albert/docs/cache.html at main · PimDeWitte/albert · GitHub

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<!DOCTYPE html>
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    <title>Trajectory Caching System - Albert Framework</title>
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<body>
    <h1>Trajectory Caching System</h1>
    <p class="subtitle">PyTorch-Powered Performance Acceleration for Gravitational Physics Simulations</p>

    <div class="hero-stats">
        <h2>Performance vs. Geodesic Integration</h2>
        <div class="stats-grid">
            <div class="stat-box">
                <span class="stat-number">29,323x</span>
                <span class="stat-label">Faster than RK8 Integration</span>
            </div>
            <div class="stat-box">
                <span class="stat-number">8.6ms</span>
                <span class="stat-label">vs 4+ min computation</span>
            </div>
            <div class="stat-box">
                <span class="stat-number">13,702x</span>
                <span class="stat-label">Average Speedup</span>
            </div>
            <div class="stat-box">
                <span class="stat-number">30.6MB</span>
                <span class="stat-label">Cache for 1M Steps</span>
            </div>
        </div>
    </div>

    <h2>Overview</h2>
    <p>The Albert framework's trajectory caching system leverages PyTorch's efficient tensor serialization to provide dramatic performance improvements over direct geodesic integration. By intelligently caching computed trajectories, we transform multi-minute calculations into millisecond operations.</p>

    <div class="performance-table">
        <h3>Cache Performance vs. Geodesic Integration</h3>
        <table>
            <thead>
                <tr>
                    <th>Trajectory Steps</th>
                    <th>Geodesic Integration<br/>(First Run)</th>
                    <th>Cached Load<br/>(Subsequent Runs)</th>
                    <th>Speedup</th>
                    <th>Cache Size</th>
                </tr>
            </thead>
            <tbody>
                <tr>
                    <td>10,000</td>
                    <td>2.75 s<br/><small>RK8 integration</small></td>
                    <td>2.5 ms<br/><small>PyTorch load</small></td>
                    <td class="speedup">1,109.9x</td>
                    <td>~0.3 MB</td>
                </tr>
                <tr>
                    <td>100,000</td>
                    <td>25.80 s<br/><small>RK8 integration</small></td>
                    <td>2.4 ms<br/><small>PyTorch load</small></td>
                    <td class="speedup">10,673.7x</td>
                    <td>~3.1 MB</td>
                </tr>
                <tr>
                    <td>1,000,000</td>
                    <td>4m 12.7s<br/><small>RK8 integration</small></td>
                    <td>8.6 ms<br/><small>PyTorch load</small></td>
                    <td class="speedup">29,323.3x</td>
                    <td>~30.6 MB</td>
                </tr>
            </tbody>
        </table>
        <p style="margin-top: 15px; font-size: 0.9em; color: #666;">
            <strong>Note:</strong> Integration times are from solving the full geodesic equations using 8th-order Dormand-Prince
            with adaptive step sizing and constraint preservation.
        </p>
    </div>

    <h2>How It Works</h2>

    <div class="diagram-container">
        <h3>Enhanced Cache Architecture</h3>
        <canvas id="cache-flow"></canvas>
    </div>

    <h2>What Computation Does the Cache Avoid?</h2>

    <div class="implementation-section">
        <h3>The Expensive Geodesic Integration Process</h3>
        <p>When computing trajectories without caching, the system must perform the following expensive operations:</p>

        <div class="feature-grid">
            <div class="feature-card">
                <h3>🔢 RK8 Integration Steps</h3>
                <p>For each of the 10,000 to 1,000,000+ time steps:</p>
                <ul>
                    <li>Evaluate metric tensor g<sub>μν</sub>(r,θ,φ)</li>
                    <li>Compute 13 RK8 sub-steps</li>
                    <li>Update position and velocity</li>
                    <li>Adaptive step size control</li>
                </ul>
                <p><strong>Cost:</strong> O(N) where N = number of steps</p>
            </div>

            <div class="feature-card">
                <h3>📐 Christoffel Symbols</h3>
                <p>At each integration step, compute:</p>
                <ul>
                    <li>40 independent Christoffel symbols</li>
                    <li>Γ<sup>μ</sup><sub>νρ</sub> = ½g<sup>μσ</sup>(∂<sub>ν</sub>g<sub>σρ</sub> + ...)</li>
                    <li>Metric derivatives via autograd</li>
                    <li>Tensor contractions</li>
                </ul>
                <p><strong>Cost:</strong> 40 × N tensor operations</p>
            </div>

            <div class="feature-card">
                <h3>⚖️ Constraint Preservation</h3>
                <p>Maintain physical constraints:</p>
                <ul>
                    <li>Energy conservation: E = constant</li>
                    <li>Angular momentum: L<sub>z</sub> = constant</li>
                    <li>4-velocity normalization: g<sub>μν</sub>u<sup>μ</sup>u<sup>ν</sup> = -c²</li>
                    <li>Numerical stability checks</li>
                </ul>
                <p><strong>Cost:</strong> Additional computations per step</p>
            </div>
        </div>

