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Fast derivatives of likelihood functionals for ODE based models using adjoint-state method

Valdemar Melicher, Tom Haber, Wim Vanroose
2017 Computational statistics (Zeitschrift)  
We employ the adjoint state method (ASM) for efficient computation of the first and the second derivatives of likelihood functionals constrained by ODEs with respect to the parameters of the underlying  ...  The results are directly applicable in (e.g.) maximum-likelihood estimation or Bayesian sampling of ODE based statistical models, allowing for faster, more stable estimation of parameters of the underlying  ...  Acknowledgements We would like to thank Xavier Woot de Trixhe from Janssen Pharmaceutica for numerous very interesting discussions on PK/PD, virology, biological pathways modeling, NLMEMs and on life in  ... 
doi:10.1007/s00180-017-0765-8 fatcat:ubg5a524nfagbg22wbzf7k5vke

Optimization and uncertainty analysis of ODE models using second order adjoint sensitivity analysis [article]

Paul Stapor, Fabian Froehlich, Jan Hasenauer
2018 bioRxiv   pre-print
Motivation: Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational  ...  Thus, the proposed methods and implemented algorithms allow for the improvement of parameter estimation for medium and large scale ODE models.  ...  We provide detailed comparisons of optimization and profile likelihood calculation of the proposed approaches and state-of-the-art methods based on published models of biological processes.  ... 
doi:10.1101/272005 fatcat:valnrkzxjndjzlqecidpvg6f6u

An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling

Robin L. Raffard, Keith Amonlirdviman, Jeffrey D. Axelrod, Claire J. Tomlin
2008 IEEE Transactions on Automatic Control  
This paper presents an adjoint-based algorithm for performing automatic parameter identification on differential equation models of biological systems.  ...  The tractability and the speed of convergence (to local minima) of the algorithm are strongly favorable to numerical parameter search algorithms which do not make use of the adjoint.  ...  the benefit of using the adjoint-based method.  ... 
doi:10.1109/tac.2007.911362 fatcat:cyi6pva22zfyfhwtbtvnyzx4oi

An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling

R. L. Raffard, K. Amonlirdviman, J. D. Axelrod, C. J. Tomlin
2007 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
This paper presents an adjoint-based algorithm for performing automatic parameter identification on differential equation models of biological systems.  ...  The tractability and the speed of convergence (to local minima) of the algorithm are strongly favorable to numerical parameter search algorithms which do not make use of the adjoint.  ...  the benefit of using the adjoint-based method.  ... 
doi:10.1109/tcsi.2007.911362 fatcat:2egawhb3qzatxm4jj73opclgui

Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks [article]

Polina Lakrisenko, Paul Stapor, Stephan Grein, Łukasz Paszkowski, Dilan Pathirana, Fabian Fröhlich, Glenn Terje Lines, Daniel Weindl, Jan Hasenauer
2022 bioRxiv   pre-print
Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available.  ...  Here, we propose a new gradient computation method that facilitates the parameterization of large-scale models based on steady-state measurements.  ...  Adjoint sensitivity analysis (ASA) For large-scale ODE models, the objective function gradient for time-course data D t is usually calculated using ASA.  ... 
doi:10.1101/2022.08.08.503176 fatcat:tngl7bawg5emnl2b2ge7rzhiri

Scalable parameter estimation for genome-scale biochemical reaction networks [article]

Fabian Fröhlich, Barbara Kaltenbacher, Fabian J Theis, Jan Hasenauer
2016 bioRxiv   pre-print
We present the approach for time discrete measurement and compare it to state-of-the-art methods used in systems and computational biology.  ...  While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions  ...  These optimization methods use the gradient of the objective function to establish fast local convergence.  ... 
doi:10.1101/089086 fatcat:asebvm64h5c5nb55edh45kshji

CERENA: ChEmical REaction Network Analyzer—A Toolbox for the Simulation and Analysis of Stochastic Chemical Kinetics

Atefeh Kazeroonian, Fabian Fröhlich, Andreas Raue, Fabian J. Theis, Jan Hasenauer, Dennis Salahub
2016 PLoS ONE  
The availability of forward and adjoint sensitivity analyses allows for further studies such as parameter estimation and uncertainty analysis.  ...  The analysis of these stochastic chemical kinetics is important for understanding cell-to-cell variability and its functional implications, but it is also challenging.  ...  Acknowledgments The authors thank Ramon Grima and Philipp Thomas for discussions regarding the system size expansion.  ... 
doi:10.1371/journal.pone.0146732 pmid:26807911 pmcid:PMC4726759 fatcat:ikkfefujmngopbwjftfr6gkbcu

