Probabilistic Graph Neural Inference for planetary geology survey missions for low-power autonomous deployments

Probabilistic Graph Neural Inference for planetary geology survey missions for low-power autonomous deployments

It was during a late-night research session, poring over Martian terrain data from the Perseverance rover, that I had my breakthrough moment. I'd been struggling with how to make geological classification systems more robust for autonomous planetary missions when I realized: the problem wasn't just about individual rock samples, but about understanding the spatial relationships between geological features across an entire landscape. While exploring graph neural networks for geological mapping, I discovered that traditional deterministic approaches were fundamentally limited when dealing with the inherent uncertainty of planetary exploration.

Introduction: From Terrestrial Problems to Extraterrestrial Solutions

My journey into probabilistic graph neural networks began unexpectedly. I was working on optimizing mineral exploration algorithms for terrestrial mining operations when NASA released a new dataset of lunar surface compositions. The challenge was immediately apparent: how could we build AI systems that could autonomously map and classify geological formations with minimal human intervention while operating under severe computational constraints?

Through studying reinforcement learning for robotic exploration, I learned that the key limitation wasn't just processing power, but the ability to reason about uncertainty. Planetary rovers can't afford to be confident about wrong classifications—the cost of misinterpreting a rock formation could mean missing critical scientific discoveries or even mission failure.

Technical Background: The Marriage of Probability and Graph Structure

Why Graphs for Geology?

One interesting finding from my experimentation with geological data was that traditional convolutional neural networks struggled to capture the complex spatial relationships between different geological units. Geological formations aren't isolated—they exist in context with surrounding features, and their relationships follow specific patterns that geologists have documented for centuries.

import torch
import torch_geometric
import pyro.distributions as dist

class GeologicalGraph:
    def __init__(self, node_features, edge_index, spatial_coords):
        self.node_features = node_features  # Mineral composition, texture, etc.
        self.edge_index = edge_index        # Spatial adjacency
        self.spatial_coords = spatial_coords # GPS coordinates
        self.edge_attr = self.compute_geological_relationships()

    def compute_geological_relationships(self):
        # Calculate geological context: contact relationships,
        # stratigraphic sequences, cross-cutting relationships
        relationships = []
        for i, j in self.edge_index.t():
            dist_3d = torch.norm(self.spatial_coords[i] - self.spatial_coords[j])
            feature_similarity = torch.cosine_similarity(
                self.node_features[i], self.node_features[j], dim=0
            )
            relationships.append(torch.stack([dist_3d, feature_similarity]))
        return torch.stack(relationships)

Probabilistic Graphical Models Meet Neural Networks

During my investigation of uncertainty quantification in deep learning, I found that combining probabilistic graphical models with graph neural networks created systems that could not only make predictions but also quantify their confidence. This is crucial for autonomous systems that need to know when they're uncertain and should seek additional data.

import torch.nn as nn
import pyro
import pyro.distributions as dist
from torch_geometric.nn import GCNConv

class ProbabilisticGNN(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim):
        super().__init__()
        self.conv1 = GCNConv(input_dim, hidden_dim)
        self.conv2 = GCNConv(hidden_dim, hidden_dim)
        self.loc_layer = nn.Linear(hidden_dim, output_dim)
        self.scale_layer = nn.Linear(hidden_dim, output_dim)

    def forward(self, x, edge_index):
        x = torch.relu(self.conv1(x, edge_index))
        x = torch.relu(self.conv2(x, edge_index))

        # Output parameters for probability distribution
        loc = self.loc_layer(x)
        scale = torch.nn.functional.softplus(self.scale_layer(x))

        return loc, scale

    def guide(self, x, edge_index, y=None):
        loc, scale = self.forward(x, edge_index)
        # Use observed data if available for training
        with pyro.plate("data", x.size(0)):
            pyro.sample("obs", dist.Normal(loc, scale).to_event(1), obs=y)

Implementation Details: Building for Constrained Environments

Memory-Efficient Graph Processing

While learning about deployment constraints for space missions, I observed that memory bandwidth and power consumption are often more limiting than raw computational power. This led me to develop sparse graph processing techniques that could operate within these constraints.

