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Jan Hasenauer - One of the best experts on this subject based on the ideXlab platform.
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amici high performance sensitivity analysis for large Ordinary Differential Equation models
Bioinformatics, 2021Co-Authors: Fabian Frohlich, Daniel Weindl, Yannik Schalte, Dilan Pathirana, łukasz Paszkowski, Glenn T Lines, Paul Stapor, Jan HasenauerAbstract:SUMMARY Ordinary Differential Equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C ++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AVAILABILITY AMICI is published under the permissive BSD-3-Clause license with source code publicly available on https://github.com/AMICI-dev/AMICI. Citeable releases are archived on Zenodo. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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amici high performance sensitivity analysis for large Ordinary Differential Equation models
arXiv: Quantitative Methods, 2020Co-Authors: Fabian Frohlich, Daniel Weindl, Yannik Schalte, Dilan Pathirana, łukasz Paszkowski, Glenn T Lines, Paul Stapor, Jan HasenauerAbstract:Ordinary Differential Equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AMICI is published under the permissive BSD-3-Clause license with source code publicly available on this https URL. Citeable releases are archived on Zenodo.
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Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes
Methods in molecular biology (Clifton N.J.), 2018Co-Authors: Fabian Frohlich, Carolin Loos, Jan HasenauerAbstract:Ordinary Differential Equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.
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Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes
arXiv: Quantitative Methods, 2017Co-Authors: Fabian Frohlich, Carolin Loos, Jan HasenauerAbstract:Ordinary Differential Equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and thus gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability.
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tailored parameter optimization methods for Ordinary Differential Equation models with steady state constraints
BMC Systems Biology, 2016Co-Authors: Anna Fiedler, Sebastian Raeth, Fabian J Theis, Angelika Hausser, Jan HasenauerAbstract:Background Ordinary Differential Equation (ODE) models are widely used to describe (bio-)chemical and biological processes. To enhance the predictive power of these models, their unknown parameters are estimated from experimental data. These experimental data are mostly collected in perturbation experiments, in which the processes are pushed out of steady state by applying a stimulus. The information that the initial condition is a steady state of the unperturbed process provides valuable information, as it restricts the dynamics of the process and thereby the parameters. However, implementing steady-state constraints in the optimization often results in convergence problems.
Fabian Frohlich - One of the best experts on this subject based on the ideXlab platform.
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amici high performance sensitivity analysis for large Ordinary Differential Equation models
Bioinformatics, 2021Co-Authors: Fabian Frohlich, Daniel Weindl, Yannik Schalte, Dilan Pathirana, łukasz Paszkowski, Glenn T Lines, Paul Stapor, Jan HasenauerAbstract:SUMMARY Ordinary Differential Equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C ++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AVAILABILITY AMICI is published under the permissive BSD-3-Clause license with source code publicly available on https://github.com/AMICI-dev/AMICI. Citeable releases are archived on Zenodo. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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amici high performance sensitivity analysis for large Ordinary Differential Equation models
arXiv: Quantitative Methods, 2020Co-Authors: Fabian Frohlich, Daniel Weindl, Yannik Schalte, Dilan Pathirana, łukasz Paszkowski, Glenn T Lines, Paul Stapor, Jan HasenauerAbstract:Ordinary Differential Equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AMICI is published under the permissive BSD-3-Clause license with source code publicly available on this https URL. Citeable releases are archived on Zenodo.
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Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes
Methods in molecular biology (Clifton N.J.), 2018Co-Authors: Fabian Frohlich, Carolin Loos, Jan HasenauerAbstract:Ordinary Differential Equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.
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Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes
arXiv: Quantitative Methods, 2017Co-Authors: Fabian Frohlich, Carolin Loos, Jan HasenauerAbstract:Ordinary Differential Equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and thus gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability.
Kh L Gadzova - One of the best experts on this subject based on the ideXlab platform.
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boundary value problem with shift for a linear Ordinary Differential Equation with the operator of discretely distributed differentiation
Journal of Mathematical Sciences, 2020Co-Authors: Kh L GadzovaAbstract:In this paper, we study a boundary-value problem with local shift for a linear Ordinary Differential Equation with the operator of discretely distributed differentiation, which links values of the solution at the endpoints of the considered interval with values at interior points.
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nonlocal boundary value problem for a linear Ordinary Differential Equation with fractional discretely distributed differentiation operator
Mathematical Notes, 2019Co-Authors: Kh L GadzovaAbstract:A nonlocal boundary-value problem for a linear Ordinary Differential Equation with fractional discretely distributed differentiation operator is considered. The existence and uniqueness theorem for the solution of this problem is proved.
