Within engineering there has always been the use of empirical equations for representing physics such as pressure drop and heat transfer. In the evolving landscape of computational science and engineering, a new paradigm is emerging—one that blends the rigor of physics-based models with the adaptability of artificial intelligence. This hybrid approach is reshaping how we simulate, optimize, and control complex systems, from industrial assets and energy grids to biomedical devices and autonomous agents.
Why Hybridization Matters
Traditional physics-based models are grounded in first principles – conservation laws, constitutive equations, and boundary conditions. They offer interpretability, generalizability, and trust.
But they can be:
- Computationally expensive (e.g., CFD, FEA)
- Difficult to calibrate with sparse or noisy data
- Challenging to validate with real world data
- Limited in scope when dealing with emergent or poorly understood phenomena
AI-based methods, on the other hand, excel at pattern recognition, data-driven inference, and real-time adaptation. But they often lack physical consistency, require large datasets, and can behave unpredictably outside their training domain.
Hybrid modelling seeks to combine the best of both worlds.
Four Pillars of Hybrid Modelling
1. Physics-Informed Machine Learning
Physics Informed Machine Learning embeds physical laws directly into the structure or training of machine learning models. Examples include:
- Soft constraints or regularization: Penalize physically implausible outputs (e.g., negative mass, energy non-conservation).
- Symbolic regression with physics priors: Discover interpretable equations from data while respecting known symmetries or invariants.
- Physics-Informed Neural Networks (PINNs): Solve PDEs by minimizing residuals of governing equations during training.
This approach is ideal when data is limited but physical laws are well understood.
2. Reduced Order Modelling (ROM) + AI Surrogates
High-fidelity simulations (e.g., multiphase flow, structural dynamics) are often too slow for real-time control or optimization. ROM techniques like Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), or autoencoders compress these models into low-dimensional representations that are super-fast to run compared to many hours or even days for complex 3D transient physics-based models.
AI can then:
- Learn surrogate models in latent space and provide inference between training data
- Accelerate inverse design and uncertainty quantification
- Enable digital twins that are fast, accurate, and physics-aware
This is particularly powerful in aerospace, energy, and manufacturing industries. I have had particular success in developing scheduling and value chain models and simulations/optimisations through these approaches.
3. AI-Based Optimization with Physics Constraints
Optimization tasks – like tuning process parameters, designing materials, or controlling robots – benefit from AI’s ability to explore large, nonlinear spaces. But without physics, solutions may be infeasible or unsafe.
Hybrid strategies include:
- Bayesian optimization with physics-based simulators
- Reinforcement learning with embedded simulators or safety shields
- Multi-fidelity optimization: Combine fast, coarse models with slower, high-fidelity ones
This ensures that AI-generated solutions remain grounded.
4. Agentic AI with Embedded Physical Reasoning
As agentic AI systems (e.g., autonomous vehicles, industrial co-pilots, robotic explorers) become more capable, they must reason about the physical world in real time.
Hybrid approaches enable:
- Sim-to-real transfer: Train agents in simulated environments governed by physics, then adapt to real-world conditions
- Model-predictive control (MPC) with learned dynamics
- Causal reasoning: Use physics to infer cause-effect relationships, not just correlations
This is the frontier of embodied intelligence.
Challenges and Opportunities
While hybrid modelling holds immense promise, it’s not without hurdles:
- Model integration: How to couple symbolic and sub-symbolic representations?
- Data scarcity: How to train AI models when labelled data is expensive or rare?
- Trust and explainability: How to ensure hybrid models are interpretable and auditable?
Emerging tools—like differentiable physics engines, neuro-symbolic frameworks, and foundation models for scientific domains—are helping bridge these gaps.
Final Thoughts
Hybrid modeling isn’t just a technical strategy—it’s a philosophical shift. It acknowledges that neither physics nor AI alone is sufficient to tackle the complexity of modern systems. By weaving them together, we unlock new levels of performance, insight, and autonomy.
As agentic AI becomes more prevalent, the ability to reason with, learn from, and act upon physical models will be a defining capability. The future belongs to systems that are not only intelligent—but physically grounded.
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