Octane sensitivit y (OS), de ned as the researc h o ctane n um b er (R ON) min us the motor o ctane n um b er (MON) of a giv en fuel, has gained in terest among researc hers due to its apparen t eect on kno c king conditions in in ternal com bustion engines. Comp ounds with a high OS enable higher e ciencies, esp ecially with resp ect to adv anced compression ignition engines. R ON/MON m ust b e exp erimen tally tested to determine OS; ho w ev er, the exp erimen tal metho ds utilized require a substan tial amoun t of time, a signi can t monetary in v estmen t, and sp ecialized equipmen t. T o this end, predictiv e computational mo dels trained with existing exp erimen tal data and molecular prop erties w ould allo w for the preemptiv e screening of comp ounds prior to p erforming these exp erimen ts. The presen t w ork prop oses t w o metho ds for predicting the OS of a giv en comp ound: using arti cial neural net w orks (ANNs) trained with quan titativ e structure-prop ert y relationship (QSPR) descriptors to predict R ON and MON individually to compute OS from R ON/MON predictions (deriv ed o ctane sensitivit y , dOS), and using an ANN trained with QSPR descriptors to directly predict OS. ANNs trained to predict R ON and MON ac hiev ed test set ro ot-mean-square errors (RMSEs) of 10.499 and 7.551 resp ectiv ely . dOS calculations w ere found to ha v e a test set RMSE of 6.432 while predicting OS directly resulted in a test set RMSE of 7.019, sho wing it is more b ene cial to obtain OS from R ON/MON predictions than predicting it directly . F urthermore, relationships b et w een individual QSPR descriptors and R ON/MON/OS are discussed, highligh ting correlations b et w een sp eci c molecular features and these prop erties. Keywor ds: Arti cial neural net w ork, researc h o ctane n um b er, motor o ctane n um b er, o ctane sensitivit y , quan titativ e structure-prop ert y relationship 1 In tro duction 1.1 Octane Num b er, Octane Sensitivit y Octane n um b er is represen tativ e of the ignition qualit y of a gasoline-lik e fuel in a spark ignition engine; sp eci cally , it is a measuremen t of the fuel's abilit y to resist kno c k (o ccurrence of autoignition b efore spark ignition due to high pressure) [1]. T w o distinct o ctane n um b er indices are used to quan tify kno c k, researc h o ctane n um b er (R ON) and motor o ctane n um b er (MON). R ON is t ypically utilized to represen t real-w orld engine conditions while MON is t ypically utilized to represen t high-p erformance engine conditions, and their exp erimen tal pro cedures re ect this with resp ect to Co op erativ e F uel Researc h engine inlet temp erature and rev olutions p er min ute [2] [3]. Eac h pro cedure requires t w o reference fuels to measure the R ON/MON of a giv en comp ound, the most common b eing n-heptane and iso o ctane (2,2,4-trimeth ylp en tane) whic h form a 0-100 scale. T etraeth yllead ma y b e in tro duced to iso o ctane to increase the range of the scale to 0-120. A higher v alue of R ON/MON indicates a higher resistance to kno c k. These exp erimen tal pro cedures require large quan tities of eac h reference fuel and the comp ound to b e measured (appro ximately 500 mL), as w ell as a considerable amoun t of time to carry out the pro cedures [4]. The o ctane sensitivit y (OS) of a comp ound is de ned as the dierence b et w een its R ON and MON ( RON MON ), and is used to measure the dierence in p erformance of the comp ound at v arying engine conditions. Studies ha v e sho wn that the OS of a comp ound aects its abilit y to resist kno c k at v arying pressures and temp eratures [5] [6], sp eci cally that a lo w er sensitivit y at lo w load/pressure and a higher sensitivit y at high load/pressure b oth yield a higher resistance to kno c k [7]. Kno c k is generally seen as a barrier for researc hers who w ork to w ards increasing the e ciency of spark-ignition 1 engines, and a comprehensiv e understanding of autoignition and kno c k has y et to b e ac hiev ed. It is therefore paramoun t that further studies of kno c k, including the n uanced role of OS, are p erformed to pro duce a b etter understanding of kno c k and ultimately raise the e ciency of spark-ignition engines. 