10 papers
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…
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…