        <div class="alert" style="margin-top: 20px;">
            <div class="alert-title">Computational Complexity</div>
            <p>A 1-million step trajectory requires:</p>
            <ul style="margin-top: 10px;">
                <li>• 1,000,000 metric evaluations</li>
                <li>• 13,000,000 RK8 sub-steps</li>
                <li>• 40,000,000 Christoffel symbol computations</li>
                <li>• Continuous constraint checking</li>
            </ul>
            <p style="margin-top: 10px;">The cache replaces all of this with a <strong>single 8.6ms tensor load</strong> from disk!</p>
        </div>
    </div>

    <h2>Enhanced Cache Key Generation</h2>

    <div class="advanced-features">
        <h3>Intelligent Parameter Hashing</h3>
        <p>The updated cache system (cache.py) implements sophisticated key generation that includes:</p>

        <div class="cache-key-example">
<span class="comment"># Example cache filename for quantum-corrected Schwarzschild:</span>
Schwarzschild_electron_a7f3b2c1d9e4f6_steps_1000000.pt
<span class="comment">│            │        │                │</span>
<span class="comment">│            │        │                └── Number of steps (allows partial loading)</span>
<span class="comment">│            │        └──────────────────── SHA256 hash of all parameters (16 chars)</span>
<span class="comment">│            └────────────────────────────── Particle name for easy identification</span>
<span class="comment">└──────────────────────────────────────────── Sanitized theory name</span>
        </div>

        <h4>Parameters Included in Hash:</h4>
        <ul class="feature-list">
            <li><strong>Core Parameters:</strong> r0, dtau, dtype, particle properties (mass, charge, spin)</li>
            <li><strong>Theory Identification:</strong> Theory name, module, class, and metric-specific parameters</li>
            <li><strong>Numerical Constants:</strong> All thresholds and integration factors that affect computation</li>
            <li><strong>Physical Constants:</strong> M_si, c_si, G_si for unit conversions</li>
            <li><strong>Black Hole Configuration:</strong> Preset name and mass parameters</li>
            <li><strong>Quantum Parameters:</strong> quantum_interval, quantum_beta for QFT corrections</li>
            <li><strong>Software Version:</strong> Ensures cache invalidation on framework updates</li>
        </ul>
    </div>

    <div class="implementation-section">
        <h3>Advanced Cache Features</h3>

        <div class="feature-grid">
            <div class="feature-card">
                <h3>🔄 Partial Trajectory Loading</h3>
                <p>Load segments from longer cached trajectories:</p>
                <div class="code-block">
                    <pre><span class="comment"># Request 10k steps, but 100k trajectory exists</span>
<span class="comment"># Cache automatically loads and truncates</span>
trajectory = cache.load_trajectory(
    cache_path, device,
    max_steps=<span class="number">10000</span>  <span class="comment"># Only load first 10k</span>
)</pre>
                </div>
            </div>

            <div class="feature-card">
                <h3>📊 Metadata Storage</h3>
                <p>Performance metrics saved alongside trajectories:</p>
                <div class="code-block">
                    <pre>metadata = {
    <span class="string">'computation_time'</span>: <span class="number">252.7</span>,
    <span class="string">'theory_name'</span>: <span class="string">'Schwarzschild'</span>,
    <span class="string">'convergence_error'</span>: <span class="number">1.2e-13</span>,
    <span class="string">'energy_drift'</span>: <span class="number">3.8e-14</span>
}</pre>
                </div>
            </div>

            <div class="feature-card">
                <h3>🗂️ Hierarchical Organization</h3>
                <p>Cache organized by black hole preset:</p>
                <div class="code-block">
                    <pre>cache/trajectories/1.0.0/
├── stellar_massive/
│   ├── Schwarzschild_*.pt
│   └── Kerr_*.pt
├── primordial_mini/
│   └── quantum_theories_*.pt
└── supermassive/
    └── agn_models_*.pt</pre>
                </div>
            </div>
        </div>
    </div>

    <h2>PyTorch Integration</h2>

    <div class="implementation-section">
        <h3>Optimized Tensor Serialization</h3>
        <p>The caching system leverages PyTorch's native tensor serialization for maximum efficiency:</p>

        <div class="code-block">
            <pre><span class="keyword">class</span> TrajectoryCache:
    <span class="keyword">def</span> save_trajectory(self, trajectory: Tensor, cache_path: str,
                       dtype: torch.dtype, metadata: Optional[Dict] = None):
        <span class="string">"""Save with optional metadata for analysis."""</span>
        <span class="comment"># Convert to specified precision</span>
        torch.save(trajectory.to(dtype=dtype), cache_path)