1.2 F uel Prop ert y Prediction A div erse set of metho ds exists for predicting n umerous com bustion-related prop erties of h ydro carb ons and o xygenated comp ounds. Consensus mo deling, comprised of non-linear and linear mo dels, has b een utilized to predict the cetane n um b er (CN) of alk anes and cycloalk anes [8]. A dditional studies ha v e sho wn that arti cial neural net w orks (ANNs) trained using exp erimen tal data and c heminformatic descriptors can accurately predict the CN of isopara ns and diesel fuels [9]. F urthermore, ANNs trained with exp erimen tal data and quan titativ e structure-prop ert y relationship (QSPR) descriptors, n umerical v ariables describing v arious ph ysical, c hemical, and electromec hanical asp ects of a giv en comp ound, ha v e b een sho wn to accurately predict the CN of a v ariet y of molecular classes including furanic comp ounds deriv ed from renew able resources [10]. ANNs ha v e also pro v en to b e successful in predicting the R ON/MON of gasolines and gasoline blends based on c hromatographic analysis and v olumetric con ten t resp ectiv ely [11] [12], ho w ev er the application of ANNs for predicting OS is curren tly v ery limited. ANNs are capable of generalizing predictions for data not observ ed during training based on relationships it observ es b et w een m ultidimensional (m ultiv ariate) input/target training data [13]. The presen t w ork utilizes ANNs trained with exp erimen tal R ON/MON/OS and QSPR descriptors to create predictiv e mo dels for eac h prop ert y . QSPR descriptors are emplo y ed due to the extensiv e range of attributes they describ e for a giv en comp ound, allo wing the ANN to form complex correlations b et w een m ultiple comp ounds and exp erimen tal R ON/MON/OS. A dditionally , using predicted v alues of R ON/MON to deriv e OS, or deriv ed o ctane sensitivit y (dOS) ( RON predMON pred ), is in v estigated, sp eci cally whether a higher accuracy can b e ac hiev ed compared to using an ANN to predict OS directly . F urthermore, individual relationships b et w een QSPR descriptors and R ON/MON/OS are illustrated, highligh ting k ey comp onen ts of comp ounds that relate to these prop erties. 2 Exp erimen tal Pro cedure 2.1 Exp erimen tal Data Exp erimen tal data for R ON and MON w as collected from a m ultitude of sources [1, 1427], totaling in 344 unique comp ounds eac h with an exp erimen tal v alue for R ON and MON. It w as determined that m ultiple sources rep orted predicted R ON/MON data [1, 15, 27], and this data w as therefore not utilized during the ANN training pro cedure. F urthermore, comp ounds that presen ted themselv es as outliers w ere not considered during the pro cedure, sp eci cally n-do de c ane with R ON/MON v alues of -40, and unde c ane with R ON/MON v alues of -35. Up on remo ving comp ounds with predicted R ON/MON v alues and outliers the data set consisted of 308 unique comp ounds. Their OS w ere calculated giv en their exp erimen tal R ON/MON v alues ( RON expMON exp ). The 308 comp ounds in the data set w ere split in to three subsets, denoted as the training set, v alidation set, and test set, 80%, 10%, and 10% of the total data set resp ectiv ely . Comp ounds for eac h subset w ere c hosen suc h that eac h subset con tained a prop ortionally equal n um b er of comp ounds based on the range of exp erimen tal OS v alues. Eac h prop ert y (R ON/MON/OS) utilized these subsets for ANN training, and eac h subset remained constan t to ensure an adequate comparison of ANN accuracy , sp eci cally the abilit y of the ANNs to generalize predictions for data not observ ed during training (test set predictions). Simple molecular-input line-en try system (SMILES) strings w ere pro duced/aggregated for all 308 comp ounds. alvaDesc w as used to generate 5305 QSPR descriptors for eac h comp ound using the SMILES strings, forming unique sets of quan titativ e v alues for eac h comp ound (h ttps://www.alv ascience.com/alv adesc/). QSPR descriptors and kno wn exp erimen tal data for eac h comp ound represen t the input and target data used b y the ANNs during training. 