LLGD: A Physics-Informed, Hardware-Aware Spin-Dynamics Approach to Deep Neural Network Training

Optimization in deep learning remains dominated by heuristic gradient methods such as Adam, lacking explicit physical grounding and hardware efficiency. We introduce LLGD (Landau-Lifshitz-Gilbert-Descent), a physics-inspired optimizer that maps neural network parameters onto normalized spin vectors evolving under the Landau-Lifshitz-Gilbert equation. To our knowledge, this work presents one of the earliest physics-informed neural-network optimizers that explicitly incorporates angular-momentum spin dynamics in parameter space, introducing rotational inertia that helps optimization trajectories circumvent high-loss barriers while balancing exploration and convergence through precessional motion and damping.Thermal noise with annealing introduces stochasticity, aiding escape from plateaus and saddles. Experiments on rugged analytical surfaces and deep networks show that ALLGD (Adaptive LLGD) achieves faster convergence, lower loss, and better generalization than Adam and SGD under equal gradient budgets with improved robustness to ill-conditioning. Because the update rule is native to spin precession and damping physics, the approach couples with spintronic (Magnetic tunnel junction) hardware, offering a path to compact, and extremely energy-efficient Machine learning accelerators. Our results indicate that embedding physical laws into optimization can open new algorithmic regimes where learning behaves like a dissipative physical process.