PARAMETER IDENTIFICATION VIA THE ADJOINT METHOD: APPLICATION TO PROTEIN REGULATORY NETWORKS

Robin L. Raffard, Keith Amonlirdviman, Jeffrey D. Axelrod, Claire J. Tomlin
2006 IFAC Proceedings Volumes  
An adjoint-based algorithm for performing automatic parameter identification on differential equation based models of biological systems is presented.  ...  Preliminary results of the application of this algorithm to a previously presented mathematical model of planar cell polarity signaling in the wings of Drosophila melanogaster are presented.  ...  ACKNOWLEDGEMENTS We would like to thank Professor Jonathan Goodman for his help on the optimization procedure.  ... 
doi:10.3182/20060402-4-br-2902.00475 fatcat:3cjx5sksczchfnvslf6q53zbii

Optimization Framework for Codesign of Controlled Aerodynamic Systems

Kuan Waey Lee, William Moase, Andrew Ooi, Chris Manzie, Eric C. Kerrigan
2016 AIAA Journal  
adjoint method.  ...  A gradient-based optimization framework is proposed for the aerodynamic shape and controller design of aerodynamic systems using computationally intensive high fidelity models.  ...  Support of BAE Systems Australia and the Defence Sciences Institute is also acknowledged.  ... 
doi:10.2514/1.j054711 fatcat:m7efactgjbftrgvujt2l6lvwca

"Hey, that's not an ODE": Faster ODE Adjoints via Seminorms [article]

Patrick Kidger and Ricky T. Q. Chen and Terry Lyons
2021 arXiv   pre-print
Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential  ...  Experiments on a wide range of tasks – including time series, generative modeling, and physical control – demonstrate a median improvement of 40 function evaluations, so that the overall training time  ...  Model-specific techniques For Neural ODEs only, Ghosh et al. (2020) Further work Our seminorm-based approach means that the integrals for a θ , a t in equation (2) are estimated based on the points  ... 
arXiv:2009.09457v2 fatcat:jelnlu5uafbf5n46o33lm72ksy

Approximate Latent Force Model Inference [article]

Jacob D. Moss, Felix L. Opolka, Bianca Dumitrascu, Pietro Lió
2022 arXiv   pre-print
Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation.  ...  Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems.  ...  For ODEs: We calculate the forward solution using an ODE solver (including memory-efficient adjoint methods).  ... 
arXiv:2109.11851v3 fatcat:fx6tcxwgcbaxznudxshy4ziiba

First-arrival traveltime tomography for anisotropic media using the adjoint-state method

Umair bin Waheed, Garret Flagg, Can Evren Yarman
2016 Geophysics  
Some of these difficulties can be addressed using the adjoint-state method, due to its low memory requirement and numerical efficiency.  ...  However, previous literature on the adjoint-state method has only addressed the isotropic approximation of the subsurface.  ...  Williams for useful discussions. We extend gratitude to K. Innanen, J. Cao, A. Bona, and S. Charles for many useful suggestions that greatly helped in improving the quality of the paper.  ... 
doi:10.1190/geo2015-0463.1 fatcat:rj3vden7fzgfhm3afjvl6ra4fy

Solving Parameter Estimation Problems with Discrete Adjoint Exponential Integrators [article]

Ulrich Roemer, Mahesh Narayanamurthi, Adrian Sandu
2017 arXiv   pre-print
This work derives the discrete adjoint formulae for a W-type exponential propagation iterative methods of Runge-Kutta type (EPIRK-W).  ...  The use of Jacobian approximation matrices that do not depend on the model state avoids the complex calculation of Hessians in the discrete adjoint formulae, and allows efficient adjoint code generation  ...  Acknowledgements The work of M. Narayanamurthi and A.  ... 
arXiv:1704.02549v1 fatcat:sbwnaekvhnh63eyf6xrvnakava

Scalable Gradients for Stochastic Differential Equations [article]

Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, David Duvenaud
2020 arXiv   pre-print
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations.  ...  In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations.  ...  We also thank Guodong Zhang, Kevin Swersky, Chris Rackauckas, and members of the Vector Institute for helpful comments on an early draft of this paper.  ... 
arXiv:2001.01328v6 fatcat:k6q44v5w5zg4jkrdn2wm32mrdi

Efficient parameterization of large-scale dynamic models based on relative measurements

2019 Bioinformatics  
We evaluate the properties of the methods by parameterizing a pan-cancer ordinary differential equation model (>1000 state variables, >4000 parameters) using relative protein, phosphoprotein and viability  ...  gradients using adjoint sensitivity analysis.  ...  Conflict of Interest: none declared.  ... 
doi:10.1093/bioinformatics/btz581 pmid:31347657 fatcat:2ffs5yjll5d57ppizerdkqs2ea
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