Related papers: Discovering Interpretable Ordinary Differential Eq…

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…

We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…

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 a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…

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…

Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…

Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…

In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

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…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…

We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

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…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…