This paper shows the prediction of a critical transition from time-series data generated by LTspice, employing parameter space estimation. By conceptualizing the critical transition as a bifurcation phenomenon, we can predict the critical transition by constructing a bifurcation diagram utilizing time-series datasets procured prior to the transition. The target dataset, comprised of time-series data sets, is generated by LTspice whose electronic circuit represents the critical transition inherent in a vegetation biomass model. Numerical experiments show the capability to predict the critical transition by estimating a parameter space only from the generated datasets. In addition, we compare results detected using an early warning signal and predicted using the parameter space estimation.

We describe the reconstruction of bifurcation diagrams using an extreme learning machine with a pruning algorithm. We can reconstruct the bifurcation diagram from only some time-series data by using a neural network. However, the reconstruction accuracy is influenced by the structure of the neural network. To improve reconstruction accuracy we apply a pruning algorithm to the neural network used for the reconstruction of bifurcation diagrams. In this study, we use a pruned extreme learning machine (ELM) based on sensitivity analysis. In numerical experiments, first we compare time-series predictions using the ELM with and without the pruning algorithm. Then, we show the effectiveness of the pruned extreme learning machine for the reconstruction of bifurcation diagrams.

A scientific parallel processor called the R256 has been developed. The R256 is composed of 16x16 processing elements, and has the outstanding features of a “distributed parallel network” as well as on IEEE 80-bit extended floating point computation ability. The computation accuracy, required by an exhaustive number of iterations in scientific computations, is resolved by the dedicated 80-bit VLSI processor, which was developed here for the R256. The innovative distributed parallel network was designed so as to effectively resolve heavy communication problems, which are found in applications based on the Monte Carlo simulation technique. The R256 network was very economical at a hardware cost of √N-folds (16 folds in this case) to that of an ideal full-crossbar switch, at the same time keeping the rates comparable to that of an ideal switch. The R256 demonstrates high performance of 2-GB/s data transfer rates and 500-MFLOPS computation rates on a semiconductor device simulation application.