Algebraic identifiability of partial differential equation models

no code implementations • 6 Feb 2024 • Helen Byrne, Heather Harrington, Alexey Ovchinnikov, Gleb Pogudin, Hamid Rahkooy, Pedro Soto

This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed.

Dissipative quadratizations of polynomial ODE systems

1 code implementation • 4 Nov 2023 • Yubo Cai, Gleb Pogudin

Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side.

Identifiable specializations for ODE models

1 code implementation • 30 Aug 2023 • Alexey Ovchinnikov, Anand Pillay, Gleb Pogudin, Thomas Scanlon

The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system.

Exact hierarchical reductions of dynamical models via linear transformations

1 code implementation • 27 Jan 2023 • Alexander Demin, Elizaveta Demitraki, Gleb Pogudin

We present an algorithm which, given a polynomial ODE model, computes a longest possible chain of exact linear reductions of the model such that each reduction refines the previous one, thus giving a user control of the level of detail preserved by the reduction.

More Efficient Identifiability Verification in ODE Models by Reducing Non-Identifiability

no code implementations • 4 Apr 2022 • Ilia Ilmer, Alexey Ovchinnikov, Gleb Pogudin, Pedro Soto

Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise.

Exact linear reduction for rational dynamical systems

1 code implementation • 31 Jan 2022 • Antonio Jiménez-Pastor, Joshua Paul Jacob, Gleb Pogudin

Since rational dynamics occurs frequently in the life sciences (e. g., Michaelis-Menten or Hill kinetics), it is desirable to extend CLUE to the models with rational dynamics.

Interpretable exact linear reductions via positivity

1 code implementation • 29 Apr 2021 • Gleb Pogudin, Xingjian Zhang

We design and implement an algorithm that, given an exact linear reduction, re-parametrizes it by performing an invertible transformation of the new coordinates to improve the interpretability of the new variables.

CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations

2 code implementations • 24 Apr 2020 • Alexey Ovchinnikov, Isabel Cristina Pérez Verona, Gleb Pogudin, Mirco Tribastone

Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables.

Computing all identifiable functions of parameters for ODE models

2 code implementations • 16 Apr 2020 • Alexey Ovchinnikov, Anand Pillay, Gleb Pogudin, Thomas Scanlon

Parameter identifiability is a structural property of an ODE model for recovering the values of parameters from the data (i. e., from the input and output variables).

Effective difference elimination and Nullstellensatz

no code implementations • 4 Dec 2017 • Alexey Ovchinnikov, Gleb Pogudin, Thomas Scanlon

We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings.

Algebraic Geometry Logic 12H10, 13P25 (Primary), 14Q20, 03C10, 03C60 (Secondary)

Bounds for elimination of unknowns in systems of differential-algebraic equations

1 code implementation • 13 Oct 2016 • Alexey Ovchinnikov, Gleb Pogudin, N. Thieu Vo

The problem of finding an a priori upper bound for the number of differentiations in elimination of unknowns in a system of differential-algebraic equations (DAEs) is an important challenge, going back to Ritt (1932).

Commutative Algebra Symbolic Computation Algebraic Geometry 12H05, 12H20, 14Q20, 34A09