Optimal Monomial Quadratization for ODE Systems

Bychkov, Andrey; Pogudin, Gleb

doi:10.1007/978-3-030-79987-8_9

Cited by 10 publications

(16 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The QBee algorithm and software for quadratization. To the best of our knowledge, there are two software tools that generate quadratizations of different kind: Biocham [2] and QBee [14]. We focus on QBee because of its performance, stricter optimality guarantees [13, Table 3], and its flexible algorithm design.…”

Section: [N]mentioning

confidence: 99%

“…Review of the original QBee algorithm. The QBee algorithm from [14] takes as an input a system of polynomial ODEs and produces as an output an optimal monomial quadratization (in the sense of Definition 2.2). The QBee software is implemented in Python.…”

Section: [N]mentioning

confidence: 99%

“…Both algorithms are implemented in the Biocham software [2]. We take a different approach in [13] where the quadratization problem for a polynomial system is framed as a tree exploration. The quadratization is obtained by building up rather the tree structure rather than pruning it as in [30].…”

mentioning

confidence: 99%

“…The quadratization is obtained by building up rather the tree structure rather than pruning it as in [30]. Attractive features of the resulting algorithm QBee [14] include optimality guarantees for the dimension of the lifted system and good performance in practice [13,Table 3]. Although the previous version of QBee performed well on a selection of benchmark models from synthetic biology and some academic examples, see [13], we found its applicability to engineering problems quite limited.…”

mentioning

confidence: 99%

“…Attractive features of the resulting algorithm QBee [14] include optimality guarantees for the dimension of the lifted system and good performance in practice [13,Table 3]. Although the previous version of QBee performed well on a selection of benchmark models from synthetic biology and some academic examples, see [13], we found its applicability to engineering problems quite limited. In particular, dynamical systems models of engineering systems have common features that the previous version of QBee cannot handle yet:…”

mentioning

confidence: 99%

See 4 more Smart Citations

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Bychkov¹,

Issan²,

Kramer³

et al. 2023

Preprint

View full text Add to dashboard Cite

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

show abstract

Section: [N]mentioning

confidence: 99%

Section: [N]mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Bychkov¹,

Issan²,

Kramer³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

Hemery

Fages

Soliman

2021

Computational Methods in Systems Biology

View full text Add to dashboard Cite

The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks.

show abstract

A Combinatorial Study of Async/Await Processes

Dien

Genitrini²,

Peschanski³

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

Optimal Monomial Quadratization for ODE Systems

Cited by 10 publications

References 14 publications

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

A Combinatorial Study of Async/Await Processes

Contact Info

Product

Resources

About