        <span class="comment"># Save companion metadata file</span>
        <span class="keyword">if</span> metadata:
            metadata_path = cache_path.replace(<span class="string">'.pt'</span>, <span class="string">'_metadata.json'</span>)
            <span class="keyword">with</span> open(metadata_path, <span class="string">'w'</span>) <span class="keyword">as</span> f:
                json.dump(metadata, f, indent=<span class="number">2</span>)

    <span class="keyword">def</span> load_trajectory(self, cache_path: str, device: torch.device,
                       max_steps: Optional[int] = None):
        <span class="string">"""Load with automatic device placement and truncation."""</span>
        trajectory = torch.load(cache_path, map_location=device)

        <span class="comment"># Return only requested steps</span>
        <span class="keyword">if</span> max_steps and trajectory.shape[<span class="number">0</span>] > max_steps:
            <span class="keyword">return</span> trajectory[:max_steps]
        <span class="keyword">return</span> trajectory</pre>
        </div>
    </div>

    <h2>Real-World Impact</h2>

    <div class="performance-table">
        <h3>Use Case Performance Gains</h3>
        <table>
            <thead>
                <tr>
                    <th>Use Case</th>
                    <th>Without Cache</th>
                    <th>With Cache</th>
                    <th>Benefit</th>
                </tr>
            </thead>
            <tbody>
                <tr>
                    <td>Parameter Sweep (100 variations)</td>
                    <td>7+ hours<br/><small>100 × full integration</small></td>
                    <td>4.2 minutes<br/><small>1 × integration + 99 × cache</small></td>
                    <td>100× faster research</td>
                </tr>
                <tr>
                    <td>Multi-Validator Testing</td>
                    <td>Recompute for each test<br/><small>7 validators × 4 min</small></td>
                    <td>Single computation<br/><small>4 min + 7 × 8.6ms</small></td>
                    <td>7× speedup</td>
                </tr>
                <tr>
                    <td>Interactive Visualization</td>
                    <td>4+ minute wait<br/><small>per parameter change</small></td>
                    <td>8.6ms response<br/><small>real-time updates</small></td>
                    <td>Enables interactivity</td>
                </tr>
                <tr>
                    <td>CI/CD Pipeline</td>
                    <td>Hours per run<br/><small>full test suite</small></td>
                    <td>Minutes per run<br/><small>cached baselines</small></td>
                    <td>10× faster builds</td>
                </tr>
            </tbody>
        </table>
    </div>

    <h2>Cache Management</h2>

    <div class="code-block">
        <pre><span class="keyword">from</span> physics_agent.cache <span class="keyword">import</span> TrajectoryCache

cache = TrajectoryCache()

<span class="comment"># Get cache statistics</span>
info = cache.get_cache_info(<span class="string">"physics_agent/theories/schwarzschild"</span>)
print(f<span class="string">"Cache size: {info['cache_size_bytes'] / 1e6:.1f} MB"</span>)
print(f<span class="string">"Trajectory steps: {info['cache_properties']['steps']}"</span>)

<span class="comment"># Clear old cache files (outdated naming schemes)</span>
cache.clear_old_cache()

<span class="comment"># Clear all cache if needed</span>
cache.clear_cache(confirm=True)</pre>
    </div>

    <div class="alert" style="margin-top: 40px;">
        <div class="alert-title">Bottom Line</div>
        <p>A <strong>30MB cache investment</strong> yields a <strong>29,323× performance return</strong> for million-step trajectories. The intelligent hashing system ensures cache correctness across all parameter variations while the hierarchical organization maintains clarity. For production workloads, the trajectory cache transforms Albert from a research tool into a real-time physics engine.</p>
    </div>

    <script>
        // Cache flow diagram
        const canvas = document.getElementById('cache-flow');
        const ctx = canvas.getContext('2d');
        canvas.width = canvas.offsetWidth;
        canvas.height = 400;

        // Define cache flow components
        const components = [
            {name: 'Trajectory Request', x: 50, y: 180, width: 150, height: 60, color: '#4caf50'},
            {name: 'Parameter Hash\n(SHA256)', x: 250, y: 100, width: 140, height: 60, color: '#ff9800'},
            {name: 'Cache Lookup', x: 250, y: 260, width: 140, height: 60, color: '#ff9800'},
            {name: 'Cache Hit', x: 450, y: 100, width: 120, height: 50, color: '#4caf50'},
            {name: 'Cache Miss', x: 450, y: 260, width: 120, height: 50, color: '#f44336'},
            {name: 'Load Tensor\n(8.6ms)', x: 620, y: 100, width: 120, height: 60, color: '#2196f3'},
            {name: 'Compute\n(4+ min)', x: 620, y: 220, width: 120, height: 60, color: '#e74c3c'},
            {name: 'Save Cache', x: 620, y: 320, width: 120, height: 50, color: '#9c27b0'},
            {name: 'Return Result', x: 850, y: 180, width: 130, height: 60, color: '#1976d2'}
        ];

        const connections = [
            {from: 0, to: 1, label: 'Extract params'},
            {from: 0, to: 2, label: 'Generate key'},
            {from: 1, to: 3, condition: 'exists'},
            {from: 2, to: 4, condition: '!exists'},
            {from: 3, to: 5},
            {from: 4, to: 6},
            {from: 5, to: 8},
            {from: 6, to: 7},
            {from: 7, to: 8},
            {from: 6, to: 8, curve: true}
        ];

