Solving geophysical inverse problems with simulated Ising systems

Abstract The increasing scale and complexity of modern geophysical inverse problems approaches the limits of conventional computing architectures, motivating the investigation of alternative computational paradigms. Ising computing, whether implemented through emerging analog hardware or simulated on classical machines, offers an intriguing alternative due to its natural alignment with quadratic unconstrained binary optimization. While substantial computational advantages are associated primarily with the parallelization capabilities of Ising computers and thus rely on advances in specialized Ising hardware, simulated Ising computing is crucial for developing compatible algorithms,leading to novel algorithmic insights, with the potential for computational gains when deployed on advanced computing platforms. In this study, we investigate the potential of simulated Ising systems to solve a broad suite of geophysical inverse problems by reformulating them in terms of binary Ising variables, coupling matrices, and external fields. After reviewing the classical Ising model and its Monte Carlo-based simulation, we develop general strategies for mapping geophysical objectives onto Ising Hamiltonians. Four representative problem classes are examined. First, an optimized experimental design problem for timelapse seismic monitoring demonstrates how acquisition sparsity and information content can be encoded directly into the Hamiltonian, enabling substantial data reduction without degrading inversion quality. Second, an amplitude-versus-offset inversion example highlights the challenges of discretizing continuous model parameters and embedding data misfit within the Ising framework. Third, we extend the approach to subsurface reconstruction problems, including traveltime tomography and gravity inversion, illustrating how structural smoothness, physical constraints, and data fidelity can be expressed through coupling and field terms. Finally, we explore a joint inversion formulation in which multiple data types are incorporated into an Ising system. Together, these examples provide insight into the formulations and natural behaviors of these Ising-compatible algorithms. They demonstrate that simulated Ising computing provides a flexible and powerful platform for developing geophysical inversion strategies that may ultimately interface with emerging analog Ising hardware.