Differential elimination for dynamical models via projections with applications to structural identifiability

Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl

Reaction of Beta Dicalcium-Silicate and Tricalcium-Silicate With Carbon-Dioxide and Water

148 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1978.Ope

Universal solutions in nonlinear anelasticity

In this work, we examine the existence and properties of universal solutions in nonlinear incompressible isotropic anelasticity. Universal solutions are those that exist for all members of a class of materials under the imposition of suitable boundary tractions. To this end, we provide a framework under which a wide array of different anelasticity theories can be recast, and use this framework to classify all anelastic universal solutions exhibiting particular symmetries, using known families of universal solutions in classical nonlinear elasticity as a starting point. We demonstrate that all known universal solutions possess one of these particular symmetries, prove that the classical universal solution families merge according to their symmetry groups once extended to the anelastic setting, and conjecture that such symmetries are necessary features of universal solutions, and hence that our classification is complete. In the process of doing this, we discover that two of these families not only possess generic solution branches depending on arbitrary functions, but also anomalous branches outside of these whose forms are fixed up to a finite number of constants. We provide graphical representations of examples from these anomalous branches, and discuss their possible applications.</p

Differential elimination for dynamical models via projections with applications to structural identifiability

Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl