Bayesian optimization for inverse problems in time-dependent quantum dynamics

Area of Science:

• Quantum Dynamics
• Computational Chemistry
• Molecular Physics

Background:

• Inverse problems in quantum dynamics are computationally intensive.
• Accurate determination of molecular properties requires solving the Schrödinger equation.

Purpose of the Study:

• To develop an efficient algorithm for solving inverse problems in time-dependent quantum dynamics.
• To reduce the computational cost of determining molecular properties like polarizability tensors.

Main Methods:

• Utilizing feedback loops between Hamiltonian parameters and Schrödinger equation solutions.
• Employing Bayesian surrogate models, specifically Gaussian processes with vector outputs and composite kernels.
• Using the Bayesian Information Criterion (BIC) for kernel selection.
• Applying Bayesian optimization for inverse problems with noisy data.

Main Results:

• The developed algorithm reduces feedback loop iterations by at least a factor of 3.
• Successfully determined molecular polarizability tensor components for SO2 and propylene oxide (PPO).
• Achieved accurate results for PPO with as few as 30 quantum dynamics calculations.

Conclusions:

• The proposed Bayesian surrogate model approach offers an efficient solution for inverse problems in quantum dynamics.
• This method significantly accelerates the determination of molecular properties from simulated quantum dynamics data.
• The algorithm is robust and applicable to complex molecules and noisy experimental data.