1) The physics laws/constraints relevant to the domain are defined (governing equations, conservation laws, contact/collisions). 2) Physical knowledge is embedded into the model: as a loss term (PINN), as a differentiable simulator in the training loop, or as a physical environment/world model. 3) The model is trained on data (real and/or simulated) while enforcing physical constraints. 4) The resulting model makes physically consistent predictions/control and transfers better to reality (important for sim-to-real in robotics).
Purely data-driven models often violate the laws of physics (non-physical predictions), require huge amounts of data and generalize poorly out of distribution. Physics-native AI enforces physical consistency, improves data efficiency and prediction reliability.
Governing equations, conservation laws and domain constraints embedded in the model (e.g. as a loss term or hard constraints).
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A network/model that learns representations and predictions consistent with the embedded physics.
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A physics simulator through which gradients can be propagated, enabling learning "through" simulation (optional, depending on the approach).
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Backpropagating through physics simulation is compute- and memory-intensive.
Soft penalties (PINN) do not guarantee strict physical compliance; hard constraints are numerically difficult.
Inaccurate simulation physics leads to errors after transfer to reality.
Raissi, Perdikaris and Karniadakis formalize PINNs — embedding governing equations into the network's loss.
Differentiable simulators (learning "through" simulation) become common in robotics and scientific ML.
Physics-faithful world models and platforms (physical AI) become a foundation for robot training and sim-to-real.
Time complexity: Zalezna od podejscia (PINN vs rozniczkowalna symulacja). Space complexity: O(model + stan symulacji).
Propagating gradients through physics simulation and strictly enforcing hard physical constraints are the most costly and numerically difficult parts; the sim-to-real gap adds to this.
Soft constraints (PINN loss) vs hard constraints vs differentiable simulator.
Trade-off between physics fidelity and compute cost.
E.g. rigid-body dynamics, fluids (CFD), materials, contact.
Depends on the approach and physical domain.
No routing — a modeling paradigm with embedded physics.
Batched training/prediction is parallel; time-stepping simulation is sequential.
Training with differentiable simulation and PINNs, and large-scale physics simulation, are compute-intensive and benefit from GPU accelerators.