2.2 Arti cial Neural Net w ork T raining Random forest regression from the Scikit-le arn Python pac k age w as utilized to rank eac h QSPR descriptor b y its corre- lation to R ON, MON, and OS, measured b y a random forest regression-deriv ed v alue, imp ortance [28]. A higher v alue of imp ortance implies a larger correlation b et w een a giv en QSPR descriptor and R ON/MON/OS [29]. The sum of all 5305 QSPR descriptor imp ortance v alues is equal to 1, for eac h prop ert y . Regression, and the subsequen t ranking of QSPR descriptors, w as p erformed with resp ect to the training and v alidation subsets. The 250 most imp ortan t QSPR descriptors for R ON, MON, and OS w ere c hosen as input v ariables for eac h prop ert y's ANN to balance accuracy and training time. Figure 1 sho ws the imp ortance v alues of the 250 most imp ortan t QSPR descriptors for R ON, MON, and OS. Including few er QSPR descriptors decreases ANN accuracy , while including more QSPR descriptors increases training time with relativ ely insigni can t impro v emen ts in ANN accuracy . App endix T ables A1, A2, and A3 list the 10 most imp ortan t descriptors for R ON, MON, and OS resp ectiv ely . ANNs w ere constructed using the ECNet Python pac k age, an op en-source Python pac k age compiled sp eci cally for constructing predictiv e mo dels for fuel prop erties [30]. The ANN arc hitecture for R ON, MON, and OS consisted of 250 2 Figure 1: QSPR descriptor imp ortance of R ON, MON, and OS, rank ed from most-to-least imp ortan t input neurons (one for eac h QSPR descriptor), t w o hidden la y ers with 128 and 64 neurons, and an output la y er with 1 neuron (corresp onding to R ON, MON, or OS). The recti ed linear unit activ ation function w as used at eac h la y er with the exception of the output la y er whic h utilized a linear scaling function. The bac kpropagation algorithm in conjunction with the A dam optimization function w ere used for regression with h yp er-parameter v alues of 0:9 for b eta 1 ,0:999 for b eta 2 ,1:0e8 for epsilon ,0:01 for le arning r ate , and 0:0 for learning rate deca y [31]. ANNs for eac h prop ert y regressed with resp ect to the training subset. After eac h training iteration (ep o c h), the mean squared error of the v alidation subset's predictions w ere ev aluated; training w as terminated once p erformance ceased to impro v e for the v alidation subset to prev en t o v er tting. P erformance of the ANN w as determined giv en the ro ot mean-squared error (RMSE) of predictions for the test set, pro viding a metric for ho w w ell the ANNs are able to generalize predictions for data not observ ed during training. 25 ANNs w ere constructed for eac h prop ert y to ensure consistency in results. In addition to constructing ANNs for OS, the ANNs constructed to predict R ON and MON w ere used to deriv e OS from R ON/MON predictions, denoted as deriv ed o ctane sensitivit y dOS ( dOS =RON predMON pred ). 