6 papers
Structural functional identifiability and model discovery in differential equation models
Torkel E Loman, Alexander P Browning, Ruth E Baker
Differential equation models are widely used to describe, interpret, and predict dynamical phenomena across science and engineering. In practice, however, the governing dynamics ar…
Reliable model selection in the presence of parameter non-identifiability
Yong See Foo, Torkel E. Loman, Alexander P. Browning +3
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that…
Learning functional components of PDEs from data using neural networks
Torkel E. Loman, Yurij Salmaniw, Antonio Leon Villares +2
Partial differential equations often contain unknown functions that are difficult or impossible to measure directly, hampering our ability to derive predictions from the model. Wor…
Exact identifiability analysis for a class of partially observed near-linear stochastic differential equation models
Alexander P Browning, Michael J Chappell, Hamid Rahkooy +2
Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be…
Functional and parametric identifiability for universal differential equations applied to chemical reaction networks
Torkel E Loman, Ruth E Baker
Mathematical modelling has traditionally relied on detailed system knowledge to construct mechanistic models. However, the advent of large-scale data collection and advances in mac…
NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
Avik Pal, Flemming Holtorf, Axel Larsson +6
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. Th…