Add AI-powered nutrition and plan modules

Introduces DSPy-based nutrition and plan generation modules, including image analysis for nutritional info and personalized diet/exercise plans. Adds new API endpoints for health metrics/goals, nutrition image analysis, and plan management. Updates models, schemas, and backend structure to support these features, and includes initial training data and configuration for prompt optimization.

backend/scripts/optimize_nutrition_v2.py

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+from dspy.teleprompt import BootstrapFewShotWithRandomSearch
+
+from app.ai.nutrition import nutrition_module
+from app.core.ai_config import configure_dspy
+from scripts.nutrition_data import train_examples
+
+# 0. Configure DSPy
+configure_dspy()
+
+
+# 1. Define Advanced Metric
+def validate_nutrition_v2(example, pred, trace=None):
+    # Condition A: Accuracy (within 15% of ground truth)
+    actual_cals = example.nutritional_info.calories
+    pred_cals = pred.nutritional_info.calories
+
+    threshold = 0.15
+    lower = actual_cals * (1 - threshold)
+    upper = actual_cals * (1 + threshold)
+    is_accurate_count = lower <= pred_cals <= upper
+
+    # Condition B: Consistency (Macros match Calories within 20%)
+    # This prevents "hallucinated" numbers that don't satisfy physics
+    p = pred.nutritional_info.protein
+    c = pred.nutritional_info.carbs
+    f = pred.nutritional_info.fats
+
+    calculated_cals = (p * 4) + (c * 4) + (f * 9)
+    # Using a slightly looser bounds (20%) for fiber/rounding
+    consistency_threshold = 0.20
+    is_consistent_math = abs(calculated_cals - pred_cals) < (pred_cals * consistency_threshold)
+
+    # We want BOTH to be true
+    return is_accurate_count and is_consistent_math
+
+
+# 2. Setup Advanced Optimizer
+# RandomSearch is more expensive but finds better reasoning traces by randomizing
+# the selection of few-shot examples.
+# num_candidate_programs=10 means it will try 10 different combinations of prompts/examples
+print("Configuring RandomSearch Optimizer...")
+teleprompter = BootstrapFewShotWithRandomSearch(
+    metric=validate_nutrition_v2,
+    max_bootstrapped_demos=4,
+    max_labeled_demos=4,
+    num_candidate_programs=5,  # Reduced to 5 for speed in this demo, typically 10-20
+    num_threads=1,  # Sequential for stability, increase for parallelism
+)
+
+# 3. Compile (Optimize) the Module
+print("Optimizing V2 (this includes random search and macro checks)...")
+# Note: assertions are compiled into the pipeline automatically in newer DSPy,
+# acting as soft constraints during the search.
+compiled_nutrition = teleprompter.compile(nutrition_module, trainset=train_examples)
+
+# 4. Save
+compiled_nutrition.save("app/ai/nutrition_compiled.json")
+print("Optimization V2 complete! Overwrote app/ai/nutrition_compiled.json")