Probabilistic Graph Neural Inference for satellite anomaly response operations during mission-critical recovery windows

Introduction: A Constellation in Distress

It was 3 AM in the mission control simulation lab when I first witnessed a cascading satellite failure. During my research fellowship at the Space Systems Laboratory, we were stress-testing a new AI-driven monitoring system against historical anomaly data. The simulation showed three communication satellites in low Earth orbit beginning to experience correlated power fluctuations. Within minutes, what started as minor telemetry deviations propagated through the constellation, threatening to disrupt global positioning services for a critical maritime rescue operation.

This experience fundamentally changed my understanding of anomaly response. Traditional threshold-based alert systems had failed to capture the subtle interdependencies between satellite subsystems and across the constellation itself. While exploring graph-based representations of space systems, I discovered that the temporal propagation of anomalies followed patterns remarkably similar to information diffusion in social networks or disease spread in epidemiological models. The satellites weren’t failing in isolation—they were nodes in a complex, dynamic system where local anomalies could trigger global failures.

Through studying probabilistic graphical models and their intersection with neural networks, I realized we needed a fundamentally different approach: one that could reason about uncertainty, learn from sparse anomaly data, and make inference decisions under the extreme time constraints of mission-critical recovery windows. This article documents my journey developing Probabilistic Graph Neural Inference (PGNI) systems for satellite operations, sharing the technical insights, implementation challenges, and practical solutions discovered through months of experimentation and research.

Technical Background: The Convergence of Probability and Structure

Why Graphs for Satellites?

During my investigation of satellite telemetry data, I found that traditional time-series analysis missed crucial relational information. Satellites exist in constellations with specific orbital geometries. Their subsystems (power, thermal, communication, attitude control) interact in predictable but complex ways. Ground stations have varying visibility windows. All these relationships naturally form a multi-relational graph.

One interesting finding from my experimentation with graph representations was that even seemingly independent anomalies often shared latent structural causes. Two satellites experiencing thermal issues might be in similar orbital positions relative to the sun, or share common manufacturing batches with susceptible components. These hidden relationships became explicit in graph formulations.

The Probabilistic Imperative

Space systems operate with inherent uncertainty. Sensor noise, communication delays, and environmental unpredictability mean we rarely have complete information. Through studying Bayesian methods and variational inference, I learned that point estimates of satellite health were insufficient. We needed distributions—ways to quantify what we didn’t know.

My exploration of probabilistic deep learning revealed that combining neural networks with probability distributions created systems that could both learn complex patterns and honestly represent uncertainty. This became crucial for recovery operations where operators needed to know not just what was most likely wrong, but how confident the system was in its diagnosis.

The Neural Advantage

While traditional Bayesian networks could handle uncertainty, they struggled with the high-dimensional, non-linear relationships in modern satellite telemetry. During my experimentation with graph neural networks (GNNs), I came across their remarkable ability to learn representations that captured both node features and graph structure. The breakthrough came when I realized we could make these representations probabilistic.

Implementation Details: Building the PGNI Framework

Graph Construction from Satellite Systems

The first challenge was constructing meaningful graphs from heterogeneous satellite data. Through trial and error across multiple datasets, I developed a multi-graph approach:

import torch
import torch_geometric
from torch_geometric.data import HeteroData
import numpy as np

class SatelliteGraphBuilder:
def __init__(self, config):
self.satellite_subsystems = config['subsystems']
self.orbital_relations = config['orbital_relations']

def build_multi_relational_graph(self, telemetry_data, constellation_data):
"""Construct heterogeneous graph from satellite telemetry"""
data = HeteroData()

# Node features for each satellite
for sat_id in telemetry_data['satellites']:
# Extract multi-modal features
power_features = self._extract_power_signatures(
telemetry_data[sat_id]['power']
)
thermal_features = self._extract_thermal_patterns(
telemetry_data[sat_id]['thermal']
)
comm_features = self._extract_comm_metrics(
telemetry_data[sat_id]['communication']
)

# Concatenate with orbital parameters
orbital_params = constellation_data[sat_id]['orbital_elements']
features = torch.cat([
power_features, thermal_features,
comm_features, orbital_params
], dim=-1)

data['satellite'].x = torch.cat([
data.get('satellite').x,
features.unsqueeze(0)
]) if hasattr(data, 'satellite') else features.unsqueeze(0)

# Build multiple edge types
edge_types = [
('satellite', 'communicates_with', 'satellite'),
('satellite', 'orbital_neighbor', 'satellite'),
('satellite', 'shares_ground_station', 'satellite'),
('satellite', 'subsystem_dependency', 'satellite')
]

for edge_type in edge_types:
adj_matrix = self._compute_relation_matrix(
edge_type, telemetry_data, constellation_data
)
edge_index = self._dense_to_sparse(adj_matrix)
data[edge_type].edge_index = edge_index

return data

def _extract_power_signatures(self, power_data):
"""Extract probabilistic features from power telemetry"""
# Compute distribution parameters
mean = torch.tensor([np.mean(power_data['voltage'])])
std = torch.tensor([np.std(power_data['voltage'])])
skewness = torch.tensor([self._compute_skewness(power_data['current'])])

