Model Exploration and Parameter Optimization VIP Exclusive

Congratulations! The model is trained and the data is cleaned. Now let's put on our detective hat, pick up our magnifying glass, and step into the world of Model Exploration — and let the algorithm tell you directly what the optimal process parameters should be. 🕵️‍♂️

⚠️ Prerequisite: You must first have a model that is activated and fitted (Fit) in the model list on the right.
Entry: Top toolbar → expand the [Analysis & Exploration] dropdown (magnifying glass icon) → Model Exploration

🗺️ Interface Overview

Model Exploration is a "cockpit" with very high information density, divided into six major blocks:

┌─────────────────────────────────────────────────────────────────────────────┐
│  ① Axes & Model Metrics  │  ② Scatter Plot (Explore/Search)  │  ③ T-Scores  │
├─────────────────────────────────────────────────────────────────────────────┤
│  ④ 3D Optimization Surface (Loss Surface)                                   │
├─────────────────────────────────────────────────────────────────────────────┤
│  ⑤ X-Space Feature Space        │  ⑥ Y-Space Target Space                   │
│      + Violations (boundary violations)                                     │
├─────────────────────────────────────────────────────────────────────────────┤
│  ⑦ Optimization Panel                                                       │
└─────────────────────────────────────────────────────────────────────────────┘

①② The Scatter Plot and Its Two Modes

What greets your eyes is a scatter plot — this is your "treasure map". Every gray dot is one of your historical records.

Red circle (Ellipse): that is the safe harbor (confidence interval). Inside the circle is normal data; outside the circle there may be "treasure" or a "trap" (an outlier).
Red dot (Target): that is the "position" you are currently exploring.

You can switch between two modes in the top right corner:

🧭 Explore Mode: Finding the Optimal Solution

Imagine you are piloting a spaceship through the data universe.

How to play? Just drag that red dot with the mouse!
What is it for? When you move the red dot, you are actually simulating: "If my data point were at this position (T1, T2 scores), what should its original features (X) and predicted results (Y) be?"
What happens behind the scenes? The platform invokes a reverse prediction algorithm to back-calculate the raw variable values from the scores.
Real-time feedback: The X-Space & Y-Space panel below updates in real time as the red dot moves, telling you the theoretical value of every variable (such as temperature, pressure, or yield rate) at the current position.

💡 This is the magic tool for "reverse optimization": drag the red dot into the region with the highest yield rate, and the X-Space below will tell you what the raw material ratio should be at that moment!

🔍 Search Mode: Time Travel

How to play? The red dot no longer obeys your commands; it becomes click-to-select. You can click any gray historical point on the plot.
What is it for? When you click a point, the system instantly "travels back" to the moment that piece of data was generated.
The truth revealed: the panel below immediately displays all the real values of that data at the time.

💡 A typical use case: "What actually happened with that abnormal batch last time?" Click it once in Search Mode and all the parameters are clear at a glance.

③ T-Scores Score List

The top right corner shows the specific score values of the currently selected point on all principal components (t1, t2, t3 …).

In Explore Mode: shows the scores of the red dot's current position
In Search Mode: shows the real scores of that historical sample

④ 3D Optimization Surface (Loss Surface)

Below the scatter plot is a 3D response surface plot:

Axis	Meaning
X axis	`t[xComponent]` (such as t1)
Y axis	`t[yComponent]` (such as t2)
Z axis	Loss (loss value)

It lays out the "goodness" of the entire latent space as a three-dimensional terrain map — the bottom of the valley is the optimal region.

After you run the optimization, the surface also overlays the optimization path (the trajectory from the starting point to the optimal solution), and is linked with the playback control bar below.

⑤⑥ X-Space and Y-Space: Variable Spaces

This is the most central output panel of Explore Mode.

Panel	Content
X-Space (feature space)	On the left is your recipe (X variables). Shows the Raw Value (the real physical value, such as 100℃) and Bounds (upper and lower limits)
Y-Space (target space)	On the right is your target (Y variables). Shows the predicted values and their safe range

📏 How the Bounds Are Determined

By default the platform uses two sets of bounds, each of which can be toggled on or off:

Bound type	Rule
Standardized bounds	`± 1.5` (standardized scale)
Raw bounds	`mean ± 1.5 × standard deviation`

Values outside the range enter the alarm zone 🚨.

🔧 Marking Variables as MV or DV

This is a key step for the optimization feature: click the tag next to a variable to set it as:

Tag	Full name	Meaning
MV	Manipulated Variable	Manipulated variable — one you can actively adjust (such as the set temperature)
DV	Disturbance Variable	Disturbance variable — uncontrollable but affects the result (such as ambient humidity)

💡 Why is marking necessary? The optimization algorithm needs to know which variables can be adjusted and which can only be accepted. If you mistakenly mark a DV as an MV, the algorithm will give unexecutable advice such as "go adjust the ambient humidity".
For the complete methodology of variable classification, see Factory Scenario Data Modeling Guide.

