flowchart LR A(Prediction) B(Discovery) C(Explanation)
Universal Physics Engine
Can AI serve as a Universal Physics Engine ?
In Stephen Wolfram’s (one of the legends in the field of computational physics and mathematics) latest writing, he explores ideas on the fields and methods with which he thinks AI will impact scientific disciplines. He starts the blog with:
“To the ultimate question of whether AI can solve Science, we’re going to see that the answer is inevitably and firmly no.”
So probably there is not much of a reason for me to explore the idea of building a universal physics engine using AI, but hey I love attempting the impossible (why do you think I ended up doing Fusion !!!).
Science can be broadly defined to fall under three categories:
Need to a background on the different kind of approaches being taken:
- Surrogate Models of all kinds.
- Foundation Models for Physics
- Generative Enginering - PhysicsX, Zoo.dev and the varioud likes of those. Generative models for statistical physics.
- Math proofing approaches
- Text-Code is all you need with the right software - Bring in the Karpathy tweet.
| Aspect | Current Limitations | Potential AI Capabilities | Novel Solutions | Challenges |
|---|---|---|---|---|
| Mathematical Framework | Limited to specific classes of PDEs; Separate frameworks for different physics domains | Unified mathematical framework spanning quantum to classical physics; Automatic detection of symmetries and conservation laws; Dynamic generation of problem-specific basis functions | Development of new mathematical structures beyond tensors and operators; Creation of hybrid symbolic-numerical methods; Discovery of new transformations between problem domains | Ensuring mathematical consistency across scales; Proving convergence for new methods; Handling mathematical singularities |
| Geometric Processing | Pre-defined mesh types; Manual domain decomposition; Limited handling of complex boundaries | Automated optimal mesh generation for arbitrary geometries; Intelligent boundary condition handling; Adaptive multi-resolution techniques | Self-designing coordinate systems; Topology-aware discretization; Geometry-informed basis functions | Dealing with moving boundaries; Handling topological changes; Ensuring mesh quality |
| Multi-physics Coupling | Manual coupling between different physics models; Limited cross-scale interactions | Automated detection of relevant physics; Seamless coupling across scales; Self-adaptive model selection | Creation of unified multi-physics formulations; Development of scale-bridging operators; Automatic derivation of reduced-order models | Maintaining conservation properties; Handling disparate time scales; Managing computational complexity |
| Error Control & Stability | Fixed error estimators; Predefined stability criteria; Manual parameter tuning | Real-time error prediction; Adaptive stability preservation; Automated parameter optimization | Development of new error metrics; Creation of self-stabilizing schemes; Learning-based error estimation | Guaranteeing global stability; Balancing accuracy vs. efficiency; Handling chaos and sensitivity |
| Computational Methods | Fixed numerical schemes; Limited parallelization; Domain-specific optimizations | Dynamic algorithm selection; Automated parallelization strategies; Problem-specific method synthesis | Creation of new numerical algorithms; Development of quantum-inspired methods; Adaptive hybrid schemes | Scaling to large problems; Managing memory hierarchy; Ensuring reproducibility |
| User Interaction | Limited feedback on solution quality; Fixed visualization options; Preset parameter ranges | Interactive problem refinement; Adaptive visualization; Automated parameter exploration | Development of intuitive interfaces; Creation of explanation systems; Generation of physical insights | Communicating complex concepts; Handling ambiguous specifications; Providing meaningful feedback |
| Physical Consistency | Manual enforcement of conservation laws; Fixed constitutive relations; Predefined material models | Automatic constraint preservation; Learning-based constitutive relations; Adaptive material modeling | Discovery of new conservation principles; Creation of physics-informed neural operators; Development of universal material models | Ensuring physical realizability; Handling unknown physics; Maintaining causality |
| Data Integration | Limited use of experimental data; Fixed model parameters; Separate calibration steps | Real-time data assimilation; Automated model calibration; Dynamic parameter updating | Development of physics-data hybrid methods; Creation of adaptive measurement operators; Automated experiment design | Handling noisy data; Dealing with sparse measurements; Ensuring model validity |