Mixture Density Network (MDN)

MDNs output parameters of a probability distribution instead of point predictions. They excel at modeling data with multiple possible outputs for a single input.

Training Data
MDN Predictions
Uncertainty
How it works: The MDN outputs mixture weights (π), means (μ), and standard deviations (σ) for multiple Gaussian components. This allows it to model complex, multi-modal distributions.
p(y|x) = Σᵢ πᵢ(x) · N(y | μᵢ(x), σᵢ²(x))

Physics-Informed Neural Network (PINN)

PINNs incorporate physical laws directly into the neural network training process, enabling them to solve differential equations with limited data.

Boundary Points
PINN Solution
Physics Residual
How it works: PINNs minimize a loss function that includes both data fitting terms and physics constraint terms. The network learns to satisfy the differential equation everywhere in the domain.
Loss = Loss_data + λ · Loss_physics

V-JEPA: Abstract Representation Learning

V-JEPA learns abstract representations by predicting masked video patches in representation space, not pixel space. The model learns to "understand" dynamics rather than "paint" pixels, demonstrating true world understanding through joint embedding predictive architecture.

Context Patches
Masked Patches
Predicted Representations
Target Representations
Key insight: V-JEPA learns in abstract representation space, not pixel space. The Context Encoder processes visible patches, the Predictor predicts target representations, and similarity is measured between predicted and actual representations. This enables understanding of dynamics without pixel-level reconstruction.
Similarity = cosine(Predictor(Context), Target_Encoder(Masked))

30-Year Evolution of Physics Understanding in AI

MDNs - Memorization Era

Probabilistic predictions, massive data needs

PINNs - Rules Era

Physics equations embedded, reduced data

Early World Models

Self-discovered physics from videos

V-JEPA - Understanding Era

Abstract concepts, not pixels

Hybrid Robotics Architecture

Physics Layer

Traditional Simulations
Deterministic Control
Safety Verification

Integration Layer

Decision Engine
Mode Switching
Data Fusion

Intelligence Layer

World Models
Adaptation & Learning
Generalization

When to Use Each Approach

Robotics Task
Precision Critical?
Use Simulation
• Surgery
• Manufacturing
• Safety testing
Novel Environment?
Use World Model
• Home robots
• Exploration
• Human interaction
Complex Real-World Tasks
Use Hybrid System
• Autonomous vehicles
• Warehouse robotics
• Humanoid robots

Training Cost Comparison

Traditional Training
$100k-600k
• Hardware: $50-500k
• Supervision: $50k
• Facility: $10k/mo
• Maintenance: $5-20k
World Model Training
$10k-50k
• Compute: $100k setup
• Data: $10-50k
• Time: 1-2 weeks
• 10x cheaper overall

Industry Adoption Map

Tesla
World models for driving, simulation for safety
Boston Dynamics
Physics for control, AI for terrain adaptation
Google
RT-X models with physics for grasping
Meta
Balanced approach for robotics research
Traditional Simulation
World Models

2025-2030 Robotics Roadmap

2025-2026

Industry standardization of hybrid pipelines
Edge computing for world models
Regulatory frameworks emerging
→

2027-2028

Digital twins as standard practice
Multi-modal world models
Automated sim-to-real transfer
→

2029-2030

Embodied foundation models
Quantum-enhanced simulation
Self-improving hybrid systems

© 2025 Krish Mehta. All rights reserved.