scholarly journals Systems biology informed deep learning for inferring parameters and hidden dynamics

2020 ◽  
Vol 16 (11) ◽  
pp. e1007575 ◽  
Author(s):  
Alireza Yazdani ◽  
Lu Lu ◽  
Maziar Raissi ◽  
George Em Karniadakis
Keyword(s):  
Deep Learning ◽  
Systems Biology ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Learning Algorithm ◽  
Optimization Procedure ◽  
System Level ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Unknown Parameters

Mathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems.

scholarly journals Systems biology informed deep learning for inferring parameters and hidden dynamics

2019 ◽  
Author(s):  
Alireza Yazdani ◽  
Lu Lu ◽  
Maziar Raissi ◽  
George Em Karniadakis
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Systems Biology ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
System Level ◽  
Model Parameters ◽  
Unknown Parameters ◽  
The Neural Networks ◽  
Noisy Measurements

AbstractMathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems.Author summaryThe dynamics of systems biological processes are usually modeled using ordinary differential equations (ODEs), which introduce various unknown parameters that need to be estimated efficiently from noisy measurements of concentration for a few species only. In this work, we present a new “systems-informed neural network” to infer the dynamics of experimentally unobserved species as well as the unknown parameters in the system of equations. By incorporating the system of ODEs into the neural networks, we effectively add constraints to the optimization algorithm, which makes the method robust to noisy and sparse measurements.

Modeling eutrophic lakes: From mass balance laws to ordinary differential equations

2017 ◽  
Vol 14 (11) ◽  
pp. 1750151
Author(s):  
Addolorata Marasco ◽  
Luciano Ferrara ◽  
Antonio Romano
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Homogeneous Model ◽  
Stable Steady State ◽  
Model Parameters ◽  
Balance Laws ◽  
State Variables ◽  
Phosphorus Cycle ◽  
Eutrophic Lakes ◽  
The Mean

Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible with the mixture theory, we prove that an ODEs model still holds but for the mean values of the state variables provided that the nonhomogeneous involved fields satisfy suitable conditions. In this model the trophic state of a lake is described by the mean densities of Phosphorus in water and sediments, and phytoplankton biomass. All the quantities appearing in the model can be experimentally evaluated. To propose restoration programs, the evolution of these state variables toward stable steady state conditions is analyzed. Moreover, the local stability analysis is performed with respect to all the model parameters. Some numerical simulations and a real application to lake Varese conclude the paper.

scholarly journals Massive MIMO Adaptive Modulation and Coding Using Online Deep Learning

2021 ◽  
Author(s):  
Evgeny Bobrov ◽  
Dmitry Kropotov ◽  
Hao Lu ◽  
Danila Zaev
Keyword(s):  
Deep Learning ◽  
Massive Mimo ◽  
Learning Algorithm ◽  
Adaptive Modulation ◽  
System Level ◽  
Adaptive Modulation And Coding ◽  
Q Learning ◽  
Deep Learning Algorithm ◽  
System Level Simulation ◽  
Fully Connected

The paper describes an online deep learning algorithm for the adaptive modulation and coding in 5G Massive MIMO. The algorithm is based on a fully connected neural network, which is initially trained on the output of the traditional algorithm and then is incrementally retrained by the service feedback of its output. We show the advantage of our solution over the state-of-the-art Q-Learning approach. We provide system-level simulation results to support this conclusion in various scenarios with different channel characteristics and different user speeds. Compared with traditional OLLA our algorithm shows 10% to 20% improvement of user throughput in full buffer case. <br>

Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation

2019 ◽  
Vol 22 (5) ◽  
pp. 1321-1350 ◽  
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Benchmark Problems ◽  
State Representation ◽  
Weakly Singular Kernel ◽  
Integration Interval ◽  
Novel Approach ◽  
Infinite State

Abstract In this paper, we propose a novel approach for the numerical solution of fractional-order ordinary differential equations. The method is based on the infinite state representation of the Caputo fractional differential operator, in which the entire history of the state of the system is considered for correct initialization. The infinite state representation contains an improper integral with respect to frequency, expressing the history dependence of the fractional derivative. The integral generally has a weakly singular kernel, which may lead to problems in numerical computations. A reformulation of the integral generates a kernel that decays to zero at both ends of the integration interval leading to better convergence properties of the related numerical scheme. We compare our method to other schemes by considering several benchmark problems.

