📄 Do Two AI Scientists Agree?

Summary

The paper asks whether independently trained AI models given the same physics data arrive at the same theory or at different ones. To test this, the authors introduce MASS (Multiple AI Scalar Scientists). For each physical system, a separate sub-network learns one scalar function. A final layer, shared across all systems, then learns how to differentiate that function to produce equations of motion. Because of this design, MASS contains both the Hamiltonian Neural Network (HNN) and the Lagrangian Neural Network (LNN) as special cases, without fixing either one in advance.

Many MASS instances with different random seeds were trained on classical-mechanics data, and the authors then compared their internal activations. As more systems were added to training, the models' theories tended to converge, though some formed separate clusters. On standard textbook problems, the models settled on either a Hamiltonian-like or a Lagrangian-like description. On harder, non-standard systems, only the Lagrangian form held up. The work offers a controlled testbed for studying how agreement among AI scientists depends on the data they see.

Key points

• MASS is described as a single network that learns per-system scalar functions plus a shared derivative layer; together these define the learned "theory." Errors are summed across all systems during training.
• Training systems include the simple pendulum, the Kepler/gravitational problem, the simple harmonic oscillator, spring-mass, the relativistic harmonic oscillator, the double pendulum and synthetic potentials.
• Results depend strongly on the random seed, which shapes both the training dynamics and the final weights. The learned scalar functions often look like conic sections, differing mainly by sign or parity swaps.
• In the appendix, MASS is extended to the spherical pendulum, the two-body problem (4D, Cartesian coordinates) and the three-body problem (6D, a perturbed figure-8 orbit), with trajectories integrated using fourth-order Runge-Kutta.
• The authors acknowledge that MASS is not a state-of-the-art solver and that training can be unstable in irregular regimes. Code is available at github.com/shinfxh/ai-scientists.