250 citations · 546 across the 17 of their papers we have counts for
17 papers
Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling
Daniel Messenger, Daniel Serino, Balu Nadiga +1
Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in…
Learning interpretable closures for thermal radiation transport in optically-thin media using WSINDy
Daniel Messenger, Ben Southworth, Hans Hammer +1
We introduce an equation learning framework to identify a closed set of equations for moment quantities in 1D thermal radiation transport (TRT) in optically thin media. While optic…
WENDy for Nonlinear-in-Parameters ODEs
Nic Rummel, Daniel A. Messenger, Stephen Becker +2
The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equati…
Learning Physically Interpretable Atmospheric Models from Data with WSINDy
Seth Minor, Daniel A. Messenger, Vanja Dukic +1
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 surr…
The Weak Form Is Stronger Than You Think
Daniel A. Messenger, April Tran, Vanja Dukic +1
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the his…
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Christophe Bonneville, Xiaolong He, April Tran +10
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in…
Coarse-Graining Hamiltonian Systems Using WSINDy
Daniel A. Messenger, Joshua W. Burby, David M. Bortz
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle syst…
Weak-Form Latent Space Dynamics Identification
April Tran, Xiaolong He, Daniel A. Messenger +2
Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this pape…
Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics
David M. Bortz, Daniel A. Messenger, Vanja Dukic
We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differen…
Asymptotic consistency of the WSINDy algorithm in the limit of continuum data
Daniel A. Messenger, David M. Bortz
In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations fro…
Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
Daniel A. Messenger, Graycen E. Wheeler, Xuedong Liu +1
Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it has proven challenging to infer the inter…
Online Weak-form Sparse Identification of Partial Differential Equations
Daniel A. Messenger, Emiliano Dall'Anese, David M. Bortz
This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WS…
Learning Mean-Field Equations from Particle Data Using WSINDy
Daniel A. Messenger, David M. Bortz
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number …
Weak SINDy For Partial Differential Equations
Daniel A. Messenger, David M. Bortz
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…
Weak SINDy: Galerkin-Based Data-Driven Model Selection
Daniel A. Messenger, David M. Bortz
We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a n…
Equilibria of an aggregation model with linear diffusion in domains with boundaries
Daniel A. Messenger, Razvan C. Fetecau
We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Throug…
Zero-diffusion Limit for Aggregation Equations over Bounded Domains
Razvan C. Fetecau, Hui Huang, Daniel Messenger +1
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in […