相关论文: Generative ODE Modeling with Known Unknowns

Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

Dynamical systems governed by ordinary differential equations (ODEs) serve as models for a vast number of natural and social phenomena. In this work, we offer a fresh perspective on the classical problem of imputing missing time series…

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

In this paper, we propose to model the video dynamics by learning the trajectory of independently inverted latent codes from GANs. The entire sequence is seen as discrete-time observations of a continuous trajectory of the initial latent…

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…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

Ordinary differential equation (ODE) is an important tool to study the dynamics of a system of biological and physical processes. A central question in ODE modeling is to infer the significance of individual regulatory effect of one signal…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…

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…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

Modern high-throughput biological datasets with thousands of perturbations provide the opportunity for large-scale discovery of causal graphs that represent the regulatory interactions between genes. Differentiable causal graphical models…

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…