# Frequency domain features
fft_features = torch.abs(torch.fft.fft(
torch.tensor(power_data['voltage'])
)[:5])  # First 5 frequency components

return torch.cat([mean, std, skewness, fft_features])

Probabilistic Graph Neural Network Architecture

The core innovation came from modifying standard GNN layers to output distribution parameters rather than deterministic embeddings. My experimentation with various probabilistic formulations led to this architecture:

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.distributions import Normal, MultivariateNormal
import torch_geometric.nn as gnn

class ProbabilisticGNNLayer(gnn.MessagePassing):
def __init__(self, in_channels, out_channels, num_relations):
super().__init__(aggr='mean')
self.in_channels = in_channels
self.out_channels = out_channels

# Separate networks for mean and variance
self.mean_mlp = nn.Sequential(
nn.Linear(in_channels * 2, out_channels),
nn.ReLU(),
nn.Linear(out_channels, out_channels)
)

self.var_mlp = nn.Sequential(
nn.Linear(in_channels * 2, out_channels),
nn.ReLU(),
nn.Linear(out_channels, out_channels),
nn.Softplus()  # Ensure positive variance
)

# Relation-specific parameters
self.relation_embeddings = nn.Embedding(
num_relations, in_channels
)

def forward(self, x, edge_index, edge_type):
# Add relation embeddings to node features
x_enhanced = x + self.relation_embeddings(edge_type)

# Perform message passing
out = self.propagate(
edge_index,
x=x_enhanced,
edge_type=edge_type
)

return out

def message(self, x_i, x_j, edge_type):
# Concatenate source and target features
paired = torch.cat([x_i, x_j], dim=-1)

# Compute mean and variance
mean = self.mean_mlp(paired)
variance = self.var_mlp(paired) + 1e-6  # Add small epsilon

# Return distribution parameters
return torch.cat([mean, variance], dim=-1)

def aggregate(self, inputs, index):
# Separate mean and variance components
means = inputs[:, :self.out_channels]
variances = inputs[:, self.out_channels:]

# Aggregate using uncertainty-aware pooling
# Weight by inverse variance (more certain messages get more weight)
weights = 1.0 / (variances + 1e-6)
weighted_means = means * weights

agg_mean = torch.zeros_like(means[0])
agg_var = torch.zeros_like(variances[0])

# Scatter add for aggregation
agg_mean = agg_mean.scatter_add_(0, index, weighted_means)
agg_var = agg_var.scatter_add_(0, index, weights)

# Normalize
agg_mean = agg_mean / agg_var
agg_var = 1.0 / agg_var

return torch.cat([agg_mean, agg_var], dim=-1)

Anomaly Detection and Diagnosis Pipeline

The complete system integrates probabilistic inference with decision-making under time constraints:

class SatelliteAnomalyPGNI(nn.Module):
def __init__(self, config):
super().__init__()
self.config = config

# Probabilistic encoder
self.encoder = ProbabilisticGNNEncoder(
input_dim=config['feature_dim'],
hidden_dims=[128, 64, 32],
num_relations=config['num_relations']
)

# Temporal attention for recovery windows
self.temporal_attention = TemporalAttentionModule(
input_dim=32,
window_size=config['recovery_window']
)

# Anomaly classifier with uncertainty
self.anomaly_classifier = ProbabilisticClassifier(
in_features=32,
num_classes=config['num_anomaly_types'],
num_mc_samples=50  # Monte Carlo samples for uncertainty
)

# Causal inference module for root cause analysis
self.causal_inference = CausalGNN(
node_dim=32,
edge_dim=config['num_relations']
)

def forward(self, graph_data, historical_windows):
"""
Process satellite graph data during recovery window

Args:
graph_data: Heterogeneous graph of current state
historical_windows: List of previous graph states
Returns:
anomaly_probs: Probability distribution over anomaly types
uncertainty: Confidence metrics
root_cause: Identified causal factors
recovery_actions: Recommended actions with expected utilities
"""

# Encode current state with uncertainty
current_embeddings, current_uncertainty = self.encoder(
graph_data.x,
graph_data.edge_index,
graph_data.edge_type
)

# Incorporate temporal context
if historical_windows:
historical_embeddings = []
for hist_graph in historical_windows:
emb, _ = self.encoder(
hist_graph.x,
hist_graph.edge_index,
hist_graph.edge_type
)
historical_embeddings.append(emb)

# Apply temporal attention
contextual_embeddings = self.temporal_attention(
current_embeddings,
historical_embeddings
)
else:
contextual_embeddings = current_embeddings

# Anomaly classification with Bayesian uncertainty
anomaly_probs, epistemic_uncertainty = self.anomaly_classifier(
contextual_embeddings
)

# Perform causal inference if anomaly detected
if torch.max(anomaly_probs) > self.config['anomaly_threshold']:
root_cause = self.causal_inference(
graph_data,
contextual_embeddings
)

