🎓 Lesson 7
D4
LSTM Networks for Time-Series Grade Forecasting
An LSTM network is a type of AI model that learns patterns from sequences of data—like past ore grades over time—to predict what the grade will be next.
🎯 Learning Objectives
- ✓ Explain how LSTM memory gates preserve long-term dependencies in grade time-series data
- ✓ Design a minimal LSTM architecture (layers, units, timesteps) for a 7-day grade forecast using assay history
- ✓ Apply sequence preprocessing techniques—including normalization, sliding-window batching, and train/validation split—to blasthole assay data
- ✓ Analyze LSTM prediction errors using RMSE and directional accuracy metrics against industry-grade control thresholds
- ✓ Interpret feature importance in hybrid LSTM-attention models for identifying dominant geological drivers of grade variability
📖 Why This Matters
In grade control, delaying decisions until assay lab results arrive (3–7 days) risks misdirecting haulage, diluting mill feed, or missing high-grade zones. Real-time forecasting—using just-in-time drill-hole assays, geophysical logs, and blasthole sampling—enables dynamic stope sequencing and selective mining. LSTMs excel here because ore grades evolve gradually but non-linearly across spatial-temporal sequences: a single hole’s assay history reflects structural controls, alteration halos, and vein continuity better than static ML models. This lesson bridges AI theory with grade control practice—turning lagged data into actionable foresight.
📘 Core Principles
LSTMs process sequences step-by-step, maintaining a hidden state (hₜ) and cell state (cₜ) that evolve via three learnable gates: (1) the forget gate decides which prior memory to discard; (2) the input gate determines what new information to store; and (3) the output gate controls what to emit as the current prediction. Critically, the cell state allows gradients to flow unchanged across many timesteps—enabling learning of multi-week grade trends despite noise from assay error (~5–10% CV) or sampling bias. For geoscientists, this means modeling grade as a stochastic process with memory: today’s grade depends not just on yesterday’s, but on the entire preceding geochemical signature—e.g., As/Sb ratios, Cu/Pb spikes, or gamma-ray log trends—captured implicitly through learned embeddings.
📐 LSTM Cell Update Equations
The core LSTM computation updates internal states at each timestep t using sigmoid (σ) and tanh activations. These equations define how information flows, persists, and transforms—key for understanding sensitivity to assay window length and noise robustness.
💡 Worked Example
Problem: Given input xₜ = [0.8, −0.2] (normalized Cu and As assays), previous hidden state hₜ₋₁ = [0.1, 0.0], previous cell state cₜ₋₁ = [0.3, −0.1], and pre-trained weights (W_f = [[0.5,0.1],[0.2,0.4]], b_f = [0.0,0.0]), calculate the forget gate output fₜ.
1.
Step 1: Compute weighted sum: W_f · [xₜ; hₜ₋₁] + b_f = [[0.5,0.1],[0.2,0.4]] · [0.8,−0.2,0.1,0.0]ᵀ + [0,0] = [0.5×0.8 + 0.1×(−0.2) + 0.0, 0.2×0.8 + 0.4×(−0.2) + 0.0] = [0.38, 0.08]
2.
Step 2: Apply sigmoid: σ([0.38, 0.08]) = [1/(1+e⁻⁰·³⁸), 1/(1+e⁻⁰·⁰⁸)] ≈ [0.594, 0.520]
3.
Step 3: Element-wise multiply with cₜ₋₁: fₜ ⊙ cₜ₋₁ = [0.594×0.3, 0.520×(−0.1)] = [0.178, −0.052]
Answer:
The forget gate retains ~17.8% of the first memory component and discards 5.2% of the second—demonstrating selective retention critical for filtering assay noise while preserving structural trends.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), an LSTM model ingests daily blasthole assay batches (Cu, Au, S) from 120+ holes across a 300-m stope panel, aligned with geological domain maps and downhole gamma logs. Trained on 18 months of historical data (2022–2023), the model forecasts 3-day-ahead average grade with RMSE = 0.12 g/t Au—outperforming ARIMA (RMSE = 0.21 g/t) and reducing grade deviation in mill feed by 22%. Key engineering enablers included: (1) sliding windows of 14 timesteps (days), (2) domain-specific normalization per lithological unit, and (3) early stopping triggered by validation loss plateau—preventing overfitting to localized assay outliers.
🔧 Interactive Calculator
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