October 5, 2023

Figure 1.The Elder drawback: domain, boundary situations, and the l=2 grid.

Figure 1.The Elder problem: area, boundary situations, and the l=2 grid.

Figure 2.Development in time of the Elder downside for 1-, 2-, and 3-finger options.

Figure 2.Development in time of the Elder drawback for 1-, 2-, and 3-finger solutions.

Figure three.The behavior of the feature (12) in time for the ensemble of N = 10,000 solutions. Figure 3.The habits of the characteristic (12) in time for the ensemble of N = 10,000 solutions.Figure four.The data-processing pipeline.

Figure four.The data-processing pipeline.

Figure 5.Asymmetric options at t>15 years.

Figure 5.Asymmetric options at t>15 years.

Figure 6.Examples of the curve (9) and the peaks (the x markers in red) comparable to the answer fingers. Figure 6.Examples of the curve (9) and the peaks (the x markers in red) corresponding to the solution fingers.Figure 7.Estimated number of fingers (median, min, max, and stddev) for 1- and 2-finger options.

Figure 7.Estimated variety of fingers (median, min, max, and stddev) for 1- and 2-finger options.

Figure 8.Visualization of the fingers of 2-finger solutions for a given subset of positions and strengths (the area contained in the green rectangle). The x markers in blue point out the peaks of the curve (9). Figure 8.Visualization of the fingers of 2-finger options for a given subset of positions and strengths (the space contained in the green rectangle). The x markers in blue indicate the peaks of the curve (9).Figure 9.Distributions of fingers in the ensemble of N = 10,000 options at t=3,5,7,9 years.

Figure 9.Distributions of fingers in the ensemble of N = 10,000 options at t=3,5,7,9 years.

Figure 10.The number of principal components wanted for the approximation with 95% precision.

Figure 10.The number of principal parts needed for the approximation with 95% precision.

Figure eleven.Average solutions at t=3,5,10,12 years.

Figure 11.Average solutions at t=3,5,10,12 years.

Figure 12.The first 10 principal elements at t=10 years.

Figure 12.The first 10 principal parts at t=10 years.

Figure 13.Machine studying pipeline.

Figure 13.Machine studying pipeline.

Figure 14.Accuracy of the Type I mannequin: imply values and 95% confidence intervals.

Figure 14.Accuracy of the Type I model: imply values and 95% confidence intervals.

Figure 15.Accuracy of the Type II mannequin: imply values and 95% confidence intervals.

Figure 15.Accuracy of the Type II model: mean values and 95% confidence intervals.

Figure sixteen.Feature significance at t=9 years for the Type II models (scaled to the vary [0, 1]).

Figure 16.Feature significance at t=9 years for the Type II models (scaled to the vary [0, 1]).

Figure 17.Accuracy of the Type III mannequin: mean values and 95% confidence intervals.

Figure 17.Accuracy of the Type III mannequin: imply values and 95% confidence intervals.

Table 1.Parameters of the Elder downside.

Table 1.Parameters of the Elder problem.

NameSymbolValueUnitPorosityn0.1-Molecular diffusion coefficientDm3.565× 10−6m2·s−1Viscosityμ0.001kg·m−1PermeabilityK4.845×10−13m2Max. salt mass fractionωmax20%-Min. densityρmin1000.0kg·m−3Max. densityρmax1200.0kg·m−3Gravityg9.81m·s−2Table 2.Number of nodes on the grid level l.

Table 2.Number of nodes on the grid level l.

l nx ny N ,70566,177263,4251,051,137 Table three.Hadoop cluster configuration.

ParameterValueNumber of nodes10CPU type×86_64, the mix of Intel and AMD CPUsTotal cores available208 (416 threads)Total reminiscence (RAM) available1792 GBRAM per nodefrom 128 to 256 GBHDFS storage available192 TBCluster managerYARNTable four.Steady-state solutions obtained for different Ra on the grid l=9.

Table four.Steady-state options obtained for various Ra on the grid l=9.

Ra SolutionS1S1S1S1S2S2S2S1S2S2Ra SolutionS1S3S3S2S2S2S1S1S1S1Table 5.Conditional possibilities P^(Sk|Ra) of Sk options, k={1,2,3}.

Table 5.Conditional probabilities P^(Sk|Ra) of Sk options, k={1,2,3}.

Sk|Ra S11.001.001.000.830.000.000.480.870.000.00S20.000.000.000.171.001.000.520.001.001.00S30.000.000.000.000.000.000.000.a hundred thirty.000.00Sk|Ra S10.700.000.000.130.000.000.520.710.860.65S20.300.220.040.570.870.860.330.290.one hundred forty.35S30.000.780.960.300.130.140.a hundred and forty.000.000.00Table 6.Estimated time T^ of 95% predictability in years (mean values and 95% confidence intervals).

Table 6.Estimated time T^ of 95% predictability in years (mean values and 95% confidence intervals).

Model TypeSVM ClassifierGB ClassifierRF ClassifierType I10.21 ∈9.seventy three,10.7611.09∈10.44,13.0913.13∈12.17,14.32Type II9.62∈8.ninety four,eleven.0510.57∈9.75,eleven.5212.75∈12.forty two,13.23Type III9.32∈8.ninety four,9.7410.30∈9.83 ,11.1113.31∈12.71,14.26