# Generate recovery actions
recovery_actions = self._plan_recovery_actions(
anomaly_probs,
root_cause,
current_uncertainty,
graph_data
)
else:
root_cause = None
recovery_actions = []

return {
'anomaly_probabilities': anomaly_probs,
'uncertainty': {
'epistemic': epistemic_uncertainty,
'aleatoric': current_uncertainty
},
'root_cause': root_cause,
'recovery_actions': recovery_actions,
'node_embeddings': contextual_embeddings
}

def _plan_recovery_actions(self, anomaly_probs, root_cause,
uncertainty, graph_data):
"""Generate optimal recovery actions under time constraints"""

actions = []

# Monte Carlo simulation of action outcomes
for action in self.config['available_actions']:
expected_utility = 0
risk_metrics = []

# Sample from uncertainty distributions
for _ in range(self.config['mc_samples']):
# Sample possible outcomes
outcome = self._simulate_action_outcome(
action, anomaly_probs, root_cause,
uncertainty, graph_data
)

# Compute utility (negative of expected downtime)
utility = -outcome['expected_downtime']

# Adjust for risk (variance in outcomes)
risk_adjusted_utility = utility - \
self.config['risk_aversion'] * outcome['variance']

expected_utility += risk_adjusted_utility

expected_utility /= self.config['mc_samples']

actions.append({
'action': action,
'expected_utility': expected_utility,
'time_to_execute': action['estimated_duration'],
'confidence': 1.0 - uncertainty['epistemic'].mean()
})

# Sort by utility per time unit (critical for recovery windows)
actions.sort(
key=lambda x: x['expected_utility'] / x['time_to_execute'],
reverse=True
)

return actions[:self.config['max_actions']]  # Return top recommendations

Real-World Applications: From Simulation to Operations

Mission-Critical Recovery Windows

During my research of actual satellite anomaly responses, I realized that the concept of "recovery windows" was more nuanced than simple time constraints. Different anomalies had different temporal criticality profiles. A thermal anomaly might have hours before permanent damage, while a communication failure during a critical data downlink might have only minutes of viable recovery time.

One practical insight from implementing PGNI for operational testing was that the system needed to adapt its inference strategy based on available time. When time was abundant, it could perform extensive Monte Carlo sampling and consider complex intervention sequences. During tight windows, it had to fall back to simpler, higher-certainty heuristics learned from similar historical situations.

Multi-Satellite Constellation Management

My exploration of large-scale constellation operations revealed that PGNI’s graph-based approach scaled remarkably well. The system could reason about anomalies propagating through constellations, identifying which satellites were at risk and prioritizing recovery actions to prevent cascading failures.

class ConstellationRecoveryPlanner:
def __init__(self, pgn_model, constraint_solver):
self.model = pgn_model
self.solver = constraint_solver

def optimize_recovery_sequence(self, constellation_graph,
initial_anomalies, time_budget):
"""
Optimize recovery actions across entire constellation
considering resource constraints and time windows
"""

# Identify critical paths through constellation
critical_paths = self._find_critical_propagation_paths(
constellation_graph, initial_anomalies
)

# Generate candidate actions for each affected satellite
candidate_actions = []
for sat_id, anomaly_info in initial_anomalies.items():
actions = self.model.generate_recovery_actions(
sat_id, anomaly_info
)
candidate_actions.extend(actions)

# Formulate as constrained optimization
optimization_problem = {
'variables': candidate_actions,
'constraints': [
self._time_constraint(time_budget),
self._ground_station_visibility_constraint(),
self._personnel_constraint(),
self._propellant_constraint()
],
'objective': self._minimize_total_risk
}

# Solve using hybrid approach
solution = self.solver.solve(
optimization_problem,
method='branch_and_bound_with_heuristics'
)

return self._compile_recovery_plan(solution)

Uncertainty-Aware Decision Support

Through experimentation with operator interfaces, I discovered that presenting uncertainty estimates was as important as presenting recommendations. Operators needed to know when the system was making educated guesses versus high-confidence diagnoses. The PGNI system provided calibrated confidence scores that helped operators allocate their limited attention during crises.

Challenges and Solutions: Lessons from the Trenches

Sparse Anomaly Data

One significant challenge I encountered was the extreme sparsity of actual anomaly data. Satellites are remarkably reliable, meaning we had few real anomalies to learn from. My solution involved several complementary approaches:

1. Physics-informed simulation: Creating high-fidelity simulators that could generate realistic anomaly scenarios based on first principles
2. Transfer learning: Pre-training on related domains like industrial IoT sensor networks or aircraft telemetry
3. Synthetic data generation: Using generative adversarial networks conditioned on normal operation data to create plausible anomalies

python
class AnomalyDataAugmenter:
def __init__(self, physics_simulator, gan_generator):
self.simulator = physics_simulator
self.gan = gan_generator

def generate_plausible_anomalies(self, normal_telemetry,
anomaly_type, severity):
"""Generate realistic anomaly data through multiple methods"""

# Method 1: Physics-based simulation
physics_based = self.simulator.inject_anomaly(
normal_telemetry, anomaly_type, severity
)

# Method 2: GAN-based generation
latent_vector = torch.randn(1, self.gan.latent_dim)
conditions = torch.tensor([self._anomaly_to_label(anomaly_type)])
gan_based = self.gan.generate(