A Swarm Variant for the Schrödinger Solver
This work addresses the challenge of solving differential equations with neural networks for researchers in computational physics, but it is incremental as it adapts an existing PSO variant to a specific problem.
The paper tackled the problem of solving the Schrödinger equation for the Particle-in-a-Box using neural networks by applying the Exponentially Averaged Momentum Particle Swarm Optimization (EM-PSO) as a derivative-free optimizer, resulting in a method that explores the search space and is robust to local minima compared to gradient-based optimizers like Adam.
This paper introduces application of the Exponentially Averaged Momentum Particle Swarm Optimization (EM-PSO) as a derivative-free optimizer for Neural Networks. It adopts PSO's major advantages such as search space exploration and higher robustness to local minima compared to gradient-descent optimizers such as Adam. Neural network based solvers endowed with gradient optimization are now being used to approximate solutions to Differential Equations. Here, we demonstrate the novelty of EM-PSO in approximating gradients and leveraging the property in solving the Schrödinger equation, for the Particle-in-a-Box problem. We also provide the optimal set of hyper-parameters supported by mathematical proofs, suited for our algorithm.