class SparseProbabilisticGNN(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim, num_components=3):
        super().__init__()
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.num_components = num_components

        # Sparse message passing layers
        self.conv1 = GCNConv(input_dim, hidden_dim)
        self.conv2 = GCNConv(hidden_dim, hidden_dim)

        # Mixture density network output
        self.mdn_components = nn.Linear(hidden_dim, output_dim * num_components * 3)

    def forward(self, x, edge_index, batch_size=32):
        # Process in mini-batches to reduce memory usage
        total_nodes = x.size(0)
        outputs = []

        for i in range(0, total_nodes, batch_size):
            batch_nodes = slice(i, min(i + batch_size, total_nodes))
            batch_x = x[batch_nodes]

            # Extract subgraph for current batch
            batch_mask = torch.zeros(total_nodes, dtype=torch.bool)
            batch_mask[batch_nodes] = True

            # Sparse neighborhood sampling
            batch_edge_index = self._extract_subgraph_edges(edge_index, batch_mask)

            x_batch = torch.relu(self.conv1(batch_x, batch_edge_index))
            x_batch = torch.relu(self.conv2(x_batch, batch_edge_index))

            outputs.append(x_batch)

        return torch.cat(outputs, dim=0)

    def _extract_subgraph_edges(self, edge_index, node_mask):
        # Efficient subgraph extraction for sparse processing
        mask = node_mask[edge_index[0]] & node_mask[edge_index[1]]
        subgraph_edges = edge_index[:, mask]

        # Remap node indices to local indices
        local_indices = torch.where(node_mask)[0]
        mapping = torch.zeros(node_mask.size(0), dtype=torch.long)
        mapping[local_indices] = torch.arange(local_indices.size(0))

        return mapping[subgraph_edges]

Quantization-Aware Probabilistic Training

My exploration of low-power deployment revealed that standard quantization techniques often destroyed the subtle uncertainty estimates that make probabilistic models valuable. I developed a quantization-aware training approach specifically for probabilistic graph networks.

class QuantizedProbabilisticGNN(nn.Module):
    def __init__(self, base_model, bits=8):
        super().__init__()
        self.base_model = base_model
        self.bits = bits
        self.quant = torch.quantization.QuantStub()
        self.dequant = torch.quantization.DeQuantStub()

    def forward(self, x, edge_index):
        # Quantize inputs
        x_q = self.quant(x)

        # Forward pass through base model
        loc, scale = self.base_model(x_q, edge_index)

        # Dequantize outputs
        loc = self.dequant(loc)
        scale = self.dequant(scale)

        return loc, scale

    def prepare_quantization(self):
        self.base_model.eval()
        self.qconfig = torch.quantization.get_default_qconfig('fbgemm')
        torch.quantization.prepare(self, inplace=True)

    def convert_to_quantized(self):
        torch.quantization.convert(self, inplace=True)

# Training with quantization simulation
def train_quantization_aware(model, data_loader, epochs=100):
    model.prepare_quantization()

    for epoch in range(epochs):
        for batch in data_loader:
            # Forward pass with fake quantization
            loc, scale = model(batch.x, batch.edge_index)

            # Probabilistic loss
            distribution = dist.Normal(loc, scale)
            loss = -distribution.log_prob(batch.y).mean()

            loss.backward()
            optimizer.step()
            optimizer.zero_grad()

    model.convert_to_quantized()

Real-World Applications: From Simulation to Planetary Deployment

Geological Unit Classification with Uncertainty

In my research of autonomous geological mapping, I realized that traditional classification systems provided point estimates without confidence intervals. This made it difficult for autonomous systems to decide when to collect additional samples or seek human guidance.

class GeologicalClassifier:
    def __init__(self, model, confidence_threshold=0.8):
        self.model = model
        self.confidence_threshold = confidence_threshold
        self.rock_classes = ['basalt', 'sandstone', 'shale', 'limestone', 'anorthosite']

    def classify_formation(self, graph_data):
        with torch.no_grad():
            loc, scale = self.model(graph_data.x, graph_data.edge_index)

