2024/02/06 by Helen M. Byrne, Heather A. Harrington, Byrne, Helen +9 · 2 citations
Engineering · #12H05 #35R30 #92B05 #93B25 #93B30 #93C20 #Advanced Control Systems Optimization #Advanced Data Processing Techniques #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Quantitative Methods (q-bio.QM) #Symbolic Computation (cs.SC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2402.04241
openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences.