This report was completed to analyze the cross-secitonal time series dataset AMC1 Modified.xlsx.

1 Data

	EtACAC (equiv)	Lewis Acid (equiv)	Solvent (vol)	Temp. (℃)	Time (h)	BQO (% IPC)	AMC1 (% IPC)	Dimer (% IPC)	HQN Imp	Key Imp
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Descriptive Statistics

	EtACAC (equiv)	Lewis Acid (equiv)	Solvent (vol)	Temp. (℃)	Time (h)	BQO (% IPC)	AMC1 (% IPC)	Dimer (% IPC)	HQN Imp	Key Imp
count	17.000000	17.000000	17.000000	17.000000	17.000000	17.000000	17.000000	17.000000	17.000000	17.000000
mean	1.011765	0.700000	20.411765	100.588235	6.705882	0.661765	46.412353	16.786471	4.835294	8.758235
std	0.239485	0.203101	14.495943	16.093705	3.653161	1.047707	10.824634	12.469459	2.620609	6.162751
min	0.800000	0.400000	8.000000	85.000000	3.000000	0.000000	20.420000	2.320000	2.240000	0.000000
25%	0.800000	0.500000	10.000000	85.000000	4.000000	0.100000	39.930000	4.860000	3.020000	4.960000
50%	1.000000	0.800000	10.000000	95.000000	6.000000	0.540000	44.300000	16.750000	4.360000	7.630000
75%	1.200000	0.800000	30.000000	115.000000	12.000000	0.730000	55.020000	24.700000	4.990000	14.380000
max	1.600000	1.100000	50.000000	120.000000	12.000000	4.530000	60.680000	38.950000	10.920000	19.520000

Input Variable Configuration

For reference, the following Python dictionary describes the input and output conditions indicated by the client for the optimization.

```
{
    "EtACAC (equiv)": {
        "type": "float",
        "lim": [
            0.5,
            3.0
        ],
        "sigfigs": 1
    },
    "Lewis Acid (equiv)": {
        "type": "float",
        "lim": [
            0.4,
            2.0
        ],
        "sigfigs": 1
    },
    "Solvent (vol)": {
        "type": "int",
        "lim": [
            5,
            50
        ]
    },
    "Temp. (\u2103)": {
        "type": "int",
        "lim": [
            25,
            120
        ]
    },
    "Time (h)": {
        "type": "time",
        "lim": [
            3,
            4,
            6,
            12
        ],
        "int_mapping": {
            "3": 0,
            "4": 1,
            "6": 2,
            "12": 3
        },
        "doe_int_lim": [
            0,
            3
        ]
    }
}
```

Output Variable Configuration

```
{
    "BQO (% IPC)": {
        "optimization_target": "min",
        "optimization_important": true,
        "y_bounds": [
            0,
            null
        ],
        "y_constraint": null,
        "weight": 0.5
    },
    "AMC1 (% IPC)": {
        "optimization_target": "max",
        "optimization_important": true,
        "y_bounds": [
            0,
            null
        ],
        "y_constraint": null,
        "weight": 0.9
    },
    "Dimer (% IPC)": {
        "optimization_target": "min",
        "optimization_important": true,
        "y_bounds": [
            0,
            null
        ],
        "y_constraint": null,
        "weight": 0.5
    },
    "HQN Imp": {
        "optimization_target": "min",
        "optimization_important": true,
        "y_bounds": [
            0,
            null
        ],
        "y_constraint": null,
        "weight": 0.5
    },
    "Key Imp": {
        "optimization_target": "min",
        "optimization_important": true,
        "y_bounds": [
            0,
            null
        ],
        "y_constraint": null,
        "weight": 0.5
    }
}
```

Variable Distribution

Figure 1: Each histogram indicates the frequency of variable values throughout the full dataset

Variable Association

WARNING: EtACAC (equiv) and Solvent (vol) have a correlation of 0.91

Figure 2: Values close to either -1 or 1 indicate correlation. A value of 0 indicates no correlation.

2 Variable Effects

Variable Importance

Figure 3: Variable importance is in descending order -with the most important variable at the top.

Importance Across Predictions

This beeswarm plot visualizes the feature importance from the machine learning model. Each point on the plot corresponds to a prediction made by the model. The position on the x-axis shows the impact of the feature on the model’s prediction, while the color of the point represents the value of the feature.

Importance is in descending order.

Parallel Coordinates

A parallel coordinates plot is a visualization that displays multivariate data by representing each data point as a line connecting parallel axes. On a vertical axis, each variable is represented by a horizontal line or axis. The value of the variable is plotted as a point on the axis. This allows for the comparison of multiple variables at once.

Interaction

The interaction heatmaps visualizes potential interaction effects between inputs. Higher values indicate the possibility of interaction.The interaction values are relative, and they are not definitive indicators of interaction. Check the partial dependence plots for more information.

3 Model

	Model Type
BQO (% IPC)	Gradient Boosted Trees
AMC1 (% IPC)	Gradient Boosted Trees
Dimer (% IPC)	Gradient Boosted Trees
HQN Imp	Gradient Boosted Trees
Key Imp	Gradient Boosted Trees

Observed vs. Predicted

The observed vs. predicted plot shows the model’s predictions against the actual values. The closer the points are to the diagonal line, the better the model’s predictions are at predicting the training set.