⑦ Violations: Real-Time Boundary Violation List

The panel title looks like Violations (N) and lists, in real time, all variables that violate the boundary constraints at the current point.

In Explore Mode, dragging the red dot outside the reasonable range → this list immediately refreshes
Each entry indicates the variable name and which bound it violates

💡 Its practical value: the optimization algorithm may produce a point that is "mathematically optimal but physically impossible". Violations is your first checkpoint for judging "can this recommendation actually be implemented" — if the list is long, that optimal solution will be hard to realize in reality.

🚀 Optimization: The Optimization Engine

At the very bottom is the Optimization panel, responsible for automatically solving for the optimal parameters.

Parameter settings

Parameter	Range/step	Meaning
Max Iter	1 ~ 1000	Maximum number of iterations, controlling the "patience" of the search
Tol	step size about 1e-6	Convergence tolerance; smaller is more precise but slower

Running

Click Run Optimization, and the algorithm automatically searches and returns the optimal solution together with the complete optimization path trajectory.

When it finishes, the status bar shows:

✅ Optimization Converged —— converged successfully
❌ Optimization Failed: <reason> —— did not converge (you can try loosening Tol or increasing Max Iter)

Path playback

After the result is obtained, a playback control bar appears below the panel:

▶️ / ⏸️ Play/pause button —— automatically plays the entire optimization process
Slider —— drag manually to any step
Step label —— looks like 12 / 48, current step / total steps

During playback, the red dot on the scatter plot, the path on the 3D surface, and the values in X/Y-Space all change in sync, so you can clearly see "how the algorithm walked step by step to the optimal solution".

💡 Playback is not just for show: it helps you judge whether the algorithm "went astray". If the path loops around a lot before reaching the end, the optimal solution is very sensitive to the parameters and its robustness in actual production may be poor.

🧠 Companion Feature: Causal Inference (DML)

Location: The same [Analysis & Exploration] dropdown menu → Causal Inference (DML)

⚠️ Correlation ≠ causation. All the previous analyses (VIP, SHAP, correlation coefficients) tell you "who changes together with whom", not "changing whom will make the result better". DML is what bridges that gap.

How to use it

The interface provides three selectors:

Selector	Meaning
Outcome variable (Y - Outcome)	The metric you want to improve
Treatment variable (T - Treatment)	The variable you intend to "move"
Confounder feature set (W - Confounders)	Other variables that need to be controlled for (to prevent spurious correlation)

Once configured, click Run Causal Inference Engine.

💡 A typical question: "Does raising the reaction temperature really increase the yield? Or is the higher temperature just because the raw materials were better?" DML uses double machine learning to strip out confounding factors and produce an effect estimate that is closer to causal.

🎯 Complete Hands-On Workflow

1. Fit a PLS / OPLS model
        ↓
2. Enter "Model Exploration"
        ↓
3. In X-Space, mark the adjustable variables as MV and the uncontrollable ones as DV
        ↓
4. Run Optimization (adjust Max Iter / Tol as needed)
        ↓
5. Play back the optimization path to confirm the algorithm did not go astray
        ↓
6. Check Violations: are all the variables of the optimal solution within the physically feasible range?
        ↓
7. Read the Raw Value in X-Space → these are the recommended process parameters
        ↓
8. If you are unsure about causality → use "Causal Inference (DML)" for further verification
        ↓
9. Run a pilot production, collect new data, and go back to step 1 to iterate

⚠️ Usage Notes

The exploration result is the optimum "in the model's opinion", not something that is "definitely feasible in reality" — be sure to judge it together with Violations and your process know-how
Extrapolation is risky: dragging the red dot to a region far from the historical data significantly reduces the credibility of the model's predictions
DV tags must be accurate: a wrong tag will make the optimization recommendations impossible to execute
When you need temporal information: lag-type analysis requires the model to have used a "not random" split during training; see Lag Influence Analysis for details

Model Prediction (with Copy-Paste) —— The sibling of reverse prediction: predicting Y from X
Factory Scenario Data Modeling Guide —— The MV / DV / CV / PV variable classification system
Industrial Control Systems and the Data Insight Platform —— How optimization results connect to APC/RTO
S-Plot Marker Plot —— Marker screening under OPLS models

Model Exploration and Parameter Optimization VIP Exclusive ​

🗺️ Interface Overview ​

①② The Scatter Plot and Its Two Modes ​

🧭 Explore Mode: Finding the Optimal Solution ​

🔍 Search Mode: Time Travel ​

③ T-Scores Score List ​

④ 3D Optimization Surface (Loss Surface) ​

⑤⑥ X-Space and Y-Space: Variable Spaces ​

📏 How the Bounds Are Determined ​

🔧 Marking Variables as MV or DV ​

⑦ Violations: Real-Time Boundary Violation List ​

🚀 Optimization: The Optimization Engine ​

Parameter settings ​

Running ​

Path playback ​

🧠 Companion Feature: Causal Inference (DML) ​

How to use it ​

🎯 Complete Hands-On Workflow ​

⚠️ Usage Notes ​

🔗 Related Reading ​