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boundary value problem for a linear Ordinary Differential Equation with a fractional discretely distributed differentiation operator
Differential Equations, 2018Co-Authors: Kh L GadzovaAbstract:A nonlocal boundary-value problem for a linear Ordinary Differential Equation with fractional discretely distributed differentiation operator is considered. The existence and uniqueness theorem for the solution of this problem is proved.
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boundary value problem for a linear Ordinary Differential Equation with a fractional discretely distributed differentiation operator
Differential Equations, 2018Co-Authors: Kh L GadzovaAbstract:The boundary value problem with Robin conditions has been solved for a linear Ordinary Differential Equation with a fractional discretely distributed differentiation operator. The Green function has been constructed.
Barak A Pearlmutter - One of the best experts on this subject based on the ideXlab platform.
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neural Ordinary Differential Equation based recurrent neural network model
Irish Signals and Systems Conference, 2020Co-Authors: Mansura Habiba, Barak A PearlmutterAbstract:Neural Differential Equations are a promising new member in the neural network family. They show the potential of Differential Equations for time-series data analysis. In this paper, the strength of the Ordinary Differential Equation (ODE) is explored with a new extension. The main goal of this work is to answer the following questions: (i) can ODE be used to redefine the existing neural network model? (ii) can Neural ODEs solve the irregular sampling rate challenge of existing neural network models for a continuous time series, i.e., length and dynamic nature, (iii) how to reduce the training and evaluation time of existing Neural ODE systems? This work leverages the mathematical foundation of ODEs to redesign traditional RNNs such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The main contribution of this paper is to illustrate the design of two new ODE-based RNN models (GRU-ODE model and LSTM-ODE) which can compute the hidden state and cell state at any point of time using an ODE solver. These models reduce the computation overhead of hidden state and cell state by a vast amount. The performance evaluation of these two new models for learning continuous time series with irregular sampling rate is then demonstrated. Experiments show that these new ODE based RNN models require less training time than Latent ODEs and conventional Neural ODEs. They can achieve higher accuracy quickly, and the design of the neural network is more straightforward than the previous neural ODE systems.
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neural Ordinary Differential Equation based recurrent neural network model
arXiv: Learning, 2020Co-Authors: Mansura Habiba, Barak A PearlmutterAbstract:Neural Differential Equations are a promising new member in the neural network family. They show the potential of Differential Equations for time series data analysis. In this paper, the strength of the Ordinary Differential Equation (ODE) is explored with a new extension. The main goal of this work is to answer the following questions: (i)~can ODE be used to redefine the existing neural network model? (ii)~can Neural ODEs solve the irregular sampling rate challenge of existing neural network models for a continuous time series, i.e., length and dynamic nature, (iii)~how to reduce the training and evaluation time of existing Neural ODE systems? This work leverages the mathematical foundation of ODEs to redesign traditional RNNs such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The main contribution of this paper is to illustrate the design of two new ODE-based RNN models (GRU-ODE model and LSTM-ODE) which can compute the hidden state and cell state at any point of time using an ODE solver. These models reduce the computation overhead of hidden state and cell state by a vast amount. The performance evaluation of these two new models for learning continuous time series with irregular sampling rate is then demonstrated. Experiments show that these new ODE based RNN models require less training time than Latent ODEs and conventional Neural ODEs. They can achieve higher accuracy quickly, and the design of the neural network is simpler than, previous neural ODE systems.
Jeremiah Atsu - One of the best experts on this subject based on the ideXlab platform.
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stability results of solution of non homogeneous impulsive retarded Equation using the generalized Ordinary Differential Equation
Communications in Mathematics and Applications, 2021Co-Authors: D K Igobi, Lucky I Igbinosun, Jeremiah AtsuAbstract:This work is devoted to the study of a non-homogeneous impulsive retarded Equation with bounded delays and variable impulse time using the generalized Ordinary Differential Equations (GODEs). The integral solution of the system satisfying the Caratheodory and Lipschitz conditions obtained using the fundamental matrix theorem is embedded in the space of the generalized Ordinary Differential Equations and investigate the problem of stability of the system in the Lyapunov sense. In particular, results on the necessary and sufficient conditions for stability and asymptotic stability of the impulsive retarded system via the generalized Ordinary Differential Equation are obtained. An example is used to illustration the derived theory.