            # Calculate classification probabilities
            probs = torch.softmax(loc, dim=-1)
            uncertainties = scale.mean(dim=-1)

            # Decision logic based on uncertainty
            decisions = []
            for node_idx in range(len(probs)):
                max_prob, pred_class = torch.max(probs[node_idx], dim=0)
                uncertainty = uncertainties[node_idx]

                if uncertainty < self.confidence_threshold:
                    # Confident prediction
                    decision = {
                        'class': self.rock_classes[pred_class],
                        'confidence': max_prob.item(),
                        'uncertainty': uncertainty.item(),
                        'action': 'proceed'
                    }
                else:
                    # High uncertainty - flag for additional analysis
                    decision = {
                        'class': 'uncertain',
                        'confidence': max_prob.item(),
                        'uncertainty': uncertainty.item(),
                        'action': 'collect_sample'
                    }
                decisions.append(decision)

            return decisions

Adaptive Survey Planning

One interesting finding from my experimentation with rover path planning was that probabilistic GNNs could dynamically adjust survey strategies based on real-time uncertainty estimates.

class AdaptiveSurveyPlanner:
    def __init__(self, geological_model, energy_budget):
        self.model = geological_model
        self.energy_budget = energy_budget
        self.visited_locations = set()

    def plan_next_waypoint(self, current_graph, current_position):
        # Get uncertainty estimates for all nodes
        with torch.no_grad():
            _, uncertainties = self.model(current_graph.x, current_graph.edge_index)

        # Find high-uncertainty regions that are energy-feasible
        candidate_nodes = []
        for node_idx, uncertainty in enumerate(uncertainties):
            node_pos = current_graph.spatial_coords[node_idx]
            travel_cost = self.calculate_energy_cost(current_position, node_pos)

            if (travel_cost < self.energy_budget and
                node_idx not in self.visited_locations):
                candidate_nodes.append((node_idx, uncertainty, travel_cost))

        # Select target that maximizes information gain per energy unit
        if candidate_nodes:
            candidate_nodes.sort(key=lambda x: x[1] / (x[2] + 1e-6), reverse=True)
            best_node = candidate_nodes[0][0]
            self.visited_locations.add(best_node)
            self.energy_budget -= candidate_nodes[0][2]

            return best_node, current_graph.spatial_coords[best_node]

        return None, None

    def calculate_energy_cost(self, pos1, pos2):
        # Simplified energy model based on distance and terrain
        distance = torch.norm(pos1 - pos2)
        terrain_factor = 1.0  # Could incorporate slope, soil type, etc.
        return distance * terrain_factor

Challenges and Solutions: Lessons from the Trenches

The Memory-Probability Trade-off

During my investigation of probabilistic inference on resource-constrained devices, I found that the primary challenge was the memory overhead of maintaining probability distributions versus point estimates. The solution came from exploring mixture density networks and parameterized distributions.

class MemoryEfficientMixtureGNN(nn.Module):
    def __init__(self, input_dim, hidden_dim, num_classes, num_components=2):
        super().__init__()
        self.num_components = num_components

        # Shared feature extraction
        self.conv1 = GCNConv(input_dim, hidden_dim)
        self.conv2 = GCNConv(hidden_dim, hidden_dim)

        # Compact mixture parameterization
        self.mixture_params = nn.Linear(hidden_dim, num_classes * num_components * 2)

    def forward(self, x, edge_index):
        x = torch.relu(self.conv1(x, edge_index))
        x = torch.relu(self.conv2(x, edge_index))

        # Output compact mixture representation
        params = self.mixture_params(x)
        batch_size, _ = x.shape

        # Reshape to mixture components
        params = params.view(batch_size, self.num_components, -1)
        locs = params[:, :, :self.num_components]
        scales = torch.nn.functional.softplus(params[:, :, self.num_components:])

        return locs, scales

    def predict_with_uncertainty(self, x, edge_index):
        locs, scales = self.forward(x, edge_index)

