12 papers
From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws
Rainey Lyons, Vanja Dukic, David M Bortz
Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functiona…
Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
Will Houser, Vanja Dukic, David M. Bortz
Weak Sparse Identification of Nonlinear Dynamics (WSINDy) provides a noise-robust approach for learning dynamical systems from data without requiring numerical differentiation. How…
Weak-form Extended Dynamic Mode Decomposition
Christopher W. Curtis, David M. Bortz
In this work, we develop a weak-form version of Extended Dynamic Mode Decomposition that we call WEDMD. We establish a number of analytic results about the method and show explicit…
Learning Effective Soliton Dynamics from Scattering Data
Seth Minor, Vanja Dukic, David M. Bortz
The inverse scattering transform (IST) provides the standard theoretical framework for deriving soliton dynamics. Traditionally, such derivations have been of an analytical, rather…
Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
Moyi Tian, Daniel A. Messenger, Vanja Dukic +2
Social systems consist of networks of individuals who influence one another through social interactions. Studying how processes evolve on these networks can help us better understa…
Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics
April Tran, Terry Haut, David Bortz +1
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimizat…
Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movement
Seth Minor, Bret D. Elderd, Benjamin Van Allen +2
Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous fac…
Bias and Coverage Properties of the WENDy-IRLS Algorithm
Abhi Chawla, David M. Bortz, Vanja Dukic
The Weak form Estimation of Nonlinear Dynamics (WENDy) method is a recently proposed class of parameter estimation algorithms that exhibits notable noise robustness and computation…
Learning Structured Population Models from Data with WSINDy
Rainey Lyons, Vanja Dukic, David M. Bortz
In the context of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, es…
A practical identifiability criterion leveraging weak-form parameter estimation
Nora Heitzman-Breen, Vanja Dukic, David M. Bortz
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflec…
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…