25 calculations of dOS w ere p erformed for eac h subset as a result of the 25 ANNs trained for R ON and MON. The RMSEs of eac h subset w ere compared to the subset RMSEs resulting from ANNs trained directly with exp erimen tal OS data. 3 Results and Discussion Figures 2(a-d) sho w parit y plots for training, v alidation, and test set predictions, a v eraged across 25 trained ANNs, for R ON, MON, dOS, and OS. The test set RMSEs for R ON, MON, dOS, and S w ere found to b e 10.499, 7.551, 6.432, and 7.019 resp ectiv ely . Cen ter dashed lines represen t 1:1 parit y , and outside dashed lines represen t  the test set's RMSE. It is seen that the test set RMSE for dOS is lo w er than the test set RMSE for OS, indicating that deriving OS from R ON and MON predictions is more b ene cial than predicting OS directly; ho w ev er, it is apparen t that b oth metho ds for predicting OS are relativ ely similar in accuracy , highligh ting the viabilit y of b oth metho ds. Figures 3(a) and 3(b) sho w the relationships b et w een R ON/MON and GA TS2m, a QSPR descriptor of high imp ortance to b oth R ON and MON. Geary auto correlation indices, suc h as GA TS2m, are quan ti able measuremen ts of resem blance in neigh b oring p oin t v alues; when auto correlation indices are used with resp ect to comp ound structure, they indicate rep eating patterns within a giv en comp ound [32]. F urthermore, a higher v alue of the auto correlation index implies a more signi can t resem blance in neigh b oring atoms [33]. The visual relationships of GA TS2m, an auto correlation index w eigh ted b y mass, to b oth R ON and MON indicate that a comp ound with a more uniform distribution of mass (similar mass distributions at neigh b oring atoms) leads to the comp ound ha ving a lo w er v alue of R ON/MON. Figure 3(c) sho ws the relationship b et w een OS and nCsp2, a descriptor with high imp ortance relativ e to OS. nCsp2 measures the n um b er of sp2h ybridized carb on atoms in a giv en comp ound. An sp2h ybridized carb on atom will ha v e (1) electrons with a higher p oten tial energy than a non-h ybridized carb on atom, and (2) trigonal structures, resulting in three b onds to the h ybridized atom and b ond angles of 120 degrees. Figure 3(d) illustrates the distribution of OS at v arying v alues of nCsp2. F or eac h distribution, top and b ottom bars represen t the minim um and maxim um v alues of OS, the cen ter bar illustrates the median v alue of OS, and the width of distribution sho ws the o v erall distribution of OS. It is observ ed that comp ounds with 2 and 4 sp2h ybridized carb on atoms tend to ha v e higher v alues of OS; sp eci c in terpretations of the signi cance of a comp ound con taining 2 or 4 sp2h ybridized carb on atoms as it relates to OS ha v e y et to b e form ulated, and w arran ts further studies in to ho w comp ound structure aects OS. 3 Figure 2: P arit y plots sho wing predicted vs. exp erimen tal v alues for the training, v alidation, and test subsets for (a) R ON, (b) MON, (c) dOS, and (d) OS Figure 3: (a) relationship b et w een R ON and GA TS2m (b) relationship b et w een MON and GA TS2m (c) relationship b et w een OS and nCsp2 (d) distribution of OS at v arying v alues of nCsp2 4 4 Conclusions and Recommendations Based on the results outlined in the presen t w ork, it can b e concluded that:  A ccurate predictiv e mo dels can b e constructed for R ON and MON, with test set RMSEs of 10.499 and 7.551 resp ectiv ely .  Predictiv e mo dels can b e constructed for OS; moreo v er, while using R ON/MON predictions to deriv e OS predic- tions sho ws more accuracy than predicting OS directly , b oth metho ds pro v e viable.  There is an in v erse relationship b et w een mass uniformit y within a comp ound and its R ON/MON.  Comp ounds with 2 or 4 sp2h ybridized carb on atoms tend to ha v e a higher OS. It is recommended that (1) the prop osed mo dels b e utilized for screening comp ounds theorized to result from renew able resources to accelerate the disco v ery of cleaner, more e cien t, and economically viable alternativ es to gasoline, and (2) further analysis b e p erformed with resp ect to QSPR-prop ert y relationships, sp eci cally to iden tify k ey structural comp onen ts that relate to R ON/MON/OS.