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Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Mobile robots, such as ground vehicles and quadrotors, are becoming increasingly important in various fields, from logistics to agriculture, where they automate processes in environments that are difficult to access for humans. However, to…
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…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn…
Deep generative models aim to learn underlying distributions that generate the observed data. Given the fact that the generative distribution may be complex and intractable, deep latent variable models use probabilistic frameworks to learn…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Foundation models have transformed language, vision, and time series data analysis, yet progress on dynamic predictions for physical systems remains limited. Given the complexity of physical constraints, two challenges stand out. $(i)$…