Over the past decade, deep learning has revolutionized artificial intelligence, driving breakthroughs in image recognition, language modeling, and game playing. Yet, persistent limitations have surfaced: data inefficiency, lack of robustness to distribution shifts, high energy demand, and a superficial grasp of physical laws. As AI adoption deepens into critical sectors—from climate forecasting to medicine—these constraints are becoming untenable.
A promising paradigm is emerging: physics-based AI, where learning is constrained and guided by the laws of nature. Inspired by centuries of scientific progress, this hybrid approach embeds physical principles into machine learning models, offering new paths to generalization, interpretability, and reliability. The question is no longer whether we need to move beyond black-box learning, but how soon we can realize this transformation.
The Case for Physics-Based AI
Why Physics, Now?
Contemporary AI—especially LLMs and vision models—rely on extracting correlations from massive, often unstructured, datasets. This data-driven approach underperforms in data-scarce, safety-critical, or physically governed environments. Physics-based AI, in contrast, leverages:
- Inductive Biases via Physical Constraints: Embedding symmetries, conservation laws, and invariances shrinks the hypothesis space and guides learning toward feasible solutions.
- Sample Efficiency: Models exploiting physical priors achieve more with less data, a critical advantage in domains like healthcare and computational science.
- Robustness and Generalization: Unlike black boxes, physics-informed models are less prone to unpredictable failures when extrapolating out-of-distribution.
- Interpretability and Trust: Predictions adhering to known laws, such as energy conservation, are more trustworthy and explainable.
The Landscape of Physics-Based AI
Physics-Informed Neural Networks: The Workhorse
Physics-Informed Neural Networks (PINNs) integrate physical knowledge by penalizing violations of governing equations (often PDEs) in the loss function. Over the past few years, this has blossomed into a rich ecosystem:
- In climate and geosciences, PINNs have shown robust predictions for free-surface flows with topographic complexity.
- In materials science and fluid dynamics, they model stress distribution, turbulence, and nonlinear wave propagation with appealing efficiency.
- In biomedical modeling, PINNs accurately simulate cardiac dynamics and tumor development under sparse observations.
Latest Developments (2024–2025):
- Unified error analysis now provides a rigorous breakdown of PINN errors, shifting emphasis to more effective training strategies.
- Physics-informed PointNet enables PINN-based solutions on irregular geometries without per-geometry retraining.
- Next-generation PINNs employ multimodal architectures, mixing data-driven and physics-guided components to tackle partial observability and heterogeneity.
Neural Operators: Learning Physics Across Infinite Domains
Classic machine learning models are limited in handling variations in physics equations and boundary conditions. Neural operators, especially Fourier neural operators (FNOs), learn mappings between function spaces:
- In weather forecasting, FNOs outperform CNNs in capturing nonlinear ocean and atmospheric dynamics.
- Their limitations, such as low-frequency bias, have been addressed with ensemble and multiscale operator techniques, boosting accuracy for high-frequency prediction.
- Multigrid and multiscale neural operators now set the state of the art in global weather forecasting.
Differentiable Simulation: Data-Physical Fusion Backbone
Differentiable simulators allow end-to-end optimization of physical predictions with learning:
- In tactile and contact physics, differentiable simulators enable learning in contact-rich manipulation, soft-body, and rigid-body physics scenarios.
- In neuroscience, differentiable simulation brings large-scale, gradient-based optimization to neural circuits.
- New physics engines like Genesis deliver unprecedented simulation speed and scale for learning and robotics.
Recent work recognizes several principal approaches for differentiable contact—LCP-based, convex optimization-based, compliant, and position-based dynamics models.
Hybrid Physics-ML Models: Best of Both Worlds
- In tropical cyclone prediction, hybrid neural-physical models combine data-driven learning with explicit physics codes, pushing the forecasting horizon well beyond previous limits.
- In manufacturing and engineering, hybrids leverage both empirical and physical constraints, overcoming the brittleness of models based purely on black-box data or first-principles alone.
- In climate science, hybrid methods enable physically plausible downscaling and uncertainty-aware prediction.
Current Challenges and Research Frontiers
- Scalability: Efficient training of physics-constrained models at scale remains challenging, with advances continuing in meshless operators and simulation speed.
- Partial Observability and Noise: Handling noisy, partial data is an open research challenge; recent hybrid and multimodal models are addressing this issue.
- Integration with Foundation Models: Research is focused on integrating general-purpose AI models with explicit physical priors.
- Verification & Validation: Ensuring that models adhere to physical law in all regimes remains technically demanding.
- Automated Law Discovery: PINN-inspired approaches are making data-driven discovery of governing scientific laws increasingly practical.
The Future: Toward a Physics-First AI Paradigm
A shift to physics-based and hybrid models is not only desirable for AI, but essential for intelligence that can extrapolate, reason, and potentially discover new scientific laws. Promising directions include:
- Neural-symbolic integration, combining interpretable physical knowledge with deep networks.
- Real-time, mechanism-aware artificial intelligence for trustworthy decision-making in robotics and digital twins.
- Automated scientific discovery using advanced machine learning for causal inference and law discovery.
These breakthroughs depend on strong collaboration between machine learning, physics, and domain experts. Explosive progress in this space is uniting data, computation, and domain knowledge, promising a new generation of AI capabilities for science and society.
References
- Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations, Raissi et al. (2019)
- Lagrangian Neural Networks, Cranmer et al. (2020)
- Hamiltonian Neural Networks, Greydanus et al. (2019)
- Fourier Neural Operator for Parametric Partial Differential Equations, Li et al. (2021)
- Neural Operator: Learning Maps Between Function Spaces, Kovachki et al. (2021)
- Scientific Machine Learning Through Physics–Informed Neural Networks: Where We Are and What’s Next, Cuomo et al. (2022)
- Numerical Analysis of Physics-Informed Neural Networks and Related Models in Physics-Informed Machine Learning, De Ryck et al. (2024)
- Physics-Informed Neural Networks and Extensions, Raissi et al. (2024)
- Spherical Multigrid Neural Operator for Improving Autoregressive Global Weather Forecasting, Hu et al. (2025)
- Applications of the Fourier Neural Operator in a Regional Ocean Modeling and Prediction, Choi et al. (2024)
- Physics‐Informed Neural Networks for the Augmented System of Shallow Water Equations with Topography, Dazzi et al. (2024)
- DiffTaichi: Differentiable Programming for Physical Simulation, Hu et al. (2020)
- DIFFTACTILE: A Physics-Based Differentiable Tactile Simulator for Contact-Rich Robotic Manipulation, Si et al. (2024)
- A Review of Differentiable Simulators, Newbury et al. (2024)
- Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?, Zhong et al. (2022)
- A Hybrid Machine Learning/Physics‐Based Modeling Framework for 2‐Week Extended Prediction of Tropical Cyclones, Liu et al. (2024)
- Jaxley: Differentiable Simulation Enables Large-Scale Training of Detailed Biophysical Models of Neural Dynamics, Deistler et al. (2024)
- Revolutionizing Physics: A Comprehensive Survey of Machine Learning Applications, Suresh et al. (2024)
- A Library for Learning Neural Operators, Kossaifi et al. (2024); GitHub
- Genesis: Universal Physics Platform for Robotics and Embodied AI, Genesis Embodied AI Team (2024)
- Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems, Beucler et al. (2021)
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