A semi-analytic method for fractional-order ordinary differential equations: Testing results

2018 ◽  
Vol 21 (6) ◽  
pp. 1598-1618 ◽  
Author(s):  
Sergiy Reutskiy ◽  
Zhuo-Jia Fu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Fractional Order ◽  
Benchmark Problems ◽  
Analytic Method

Abstract The paper presents the testing results of a semi-analytic collocation method, using five benchmark problems published in a paper by Xue and Bai in Fract. Calc. Appl. Anal., Vol. 20, No 5 (2017), pp. 1305–1312, DOI: 10.1515/fca-2017-0068.

scholarly journals Benchmark problems for Caputo fractional-order ordinary differential equations

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Dingyü Xue ◽  
Lu Bai
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Block Diagram ◽  
Numerical Algorithms ◽  
Benchmark Problems

AbstractThere are many numerical algorithms for solving the fractional-order ordinary differential equations (FODEs). They are usually very different in nature, and it is difficult to compare their performances. To solve this problem, a set of five benchmark problems of different categories of FODEs with known analytical solution are designed and proposed, they can be used as benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is used for solving these benchmark problems, with computing errors and the running times reported.

scholarly journals A BAYESIAN APPROACH BASED ON ACQUISITION FUNCTION FOR OPTIMAL SELECTION OF DEEP LEARNING HYPERPARAMETERS: A CASE STUDY WITH ENERGY MANAGEMENT DATA

2020 ◽  
Vol 2 (1) ◽  
pp. 22-27
Author(s):  
MUHAMMAD ALI ◽  
Krishneel Prakash ◽  
Hemanshu Pota
Keyword(s):  
Deep Learning ◽  
Energy Management ◽  
Bayesian Approach ◽  
Learning Algorithm ◽  
Real Life ◽  
Model Parameters ◽  
Optimal Parameters ◽  
Comparison Results ◽  
Selection Of

With the recent rollout of smart meters, huge amount of data can be generated on hourly and daily basis. Researchers and industry persons can leverage from this big data to make intelligent decisions via deep learning (DL) algorithms. However, the performance of DL algorithms are heavily dependent on the proper selection of parameters. If the hyperparameters are poorly selected, they usually lead to suboptimal results. Traditional approaches include a manual setting of parameters by trial and error methods which is time consuming and difficult process.  In this paper, a Bayesian approach based on acquisition is presented to automatic selection of optimal parameters based on provided data. The acquisition function was established to search for the best parameter from the input space and evaluate the next points based on past observations. The tuning process identifies the best model parameters by iterating the objective function and minimizing the loss for optimizable variables such as learning rate and Hidden layersize. To validate the presented approach, we conducted a case study on real-life energy management datasets while constructing a deep learning model on MATLAB platform. A performance comparison was drawn with random parameters and optimal parameters selected by presented approach. The comparison results illustrate that the presented approach is effective as it brings a notable improvement in the performance of learning algorithm.

scholarly journals A Novel Distribution and Optimization Procedure of Boundary Conditions to Enhance the Classical Perturbation Method Applied to Solve Some Relevant Heat Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
M. A. Fariborzi Araghi ◽  
J. Huerta-Chua ◽  
M. A. Sandoval-Hernandez ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Optimization Procedure ◽  
Optimized Distribution

This work introduces a novel modification of classical perturbation method (PM), denominated Optimized Distribution of Boundary Conditions Perturbation Method (ODBCPM) with the purpose to improve the performance of PM in the solution of ordinary differential equations (ODES). We will see that the main proposal of ODBCPM rests above all in the redistribution and optimization of the boundary conditions of the problem to be solved among the iterations of the proposed method. The solution of a couple of heat relevant problems indicates the potentiality of ODBCPM even for the case of large values of the perturbative parameter.

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