        # Monte Carlo sampling for uncertainty estimation
        num_samples = 100
        samples = []

        for _ in range(num_samples):
            # Sample from mixture components
            component_probs = torch.ones(x.size(0), self.num_components) / self.num_components
            component_idx = torch.multinomial(component_probs, 1).squeeze()

            # Sample from selected components
            batch_indices = torch.arange(x.size(0))
            loc_sample = locs[batch_indices, component_idx]
            scale_sample = scales[batch_indices, component_idx]

            sample = dist.Normal(loc_sample, scale_sample).rsample()
            samples.append(sample)

        samples = torch.stack(samples)
        mean_prediction = samples.mean(dim=0)
        uncertainty = samples.std(dim=0)

        return mean_prediction, uncertainty

Handling Non-Stationary Geological Processes

Through studying geological time series data, I learned that planetary surfaces exhibit non-stationary behavior due to weathering, impacts, and other processes. This required developing time-aware graph models.

class TemporalGeologicalGNN(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim, temporal_window=5):
        super().__init__()
        self.temporal_window = temporal_window

        # Spatial graph convolutions
        self.spatial_convs = nn.ModuleList([
            GCNConv(input_dim, hidden_dim) for _ in range(temporal_window)
        ])

        # Temporal attention
        self.temporal_attention = nn.MultiheadAttention(
            hidden_dim, num_heads=4, batch_first=True
        )

        # Probabilistic output
        self.output_loc = nn.Linear(hidden_dim, output_dim)
        self.output_scale = nn.Linear(hidden_dim, output_dim)

    def forward(self, temporal_graphs):
        # Process each time step
        temporal_features = []
        for i, graph in enumerate(temporal_graphs):
            if i >= self.temporal_window:
                break
            x = torch.relu(self.spatial_convs[i](graph.x, graph.edge_index))
            temporal_features.append(x)

        # Stack temporal features
        temporal_stack = torch.stack(temporal_features, dim=1)

        # Apply temporal attention
        attended, _ = self.temporal_attention(
            temporal_stack, temporal_stack, temporal_stack
        )

        # Aggregate temporal information
        aggregated = attended.mean(dim=1)

        # Probabilistic outputs
        loc = self.output_loc(aggregated)
        scale = torch.nn.functional.softplus(self.output_scale(aggregated))

        return loc, scale

Future Directions: Where This Technology Is Heading

Quantum-Enhanced Probabilistic Inference

My exploration of quantum computing for machine learning revealed exciting possibilities for enhancing probabilistic inference. While current quantum hardware isn't ready for deployment, hybrid classical-quantum approaches show promise for the future.

# Conceptual quantum-enhanced probabilistic GNN
class QuantumEnhancedProbabilisticGNN(nn.Module):
    def __init__(self, classical_backbone, num_qubits=4):
        super().__init__()
        self.classical_backbone = classical_backbone
        self.num_qubits = num_qubits

        # Quantum circuit for uncertainty estimation
        self.quantum_circuit = self._build_quantum_circuit()

    def _build_quantum_circuit(self):
        # Placeholder for actual quantum circuit implementation
        # This would use frameworks like PennyLane or Qiskit
        circuit = QuantumCircuit(self.num_qubits)
        # Quantum gates for probability amplitude estimation
        return circuit

    def forward(self, x, edge_index):
        # Classical feature extraction
        classical_features = self.classical_backbone(x, edge_index)

        # Quantum-enhanced uncertainty estimation
        quantum_uncertainty = self.estimate_quantum_uncertainty(classical_features)

        return classical_features, quantum_uncertainty

    def estimate_quantum_uncertainty(self, features):
        # Convert classical features to quantum state preparation
        # Execute quantum circuit for probability estimation
        # Return enhanced uncertainty estimates
        return torch.ones(features.size(0)) * 0.1  # Placeholder

Federated Learning for Multi-Rover Systems

As I was experimenting with multi-agent systems, I came across the challenge of collaborative