
Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…
Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel approach at the intersection of machine learning and dynamical systems theory, presenting a unique framework for classification tasks [1]. This…
A key problem in computational biology is discovering the gene expression changes that regulate cell fate transitions, in which one cell type turns into another. However, each individual cell cannot be tracked longitudinally, and cells at…
Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection,…
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…
Perception of time from sequentially acquired sensory inputs is rooted in everyday behaviors of individual organisms. Yet, most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
State-of-the-art methods for forecasting irregularly sampled time series with missing values predominantly rely on just four datasets and a few small toy examples for evaluation. While ordinary differential equations (ODE) are the prevalent…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…
Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and…