Error Summary

Table 1: These bootstrapped error metrics allow for a more comprehensive assessment of the model’s performance by considering its variability. Smaller standard deviations indicate greater confidence in the reported metric, while a larger std signals the presence of variability and potential model limitations.
		Mean	StdDev
BQO (% IPC)	mae	0.444510	0.069216
	medae	0.261022	0.064624
	mse	0.667227	0.360903
	rmse	0.783348	0.232081
	rsquared	0.354163	0.349333
AMC1 (% IPC)	mae	3.768082	0.659122
	medae	2.272002	0.908754
	mse	36.542757	12.463797
	rmse	5.970611	0.948186
	rsquared	0.668637	0.113019
Dimer (% IPC)	mae	4.384472	1.215224
	medae	2.216677	0.871223
	mse	55.313808	24.643873
	rmse	7.283778	1.507229
	rsquared	0.622021	0.168400
HQN Imp	mae	1.161839	0.109560
	medae	0.473629	0.234369
	mse	3.630523	0.855918
	rmse	1.893809	0.210314
	rsquared	0.438314	0.132421
Key Imp	mae	3.007029	0.663680
	medae	1.290539	0.629583
	mse	27.521770	10.643890
	rmse	5.158392	0.957785
	rsquared	0.230062	0.297769

Bootstrapped Error Distributions

The table above displays histograms of bootstrapped error metrics, providing a visual representation of the distribution of performance. Examine the shape of each histogram to understand the central tendency and dispersion of the error metric. A symmetrical and bell-shaped histogram suggests a stable and consistent model performance, while skewed or multi-modal distributions may indicate variability or outliers.

4 Optimal Points

	EtACAC (equiv)	Lewis Acid (equiv)	Solvent (vol)	Temp. (℃)	Time (h)	BQO (% IPC)	AMC1 (% IPC)	Dimer (% IPC)	HQN Imp	Key Imp	Type
0	2.3	0.5	49.0	120.0	4.0	1.353281	55.156666	7.940756	5.656612	0.000000	Optimal
1	2.1	0.8	34.0	118.0	6.0	1.913893	56.423599	2.668903	6.290057	11.587929	Optimal
2	2.4	1.0	27.0	34.0	3.0	0.714154	51.085278	21.338291	3.851384	12.596950	Optimal
3	2.4	1.2	17.0	65.0	3.0	0.714154	51.085278	21.338291	3.851384	12.596950	Optimal
4	1.1	0.7	17.0	84.0	12.0	0.043860	43.066807	25.331287	4.780689	3.957733	Optimal
5	1.4	2.0	32.0	120.0	4.0	1.583246	56.348412	8.207374	6.527459	5.418442	Uncertain
6	1.5	2.0	50.0	36.0	12.0	1.497841	58.229034	4.846352	6.245393	12.059023	Uncertain

These are the suggested points from the algorithm, and they include a mix of optimal and uncertain points to test.

	BQO (% IPC)	BQO (% IPC) -stdev	AMC1 (% IPC)	AMC1 (% IPC) -stdev	Dimer (% IPC)	Dimer (% IPC) -stdev	HQN Imp	HQN Imp -stdev	Key Imp	Key Imp -stdev
0	1.353281	0.720668	55.156666	2.747704	7.940754	5.670068	5.656613	1.073428	0.000000	4.426401
1	1.913893	0.909842	56.423599	2.211352	2.668901	4.453705	6.290058	0.943162	11.587931	2.814724
2	0.714154	0.775063	51.085278	1.983932	21.338289	4.580088	3.851384	0.852979	12.596950	3.117950
3	0.714154	0.762962	51.085278	1.888568	21.338289	4.513475	3.851384	0.852665	12.596950	3.057258
4	0.043860	0.513532	43.066811	2.488346	25.331285	7.110478	4.780689	0.955404	3.957733	2.831276
5	1.583246	0.942538	56.348412	3.075012	8.207374	7.006069	6.527459	0.852663	5.418442	4.111855
6	1.497841	1.148828	58.229034	2.120657	4.846352	4.460425	6.245393	1.050397	12.059023	3.575100

The table above contains the predicted outputs and along with the associated uncertainty for each point, calcualted using the bootstrapped standard deviations. A smaller standard deviation indicates greater confidence in the model’s prediction, while a larger standard deviation signals the presence of variability associated with the prediction.

	Output Optimized	EtACAC (equiv)	Lewis Acid (equiv)	Solvent (vol)	Temp. (℃)	Time (h)	BQO (% IPC)	AMC1 (% IPC)	Dimer (% IPC)	HQN Imp	Key Imp
0	BQO (% IPC)	0.5	0.6	6.0	120.0	3.0	0.000000	39.298847	21.002005	2.625654	0.485350
1	AMC1 (% IPC)	2.0	2.0	50.0	105.0	12.0	2.411254	58.527691	0.444288	5.476033	12.269161
2	Dimer (% IPC)	2.6	0.7	42.0	114.0	12.0	1.570588	57.193531	0.115234	6.573816	4.419123
3	HQN Imp	0.5	1.7	6.0	119.0	3.0	0.000000	34.954605	21.507814	2.168596	10.947542
4	Key Imp	1.0	0.6	39.0	120.0	3.0	0.748022	46.258125	23.999989	5.076136	0.000000

The table above contains the optimal points for each output variable, optimized separately. It can be helpful if you would like to see the optimal values for the outputs without considering the multi-objective trade offs.

5 Suggested Points Accross Time

Sunthetics Inc