**4. Conclusions**

Empirical models are proposed for the prediction of downdraft biomass gasifiers' outlet values (in particular the product gas composition). Both linear and quadratic expressions are considered, and a model reduction method is implemented based on cross validation with the LASSO method in order to select subsets of important parameters so that the resulting expressions can be simplified. This identifies significant parameters and reduces the number of parameters which must be regressed. We believe this is the first application of this LASSO model reduction method in the field of biomass gasification which is generally formulated in terms of linear models (combining Equations (1) and

(4)) [19] but can also be used for more complex quadratic equations (see Equations (2) and (5)), as demonstrated here.

This model reduction is particularly important for quadratic expressions which can contain a large number of parameters. For example, in the case study considered here, there are 11 inputs and a quadratic expression including all combinations of these 11 (as in Equation (2)) would have 78 different parameters to fit, but following the model reduction in the case study, there were 5–10 parameters needing to be identified. Considering the training data set contained only 25 data points, this means fitting the full quadratic expression with 78 parameters would not have been feasible.

In addition to reducing the complexity of fitted correlations, it is shown here that in almost all the outputs in the case study, the model reduction also leads to improved model prediction accuracy when the models were evaluated using test set data (which has not been used for training the models).

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/su132112191/s1, Excel data file including "experimentaldatafull" tab containing experimental data gathered from [12,21–23], "fig5+fig6" tab containing the data used to plot Figures 5 and 6, "fig7+fig8+fig9 data" tab containing data used to plot Figures 7–9, and "fitted reduced model parameters" tab containing the fitted parameters for the models given in Table 2.

**Author Contributions:** Conceptualization, M.B. and H.M.U.A.; methodology, M.B.; validation, M.B.; data curation, M.B.; writing—original draft preparation, M.B.; writing—review and editing, M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Experimental data used to build models can be found in [12], and data and models can also be found in the Supplementary file and in [21–23].

**Acknowledgments:** Support is acknowledged from the SRD scholarship, Dongguk University-Seoul, Seoul, South Korea.

**Conflicts of Interest:** The authors declare no conflict of interest.