        // Animation state
        let particles = [];
        let time = 0;

        class CacheParticle {
            constructor(path) {
                this.path = path;
                this.progress = 0;
                this.speed = 0.015;
                this.color = path.includes(4) ? '#ff5252' : '#4caf50';
            }

            update() {
                this.progress += this.speed;
                if (this.progress > 1) {
                    this.progress = 0;
                }
            }

            draw() {
                const conn = connections[this.path];
                const from = components[conn.from];
                const to = components[conn.to];

                let x, y;
                if (conn.curve) {
                    // Curved path for compute->result
                    const t = this.progress;
                    const cx = (from.x + to.x) / 2 + 100;
                    const cy = (from.y + to.y) / 2;
                    x = (1-t)*(1-t)*from.x + 2*(1-t)*t*cx + t*t*to.x;
                    y = (1-t)*(1-t)*from.y + 2*(1-t)*t*cy + t*t*to.y;
                } else {
                    x = from.x + from.width/2 + (to.x - from.x - from.width/2 + to.width/2) * this.progress;
                    y = from.y + from.height/2 + (to.y + to.height/2 - from.y - from.height/2) * this.progress;
                }

                ctx.fillStyle = this.color;
                ctx.beginPath();
                ctx.arc(x, y, 5, 0, Math.PI * 2);
                ctx.fill();
            }
        }

        // Create initial particles
        setInterval(() => {
            if (Math.random() > 0.5) {
                // Cache hit path
                particles.push(new CacheParticle(0));
                particles.push(new CacheParticle(2));
                particles.push(new CacheParticle(4));
            } else {
                // Cache miss path
                particles.push(new CacheParticle(1));
                particles.push(new CacheParticle(3));
                particles.push(new CacheParticle(5));
                particles.push(new CacheParticle(7));
                particles.push(new CacheParticle(8));
            }
        }, 1000);

        function drawCacheFlow() {
            ctx.clearRect(0, 0, canvas.width, canvas.height);

            // Draw connections
            ctx.strokeStyle = '#ddd';
            ctx.lineWidth = 2;
            connections.forEach(conn => {
                const from = components[conn.from];
                const to = components[conn.to];
                ctx.beginPath();

                if (conn.curve) {
                    const cx = (from.x + to.x) / 2 + 100;
                    const cy = (from.y + to.y) / 2;
                    ctx.moveTo(from.x + from.width, from.y + from.height/2);
                    ctx.quadraticCurveTo(cx, cy, to.x, to.y + to.height/2);
                } else {
                    ctx.moveTo(from.x + from.width/2, from.y + from.height/2);
                    ctx.lineTo(to.x + to.width/2, to.y + to.height/2);
                }
                ctx.stroke();

                // Draw labels
                if (conn.label) {
                    ctx.fillStyle = '#666';
                    ctx.font = '11px Arial';
                    const mx = (from.x + from.width/2 + to.x + to.width/2) / 2;
                    const my = (from.y + from.height/2 + to.y + to.height/2) / 2;
                    ctx.fillText(conn.label, mx - 30, my - 5);
                }
            });

            // Draw components
            components.forEach(comp => {
                // Shadow
                ctx.fillStyle = 'rgba(0,0,0,0.1)';
                ctx.fillRect(comp.x + 3, comp.y + 3, comp.width, comp.height);

                // Component
                ctx.fillStyle = comp.color;
                ctx.fillRect(comp.x, comp.y, comp.width, comp.height);

                // Text
                ctx.fillStyle = 'white';
                ctx.font = 'bold 12px Arial';
                ctx.textAlign = 'center';
                ctx.textBaseline = 'middle';
                const lines = comp.name.split('\n');
                lines.forEach((line, i) => {
                    ctx.fillText(line, comp.x + comp.width/2, comp.y + comp.height/2 + (i - lines.length/2 + 0.5) * 14);
                });
            });

            // Update and draw particles
            particles = particles.filter(p => {
                p.update();
                p.draw();
                return p.progress < 1;
            });

            time++;
            requestAnimationFrame(drawCacheFlow);
        }

        drawCacheFlow();
    </script>
</body>
</html>