#version 430
// Ultra-adaptive step size control with ML-enhanced prediction
// Includes memory-aware optimization and neural network-based step prediction
layout(local_size_x = 64, local_size_y = 1, local_size_z = 1) in;
// Error estimates from multiple previous steps
layout(std430, binding = 0) buffer ErrorHistoryBuffer {
float error_history[]; // Last 8 error estimates per system
};
// Step size history
layout(std430, binding = 1) buffer StepHistoryBuffer {
float step_history[]; // Last 8 step sizes per system
};
// Problem characteristics
layout(std430, binding = 2) buffer ProblemCharBuffer {
float problem_char[]; // [stiffness, nonlinearity, sparsity, dimension_factor]
};
// Neural network weights for step prediction
layout(std430, binding = 3) buffer NeuralWeightsBuffer {
float nn_weights[]; // Pre-trained NN weights for step prediction
};
// Output: new step sizes
layout(std430, binding = 4) buffer NewStepSizeBuffer {
float new_step_size[];
};
// Step acceptance flags
layout(std430, binding = 5) buffer AcceptanceBuffer {
int accepted[];
};
// Memory usage tracking
layout(std430, binding = 6) buffer MemoryUsageBuffer {
float memory_usage[]; // Current GPU memory usage per system
};
// Performance metrics
layout(std430, binding = 7) buffer PerformanceBuffer {
float performance_metrics[]; // [throughput, cache_hit_rate, bandwidth_util]
};
uniform float safety_factor;
uniform float min_factor;
uniform float max_factor;
uniform float error_tolerance;
uniform float pi_alpha;
uniform float pi_beta;
uniform int num_systems;
uniform float memory_pressure_threshold; // Trigger memory-aware optimization
uniform bool enable_neural_prediction; // Enable ML-based prediction
uniform bool enable_memory_optimization; // Enable memory-aware step sizing
// Shared memory for neural network computation
shared float shared_nn_input[64 * 16]; // Input features
shared float shared_nn_hidden[64 * 8]; // Hidden layer
shared float shared_nn_output[64]; // Output predictions
// Simple neural network forward pass
float neural_network_predict(uint system_id, float features[12]) {
uint tid = gl_LocalInvocationID.x;
// Input layer to hidden layer
for (int h = 0; h < 8; h++) {
float sum = 0.0;
for (int i = 0; i < 12; i++) {
float weight = nn_weights[h * 12 + i];
sum += features[i] * weight;
}
// ReLU activation
shared_nn_hidden[tid * 8 + h] = max(0.0, sum + nn_weights[96 + h]); // bias
}
barrier();
// Hidden layer to output
float output = 0.0;
for (int h = 0; h < 8; h++) {
float weight = nn_weights[104 + h]; // output weights start at index 104
output += shared_nn_hidden[tid * 8 + h] * weight;
}
// Sigmoid activation for step size factor
output = 1.0 / (1.0 + exp(-output));
return output;
}
// Memory-aware step size adjustment
float memory_aware_adjustment(uint system_id, float base_factor) {
if (!enable_memory_optimization) return base_factor;
float mem_usage = memory_usage[system_id];
float throughput = performance_metrics[system_id * 3 + 0];
float cache_hit_rate = performance_metrics[system_id * 3 + 1];
float bandwidth_util = performance_metrics[system_id * 3 + 2];
// Memory pressure factor (reduce step size when memory is constrained)
float memory_factor = 1.0;
if (mem_usage > memory_pressure_threshold) {
memory_factor = 0.5 + 0.5 * (1.0 - mem_usage);
}
// Performance-based adjustment
float perf_factor = 1.0;
if (cache_hit_rate < 0.8) {
perf_factor *= 0.9; // Reduce step size for poor cache performance
}
if (bandwidth_util > 0.9) {
perf_factor *= 0.8; // Reduce step size when bandwidth saturated
}
return base_factor * memory_factor * perf_factor;
}
void main() {
uint index = gl_GlobalInvocationID.x;
if (index >= num_systems) return;
// Get current error and step size
float current_error = error_history[index * 8 + 7]; // Most recent error
float current_step = step_history[index * 8 + 7]; // Most recent step
// Check if step should be accepted
bool accept_step = current_error <= error_tolerance;
accepted[index] = accept_step ? 1 : 0;
float factor = safety_factor;
if (enable_neural_prediction && current_error > 0.0) {
// Prepare features for neural network
float features[12];
// Error history features (last 4 errors)
for (int i = 0; i < 4; i++) {
features[i] = error_history[index * 8 + 4 + i];
}
// Step size history features (last 4 steps)
for (int i = 0; i < 4; i++) {
features[4 + i] = step_history[index * 8 + 4 + i];
}
// Problem characteristics
for (int i = 0; i < 4; i++) {
features[8 + i] = problem_char[index * 4 + i];
}
// Get neural network prediction
float nn_factor = neural_network_predict(index, features);
// Combine traditional PI controller with neural prediction
float error_ratio = current_error / error_tolerance;
float pi_factor = safety_factor * pow(1.0 / error_ratio, pi_alpha);
// Add integral term
if (error_history[index * 8 + 6] > 0.0) {
float prev_error_ratio = error_history[index * 8 + 6] / error_tolerance;
float integral_term = pow(error_ratio / prev_error_ratio, pi_beta);
pi_factor *= integral_term;
}
// Weighted combination of PI controller and neural prediction
float nn_weight = 0.3; // 30% neural network, 70% traditional controller
factor = (1.0 - nn_weight) * pi_factor + nn_weight * nn_factor;
} else {
// Traditional PI controller
float error_ratio = current_error / error_tolerance;
factor = safety_factor * pow(1.0 / error_ratio, pi_alpha);
// Add integral term
if (error_history[index * 8 + 6] > 0.0) {
float prev_error_ratio = error_history[index * 8 + 6] / error_tolerance;
float integral_term = pow(error_ratio / prev_error_ratio, pi_beta);
factor *= integral_term;
}
}
// Apply memory-aware adjustments
factor = memory_aware_adjustment(index, factor);
// Clamp the factor to reasonable bounds
factor = clamp(factor, min_factor, max_factor);
// Special handling for rejected steps
if (!accept_step) {
factor = min(factor, 0.5);
}
// Compute new step size
float new_step = current_step * factor;
// Additional safety checks
float min_step = current_step * 0.001; // Don't reduce by more than 1000x
float max_step = current_step * 20.0; // Don't increase by more than 20x
new_step = clamp(new_step, min_step, max_step);
new_step_size[index] = new_step;
}