A dimension-reduced neural network-assisted approximate Bayesian computation for inverse heat conduction problems

Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.

Improving Approximate Bayesian Computation with Pre-judgment Rule

Approximate Bayesian Computation(ABC)is a popular approach for Bayesian modeling,when these models exhibit an intractable likelihood.However,during each proposal of ABC,a great number of simulators are required and each simulation is always time-consuming.The overall goal of this work is to avoid inefficient computational cost of ABC.A pre-judgment rule(PJR)is proposed,which mainly aims to judge the acceptance condition using a small fraction of simulators instead of the whole simulators,thus achieving less computational complexity.In addition,it provided a theoretical study of the error bounded caused by PJR Strategy.Finally,the methodology was illustrated with various examples.The empirical results show both the effectiveness and efficiency of PJR compared with the previous methods.

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system.Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed,which verifies the effectiveness of the proposed method.Finally,a partial response sample of the regular and chaotic responses,determined by the maximum Lyapunov exponent,is applied to detect whether chaotic motion occurs in them by a 0-1 test.This paper can provide a reference for data-based parameter iden-tification and chaotic prediction of chaotic vibration energy harvester systems.

Data-Driven Model Falsification and Uncertainty Quantification for Fractured Reservoirs

Many properties of natural fractures are uncertain,such as their spatial distribution,petrophysical properties,and fluid flow performance.Bayesian theorem provides a framework to quantify the uncertainty in geological modeling and flow simulation,and hence to support reservoir performance predictions.The application of Bayesian methods to fractured reservoirs has mostly been limited to synthetic cases.In field applications,however,one of the main problems is that the Bayesian prior is falsified,because it fails to predict past reservoir production data.In this paper,we show how a global sensitivity analysis(GSA)can be used to identify why the prior is falsified.We then employ an approximate Bayesian computation(ABC)method combined with a tree-based surrogate model to match the production history.We apply these two approaches to a complex fractured oil and gas reservoir where all uncertainties are jointly considered,including the petrophysical properties,rock physics properties,fluid properties,discrete fracture parameters,and dynamics of pressure and transmissibility.We successfully identify several reasons for the falsification.The results show that the methods we propose are effective in quantifying uncertainty in the modeling and flow simulation of a fractured reservoir.The uncertainties of key parameters,such as fracture aperture and fault conductivity,are reduced.

Parapatric speciation with recurrent gene flow of two sexual dichromatic pheasants

Understanding speciation has long been a fundamental goal of evolutionary biology.It is widely accepted that speciation requires an interruption of gene flow to generate strong reproductive isolation between species.The mechanism of how speciation in sexually dichromatic species operates in the face of gene flow remains an open question.Two species in the genus Chrysolophus,the Golden Pheasant(C.pictus)and Lady Amherst’s Pheasant(C.amherstiae),both of which exhibit significant plumage dichromatism,are currently parapatric in southwestern China with several hybrid recordings in field.In this study,we estimated the pattern of gene flow during the speciation of the two pheasants using the Approximate Bayesian Computation(ABC)method based on data from multiple genes.Using a newly assembled de novo genome of Lady Amherst’s Pheasant and resequencing of widely distributed individuals,we reconstructed the demographic history of the two pheasants by the PSMC(pairwise sequentially Markovian coalescent)method.The results provide clear evidence that the gene flow between the two pheasants was consistent with the predictions of the isolation with migration model during divergence,indicating that there was long-term gene flow after the initial divergence(ca.2.2 million years ago).The data further support the occurrence of secondary contact between the parapatric populations since around 30 kya with recurrent gene flow to the present,a pattern that may have been induced by the population expansion of the Golden Pheasant in the late Pleistocene.The results of the study support the scenario of speciation between the Golden Pheasant and Lady Amherst’s Pheasant with cycles of mixing-isolation-mixing,possibly due to the dynamics of geographical context in the late Pleistocene.The two species provide a good research system as an evolutionary model for testing reinforcement selection in speciation.